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Ken G
2014-Nov-29, 03:55 PM
I'm wondering what is the method for correcting errors in the "Explore" encylopedia that this forum links to? There are a number of misconceptions about stars that are propagated there (some really blatant, such as it claims that the pressure inside stars increases as the mass of a main-sequence star increases, and that light pressure is what balances gravity). Is there some Wiki-like mechanism for fixing those?

Solfe
2014-Nov-29, 05:01 PM
The data is feeding in from the http://www.teachastronomy.com/ site. It doesn't look like a wiki style page.

Ken G
2014-Nov-29, 06:23 PM
I was wondering about that-- it links to that site, but it also seems to have its own content. It felt like cosmoquest was responsible for that content, so it could be replaced by cosmoquest as well. For example, the entry at http://cosmoquest.org/x/explore/2014/01/09/main_sequence/ links to "Astropedia", which is what you are talking about, but the link I gave seems to be a kind of blog entry on main sequence stars that contains different information than the astropedia entry on main sequence stars (the differences contain their own different errors, actually!).

One might naturally assume that all these different sources of information about something as basic as "main sequence stars" would be both correct and mutually consistent, but closer examination reveals that neither of those assumptions are true. I don't see any way to comment on those blog entries, I'm wondering if a thread on here could result in the replacement of the incorrect text? This doesn't seem like a satisfactory state of affairs, much better knowledge exists about stars that can be stated just as simply, but be correct.

NoisyAstronomer
2014-Dec-08, 07:00 PM
Hi there! We'd appreciate comments and corrections here on this thread. I'll subscribe to it so we stay updated. We're happy to take them at educate@cosmoquest.org as well. Thank!

Ken G
2015-Jan-11, 09:56 PM
Sorry I missed this post, my bad! I would be happy to present my comments here. The article is generally good, but does have some problems that need correcting. Some could be considered minor, so perhaps can be let slip (I'd be happy to go into them, they center on the fact that fusion doesn't provide radiation pressure, it simply replaces the heat being lost, so the regular old gas pressure can stay constant-- radiation pressure is always pretty negligible in the Sun). The real problem comes later on, with:

"Why does luminosity depend so strongly on mass? A modest increase in mass corresponds to a star with a substantially higher pressure and temperature in the core. Since the rate of nuclear reactions depends sensitively on temperature, more massive stars have much larger rates of nuclear fusion. This in turn leads to a much higher luminosity."

That argument is quite wrong, on several counts. First of all, the more massive is a main sequence star, the lower is its pressure, not the higher. This is why high-mass stars don't go degenerate and make white dwarfs, they are low-density, low-pressure objects. Secondly, the luminosity is not high because the fusion happens faster, the fusion rate happens faster because the luminosity is higher. Fusion is self-regulated to simply replace whatever heat is being lost, and that's true at any mass for the star. The real reason that higher mass stars are more luminous is that light escapes from them faster, as was known by Eddington (even before he had ever heard of nuclear fusion).

ETA: The error is compounded later with:
"More massive stars have greater gravity that creates higher pressure in the stellar interior. The higher pressure results in higher temperature that causes higher energy output by the fusion process, giving both higher luminosity and higher surface temperature."
The gravity, generally defined as the gravitational acceleration at the surface, of high-mass stars is lower than for low-mass stars. The gravitational energy per particle, on the other hand, is about the same for all masses on the main sequence, because the core temperatures are similar. The reason high-mass stars have higher core temperatures has nothing directly to do with their gravity, it has to do with their aforementioned need to self-regulate their fusion rate to be much faster than low-mass stars, because they "leak light" faster.

Hornblower
2015-Jan-12, 03:36 AM
Now I am curious about how a star would continue to evolve in the absence of nuclear fusion after reaching the luminosity predicted by Eddington. I would expect it to continue contracting slowly as the heat leaks away and is not replenished. As it gradually becomes denser and more opaque, would the luminosity decrease? Would a supermassive star eventually settle into a black hole without any fireworks?

Ken G
2015-Jan-12, 04:39 AM
Now I am curious about how a star would continue to evolve in the absence of nuclear fusion after reaching the luminosity predicted by Eddington. It turns out the luminosity of a star, usually both before and during the main sequence, is mostly dependent only on the mass of the star and little else. So if there were no fusion, stars would maintain the same luminosity they have on the main sequence for a long time, basically until they become white dwarfs (for lower mass) or go supernova (for higher mass). This is generally called the "Henyey track."

I would expect it to continue contracting slowly as the heat leaks away and is not replenished. As it gradually becomes denser and more opaque, would the luminosity decrease? Not much, it would stay fairly constant if the mass stays fairly constant.

Would a supermassive star eventually settle into a black hole without any fireworks?Yes I think that's true, the current supernova fireworks have to do with a rapid instability that occurs when stars get so hot and dense that strange processes eat up kinetic energy as their cores shrink. Those processes include the "Urca" process (which involves neutrino emission), the photodisintegration of the nuclei (which is kind of like undoing all the fusion the core has done), and neutronization (which also involves escape of neutrinos). When these processes remove kinetic energy, the star loses support, and collapses, only for the envelope to "bounce back" when the core converts to the strange forces available to a neutron star (like strong forces and relativistic gravity), leading to the "fireworks". But if we were going back into the days of Eddington, and give him the quantum mechanics of a white dwarf, but take away all knowledge of nuclear processes so everything always stays protons and electrons, then you're right-- there wouldn't be much fireworks, the core would just shrink away into a black hole as mass was added to it.

For some reason, Eddington thought stars were always stable, so I don't think he imagined models where stars shrink away into black holes. He thought the Sun was much younger than it is, of course, because he didn't know about fusion, and when quantum mechanics and observations of white dwarfs came along, he would have realized that the Sun would eventually become one of those. But I don't know why he didn't think more massive stars would shrink down into black holes as they lost heat-- maybe he did, he just thought it would be gradual, like you are saying.

Hornblower
2015-Jan-18, 03:06 AM
Perhaps it would be good to put this discussion in the Astronomy forum.

My educated guess is that when Eddington was doing this theoretical work, nobody knew enough about subatomic structure to carry stellar evolution to the bitter end. Suppose fusion could not happen and we have nothing but hydrogen. I can imagine a star slowly contracting and getting hotter at the photosphere, and staying about the same luminosity. Eventually it would reach some compression limit, at which time it would start cooling and fading. White dwarfs were known by then, and it would not have been unreasonable to expect stars of all masses to end up that way. If I am not mistaken, nobody yet knew about electron and neutron degeneracy, let alone their upper limits on how much collapsed mass they could support.

It is noteworthy that low-mass stars such as Proxima Centauri, at about 0.1 solar mass, are expected to gradually contract and get hotter and somewhat brighter, and never swell into a red giant stage (Sky and Telescope, November 1997, p. 20). That is because they are convective throughout and thus never get stratified. As hydrogen fuses into helium, the two gases become blended throughout the star. As the fusion progresses the result is fewer particles, and that appears to me to explain the contraction on the basis of gas laws. When the fusion finally runs out the contraction and brightening hasten until electron degeneracy is reached, after which time the star is a fading "white dwarf". My educated guess now is that a hypothetical one-solar-mass star with no fusion would do something similar at a faster rate and end up resembling Sirius B. Perhaps high-mass stars would collapse into neutron stars or black holes, with no red giant stage before the final crunch.

Ken G, as I read your explanations in this thread, and also in that one you did at length several years ago, I am flabbergasted at the mistakes by those who should have known better about the pressure and temperature inside a massive star. We know from observation that main sequence stars of 10 times the Sun's mass are also roughly 10 times its diameter. It follows easily that each increment of mass has only about 1/100 of the gravitational weight it would have if compacted into one solar diameter, so the pressure must be only about 1/10 that inside the Sun. From the familiar gas law equation PV = nRT (R is the gas constant, not a radius), it follows that the temperature inside will not be much different. This is all Physics 101. Keep up the good work in sniffing out these errors and calling them to our attention.

Ken G
2015-Jan-18, 04:20 PM
Perhaps it would be good to put this discussion in the Astronomy forum.Yes it is appropriate there, though if the Explore encyclopedia is monitoring it, this discussion could be relevant to their deliberations.

Suppose fusion could not happen and we have nothing but hydrogen. I can imagine a star slowly contracting and getting hotter at the photosphere, and staying about the same luminosity. Yes, that's what would happen. The physics of it is what goes into the "Henyey track," which is not as widely known as it probably should be.

Eventually it would reach some compression limit, at which time it would start cooling and fading. White dwarfs were known by then, and it would not have been unreasonable to expect stars of all masses to end up that way.Since they had special relativity, they knew that if stars can lose enough heat, they have to become black holes eventually (because they eventually have to go relativistic, even the protons, and that will cause extreme shrinking as the star continues to lose heat). Since they also had quantum mechanics, they knew that a star could reach a ground state where it could lose no further heat. So the issue was always, which happens first? Chandrasekhar showed that the mass of the star is the key issue in deciding that, but Eddington just didn't believe that any star could keep shrinking away to a black hole. He felt that special relativity must be wrong since it predicted that this could happen above the Chandrasekhar limit, and indeed he even tried to modify special relativity so that did not happen. Had he been right, he would have been heralded as someone with the insight of Einstein-- winners write history.
If I am not mistaken, nobody yet knew about electron and neutron degeneracy, let alone their upper limits on how much collapsed mass they could support.It depends on what time in history you take. An interesting time to look at is at the time of the Eddington vs. Chandrasekhar controversy, at which time white dwarfs were understood via quantum mechanics, but compact stars like neutrons stars and black holes were not known to exist. Once Eddington had gotten over his incredulity around the observations of white dwarfs, he did not take the lesson and apply skepticism to his incredulity about the existence of black holes! It was as though he felt he could believe in the quantum mechanics of white dwarfs because we observe them and because they will not contract any further, but he could not stomach a type of object that just kept contracting vastly more than a white dwarf already has, until it becomes an object on the scale of everyday human experience! When physics said such could happen, he said, then we need new physics. His stature and credibility in astrophysics at the time were no less than Einstein's, so people generally did not reject his opinion on that, and Chandrasekhar was given a hard time. It was not astronomy's finest hour in its culture clashes with physics (astronomy fared much better in the solar neutrino problem!).


It is noteworthy that low-mass stars such as Proxima Centauri, at about 0.1 solar mass, are expected to gradually contract and get hotter and somewhat brighter, and never swell into a red giant stage (Sky and Telescope, November 1997, p. 20). That is because they are convective throughout and thus never get stratified. As hydrogen fuses into helium, the two gases become blended throughout the star. As the fusion progresses the result is fewer particles, and that appears to me to explain the contraction on the basis of gas laws. Yes, when the lost heat is being replaced, there would not be contraction if not for the lower number of particles. Contraction is usually something that happens mostly when there is not fusion going on, but here's a case where it proceeds even with fusion.
When the fusion finally runs out the contraction and brightening hasten until electron degeneracy is reached, after which time the star is a fading "white dwarf".Yes, now the heat is not replaced so contraction can happen more quickly.

My educated guess now is that a hypothetical one-solar-mass star with no fusion would do something similar at a faster rate and end up resembling Sirius B. Exactly.

Perhaps high-mass stars would collapse into neutron stars or black holes, with no red giant stage before the final crunch.Yes, and no supernova either, because the contraction would be gradual until the very latest stages when there's not much gravitational energy left that can still be extracted. When the core contracts at the very end, it might create a temporary red giant, in place of a supernova, so it would be more like an LBV.


Ken G, as I read your explanations in this thread, and also in that one you did at length several years ago, I am flabbergasted at the mistakes by those who should have known better about the pressure and temperature inside a massive star. We know from observation that main sequence stars of 10 times the Sun's mass are also roughly 10 times its diameter. It follows easily that each increment of mass has only about 1/100 of the gravitational weight it would have if compacted into one solar diameter, so the pressure must be only about 1/10 that inside the Sun. From the familiar gas law equation PV = nRT (R is the gas constant, not a radius), it follows that the temperature inside will not be much different. This is all Physics 101. Keep up the good work in sniffing out these errors and calling them to our attention.Thanks, I was pretty amazed as well. So far, I have not seen any significant corrections appearing-- the same errors are still out there, which is why I am trying to raise this issue to the attention of the Explore encyclopedia. They only seem to check the thread infrequently, but the main thing is that the corrections eventually get made.

Hornblower
2015-Jan-18, 05:36 PM
Thanks for filling in my information gaps. I was thinking in terms of about 1905, though I knew about Eddington's treatment of Chandra at later dates, which I thought was pretty shabby.

Ken G
2015-Jan-18, 06:04 PM
It certainly serves as a cautionary tale against getting so much self-confidence that it amounts to hubris that nature will behave the way we expect her to, as though nature must defer to our great insight. I think nature gets quite a few laughs at our expense on that issue, though we have had some impressive successes (most recently, the Higgs, and probably soon, gravitational waves). The lesson seems to be that most central one in science: follow the evidence, not the preconceptions of the authorities, but the authorities aren't always wrong either!

Ken G
2015-Jan-26, 01:44 PM
The explore encyclopedia at http://cosmoquest.org/x/explore/2014/01/09/main_sequence/ still says "More massive stars have greater gravity that creates higher pressure in the stellar interior." That's totally wrong, and needs replacing.

Ken G
2015-Apr-04, 12:22 PM
That link still says "A modest increase in mass corresponds to a star with a substantially higher pressure and temperature in the core. Since the rate of nuclear reactions depends sensitively on temperature, more massive stars have much larger rates of nuclear fusion. This in turn leads to a much higher luminosity." The error is doubled-down on in the next paragraph: "More massive stars have greater gravity that creates higher pressure in the stellar interior. The higher pressure results in higher temperature that causes higher energy output by the fusion process, giving both higher luminosity and higher surface temperature."

Both the quoted remarks are just as completely wrong as when I pointed it out three months ago. Perhaps the author and administrator's of the encyclopedia don't care about accuracy, but that surprises me. The problems with the statement are:

1) The second statement claims that higher pressure causes higher temperature, but in fact temperature and pressure are independent quantities in the ideal gas law, and examples abound where higher temperatures can be associated with either lower or higher pressure. Consider the stratosphere of the Earth, for example. This would be a minor complaint, if not for the two much worse problems:
2) It makes easily falsifiable claims. Higher-mass main-sequence stars have lower pressures every where in the star, which is a basic consequence of something called "the virial theorem," as explained in more detail above.
3) The argument is incorrect, even if it had gotten the pressure difference right, and even if it had treated temperature and pressure as independent variables. The reason higher-mass main-sequence stars have higher luminosities has little to do with the physics of fusion, though fusion physics could be used in an iterative way to make small corrections to the simplest argument (if such detailed corrections were warranted, which they generally are not). It is clear that fusion physics is not particularly relevent to the issue of the luminosity, for two reasons:

i) astronomers like Russell and Eddington were able to account for the higher luminosity of higher-mass main-sequence stars without even knowing that fusion exists, and
ii) solar-like and more massive main-sequence stars reach their approximate main-sequence luminosity before fusion even initiates in the star, as can be seen from any H-R diagram showing stellar evolution models. This makes it clear that the basic processes that are mostly responsible for setting the luminosity have nothing at all to do with nuclear fusion, except for the lowest-mass stars (and for them one needs to include electron degeneracy to have anything close to a correct description of the processes that set the luminosity).

The actual physics that sets the luminosity of main-sequence stars is radiative diffusion and force balance, not nuclear fusion-- google the "Henyey track" or look at the discussion above. This has all been known for 50 years or more, but for some reason does not translate into the popular science textbooks or online resources, and it's high time that it did. Perhaps I am being impatient-- this stuff has been wrong in the textbooks for decades, another three months is probably not a big deal. Still, new young minds are encountering it every day, and getting misled, and I know the highly conscientious and capable people that make this information accessible to the public would not be satisfied with that state of affairs, they need only be made aware of it.

Ken G
2015-May-14, 12:18 AM
Another month goes by, and yet more young minds misinformed by the claim: "Why does luminosity depend so strongly on mass? A modest increase in mass corresponds to a star with a substantially higher pressure and temperature in the core." No, what the young mind needs to understand is why the higher mass main-sequence star must have a lower core pressure, which is a perfectly well known fact about main-sequence stars. Without understanding why that's true, as the Astropedia entry apparently does not understand, we cannot claim any understanding at all of the guts of main-sequence stars. So I'll keep pinging this, just in case those in a position to fix it, who I know care about correct astronomy education, will have the chance to do it.

CJSF
2015-May-14, 02:40 PM
Ken,

Did you try e-mailing the address Dr. Gugliucci provided in December? If no one is having the time (or inclination) to visit the Forum (which is sad for a host of reasons), maybe they are less apt to ignore an e-mail?

CJSF

Ken G
2015-May-14, 02:45 PM
Yes, I had a brief exchange with Pamela Gay back then, and I believe she was in contact with Chris Impey, the author. But I realize these things take time to get changed. I'm just being the squeaky wheel, because this has to start somewhere or it might be a decade before the textbooks get a clue on this matter. I figured if people come through this forum on the way to the Astropedia link, they will have a "heads up" because of this thread. But it sounds like this forum is not the appropriate place because the word is not getting out, so it will make more sense to use email directly. I also don't want to sound too critical of the textbooks-- they do a great job and I know they will want to get this right.

Hornblower
2015-May-14, 05:27 PM
I may have asked this in another thread but I will repeat it here. Are college freshman astronomy majors-to-be getting misinformation they will have to unlearn in advanced astrophysics courses?

Ken G
2015-May-14, 07:34 PM
Sure. Having taught such courses, I'm sure I've given them misinformation they needed to unlearn too! But this issue with the luminosity of main-sequence stars is particularly insidious, because it is important, widespread, and easy to fix. In fact, I have one intro textbook that called the reason for the higher luminosity of higher-mass main-sequence stars as one of the most important effects in stellar astronomy, and then promptly went on to completely botch it by saying that the cause of that higher luminosity was the higher fusion rate! (Of course, it also claimed the fusion rate was higher because of the "stronger gravity", so it was a total flub.) This is indeed something that will be hard to unlearn later, it gets hardwired in there pretty deeply, because it seems intuitively correct, but this just means there is a new intuition that needs training. I think the textbooks just get this information from each other, a minor sin that I'm sure we're all party to, but it's time to clean this one up.

Hornblower
2015-May-14, 07:45 PM
My hunch is that someone early in the 20th century confused the innards of a main sequence star and an evolved giant of the same mass with the innards of two main sequence stars of different mass. In the former, if I am not mistaken, the core is more dense and hotter, a state enabled by the stratification in stars other than low mass M dwarfs, and the subsequent exhaustion of hydrogen in the core.

Ken G
2015-May-14, 08:31 PM
It is true that when the Sun becomes a red giant, it will have a much higher temperature core. It won't have a higher pressure in its fusion zone though, in fact the main reason that red giants are "giant" is their need to deal with their high fusion temperature-- they have to find a way to drastically lower the pressure in the fusion region or the fusion goes through the roof. So instead, the fusion zone itself goes through its own roof, drastically lowering the density and pressure there as a net result.

Ken G
2015-Jul-22, 07:17 AM
Coming up on 9 months, the explore encyclopedia still says:

Why does luminosity depend so strongly on mass? A modest increase in mass corresponds to a star with a substantially higher pressure and temperature in the core. Since the rate of nuclear reactions depends sensitively on temperature, more massive stars have much larger rates of nuclear fusion. This in turn leads to a much higher luminosity.
That's still just as completely wrong as it was when I pointed it out 9 months ago. Does anybody care what information is out there masquerading as good scientific explanations? It is cause to doubt the reliability of any source that can be left so wrong for so long. I'm sure the whole encyclopedia is not that bad, but how can anyone tell which parts are any good without learning it for themself, and then they would't need an encyclopedia?

Arneb
2015-Aug-23, 06:31 PM
(1 month bump)

Ken G, you might be interested in, although not pleased by, the fact that the Bad Astronomer reiterates the more-mass-more-pressure meme in his Crash Course Astronomy video series (Chapter 29: Low Mass Stars (https://www.youtube.com/watch?v=jfvMtCHv1q4), almost right after the introduction and exposition of hydrogen fusion about 1:00 min).

Ken G
2015-Aug-23, 09:19 PM
You are correct on all counts. Thanks for pointing that out, it really shows how out of control this meme has gotten-- when even the Bad Astronomer falls for its bad astronomy!

Luckmeister
2015-Aug-24, 03:22 PM
I can't stop grinning as I imagine him coming here to discuss it and being told to "take it to ATM." :D

Ken G
2015-Aug-24, 07:06 PM
Yes, and ironically, if the mods consult intro textbooks, we'd be the ones over there! But if you look at advanced texts, or Eddington's paper, the story is very different. All of which raises the interesting question that thankfully is not so often an issue for science: just what is the "mainstream" anyway?

slang
2015-Aug-24, 11:11 PM
[...] just what is the "mainstream" anyway?

But let's not consider that an invitation to discuss this question here! I don't need an intro nor advanced textbook to see what that would do to this thread. :)

Ken G
2015-Aug-25, 01:55 AM
Good point. I guess it's clear enough that the mainstream view here is that of the advanced textbooks and research papers. Usually the intro textbooks do a very nice job of summarizing that material at an appropriate level. But it seems that sometimes, an error can creep in, and kind of pick up a life of its own! Then we're faced with the task of getting the error corrected, which can be an uphill battle as we're seeing here. If I wrote a textbook or online encylopedia, I really wouldn't want to have to change it either, but the right answer is really more interesting than the oft-repeated meme-- which is so often true in science!

Arneb
2015-Aug-25, 07:03 PM
Is there an "astronomy 101" level text anywhere on the net that gets the story right?

loglo
2015-Aug-25, 07:39 PM
If not, will you write one?

Ken G
2015-Aug-26, 04:03 AM
Actually, the only intro-textbook-like source I've ever found on the web that gets it basically right is the Wiki entry on Main Sequence stars, and even that one requires following some links-- it's never really spelled out to the casual reader. It's not even clear that counts as "Astronomy 101", because the Wiki entries tend to get rather technical!

Frankly I'm not sure how to write a kind of encyclopedia entry on the topic, where it would be found and used by more people than might come to this forum. The explanation given above is the best I have to offer, so in a sense one could say this thread is such an astronomy 101 explanation, though it's just for that particular question. A full intro textbook is a huge undertaking, and quite frankly most of the ones out there are generally very good and don't need much correction-- so it would seem to make more sense to just point out the occasional boo-boos on places like here, until new editions come out with the problems fixed. I did submit a paper recently to the Journal of College Science Teaching to point out this common error, so maybe that will help, if they send it to good referees. But that paper just points out the problem-- the right explanation is given in better detail on this very thread.

Ken G
2015-Dec-29, 05:02 AM
Naďve readers beware: the Explore encyclopedia still says: " Why does luminosity depend so strongly on mass? A modest increase in mass corresponds to a star with a substantially higher pressure and temperature in the core. Since the rate of nuclear reactions depends sensitively on temperature, more massive stars have much larger rates of nuclear fusion. This in turn leads to a much higher luminosity."

This is just completely wrong, in all the ways explained above. Similar arguments are found in many places, so it's very likely that a beginning student will get a completely wrong idea of the physics of stars like the Sun. I think that's a shame, so I'm alerting new readers to this problem. I don't know how many are paying that close attention to the online encyclopedias and textbooks on this issue, but anyway, there you have it.

John Mendenhall
2015-Dec-29, 11:45 PM
Interesting (and encouraging) that Wiki gets it right. Keep plugging away, Ken G, someone with edit privileges will eventually see your work.

Hm. Have Fraser and/or Pamela covered this in any of this in their videos?

Ken G
2015-Dec-30, 07:59 AM
I don't know, but they may regard it as too elementary-- whether they think it's right or wrong!

John Mendenhall
2015-Dec-30, 09:30 AM
I don't know, but they may regard it as too elementary-- whether they think it's right or wrong!

LOL. What an awfu possibility. :doh:

slang
2015-Dec-30, 09:50 AM
A quick review of the thread shows met that NoisyAstronomer promised to keep an eye on this, but I'm not sure she is still working on it. Last access to the forum seems to be september 2015. As I recall Pamela indicated elsewhere that the corrections should still be in this thread but did not make any promises as to fixing.. I know the buildteam is down to a skeleton crew swamped with work, and monitoring this thread, or any part of our forum, is probably not high on the list of priorities.

Ken G
2015-Dec-30, 03:04 PM
Yes, I think the problem is very much a case of other priorities. I completely understand, maintaining online encyclopedias that don't pay anything is an unselfish and often thankless task. So I only point out the errors in case there is desire and energy to fix it, and for whatever readers might come across this thread and thereby not need the encyclopedia to be fixed.

Hornblower
2016-Jan-01, 05:30 PM
Interesting (and encouraging) that Wiki gets it right. Keep plugging away, Ken G, someone with edit privileges will eventually see your work.

Hm. Have Fraser and/or Pamela covered this in any of this in their videos?

Could you link to the article that gets it right? The general article I found on stars,
https://en.wikipedia.org/wiki/Star
asserts that the core pressure would be higher in a high-mass, hydrogen burning star. Scroll down to Age.

Ken G
2016-Jan-01, 06:28 PM
Could you link to the article that gets it right? The general article I found on stars,
https://en.wikipedia.org/wiki/Star
asserts that the core pressure would be higher in a high-mass, hydrogen burning star. Scroll down to Age.Yikes, you are so right, that Wiki entry includes the awful "The more massive the star, the shorter its lifespan, primarily because massive stars have greater pressure on their cores, causing them to burn hydrogen more rapidly." That's disappointing, Wikipedia is usually better than introductory textbooks, but certainly not there.

The entry on "mass-luminosity relation" (https://en.wikipedia.org/wiki/Mass%E2%80%93luminosity_relation) is much better, because although it does not explicitly mention the core pressure, it is easy to use its expressions to derive the fact that higher-mass main-sequence stars have significantly lower core pressures, given that the central temperatures are all roughly the fusion temperature of hydrogen.

Your Wiki citation certainly shows that the false meme about how stars work has propagated quite far and wide, even to the easily corrected Wikipedia. Apparently, false ideas maintain a certain inertia, not just in written textbooks that trace along a chain of earlier editions, but also in that most ephemeral of electron configurations known as the internet! I admit there is a certain advantage to "inertia" in knowledge, as we wouldn't want to constantly have to rethink everything all the time. But such inertia does have its down side. I have a pending submission to the JAESE journal on this, that will serve as a test of how bad the inertia problem is.

Cougar
2016-Jan-01, 07:14 PM
....not just in written textbooks that trace along a chain of earlier editions....

...about which Stephen Jay Gould famously wrote. I was wondering if this incorrect explanation was ever the scientifically accepted or assumed view, such as the static universe, later realized to be dynamic...



"They argued that the universe was eternal and unchanging, and that the Big Bang model was nonsense. This was still the establishment view." - Singh



...or perhaps astrophysicists never took such a view in this case...?

Ken G
2016-Jan-01, 08:28 PM
Ironically, I think it would be safe to say that astrophysicists originally took the correct view, when there was any view at all, because Eddington and others got it right the first time. The idea that higher mass stars have higher pressure cores, and hence more rapid fusion, would have crept in later, informally, at the pedagogical level of explaining the mass-luminosity relation, but never in the actual derivation of it (as it would never have worked in a derivation). So I don't think it was like the static universe, it was always a complete fiction, merely mistaken for a valid explanation. Perhaps it is like explanations that planes fly because the air has to move faster over a curved wing top than over a straight wing bottom, as if there was some requirement that the same air separated at the wing front must meet at the wing back.

slang
2016-Jan-02, 11:01 AM
Some posts moved here (http://cosmoquest.org/forum/showthread.php?159662-Mass-and-luminosity-discussion-moved-from-feedback).

Ken G
2016-Jan-29, 02:31 AM
JAESE recommended a different journal, the Physics Teacher, because JAESE is more about how to learn, than what to learn. Unfortunately, I know that the Physics Teacher is more about general topics than specialized astronomy issues, so I doubt they'll want it either. It turns out to be rather hard to get textbooks corrected, but if enough referees see it, it will eventually percolate into the textbooks and online material, I'm sure.

Ken G
2016-Aug-27, 09:27 AM
The Explore encyclopedia (http://cosmoquest.org/x/explore/2014/01/09/main_sequence/) still says "A modest increase in mass corresponds to a star with a substantially higher pressure and temperature in the core. Since the rate of nuclear reactions depends sensitively on temperature, more massive stars have much larger rates of nuclear fusion. This in turn leads to a much higher luminosity." This is the opposite of a true argument.

CJSF
2016-Aug-27, 09:40 PM
So, more massive stars have lower luminosity?

CJSF

Ken G
2016-Aug-27, 11:17 PM
So, more massive stars have lower luminosity?

CJSFThe explanation is an effort to say why their luminosity is higher, it is not the statement that their luminosity is higher. It is the explanation that is the opposite of true-- it is a totally false explanation, there's almost no part of it that is correct, remarkably. The only part of what I quoted that is actually correct is that fusion is sensitive to temperature, but none of the claimed ramifications of that fact are actually correct. It's a classic example of "truthiness" in science, instead of truth. Science is the place where this cannot be tolerated, but no one in a position to do it wishes to take the time to correct the Explore encylopedia. I will grant that they probably gain no benefit from it, not even a thank you in most cases.

CJSF
2016-Aug-28, 05:07 AM
*puzzled*
I think you did explain the way it actually works, somewhere in this thread, right? If so, I'll read through and find it. If not, could you send me a link to an "educated layman's" type explanation. I really want to understand, but somehow I feel like I'm missing a connection.

Thanks.

Christopher

CJSF
2016-Aug-28, 05:27 AM
Ok, yes, I read it again, and I think I understand your complaints. I wonder, though, if the matter just got lost in the shuffle of the tremendous works loads and professional (and personal!) issues Dr. Gay has had in the past couple of years. Perhaps a new round of polite request and/or questions should be sent to see if the information can be properly updated? I am guessing this incorrect explanation must have deep roots, because I've heard and read it across many media (print, electronic, radio, TV) for a long time. As an interested non-expert, I just thought it sounded right and never really wondered about it until you first brought it up in this thread.

Anyway, thanks for being patient. I hope you get it updated correctly.

CJSF

Hornblower
2016-Aug-28, 12:59 PM
Last night at a public observing session I touched on this topic when answering questions for an inquisitive 12-year-old boy. I did not get into the quantitative details of gravitational heating, heat flow as a function of density, the gas laws, etc. but I did explain that physicists had predicted how bright a star should be long before fusion was contemplated, let alone confirmed. I said that gravitational compression heating got the star hot in the first place, and that fusion induced by the internal heat keeps it hot for far longer than could be explained any other way. A complete explanation of the mass/luminosity relationship and the pressure and density in the core probably would have been over this kid's head, but still is only undergraduate stuff.

How can a novice reader tell whether or not Ken G is correct here? I confirmed his arguments by crunching the gas laws and integrating the gravitational forces inside a spherical body, having learned how to do so in college physics.

Ken G
2016-Aug-28, 01:15 PM
I wonder, though, if the matter just got lost in the shuffle of the tremendous works loads and professional (and personal!) issues Dr. Gay has had in the past couple of years.I'm sure those responsible for updating and maintaining this information have many other things to do, and get no compensation for their efforts. So I don't really fault them for it, but still, I do feel there is a certain responsibility for maintaining correctness in scientific information. Picky details are not an issue, but this information is just completely wrong.

Perhaps a new round of polite request and/or questions should be sent to see if the information can be properly updated?I don't think so, I communicated a long time ago directly with both Pamela and the author of the encyclopedia, but nothing happened. They are aware of the errors, but it's still only a tiny fraction of all the correct information that is there, so it appears it will just stay the way it is.

I am guessing this incorrect explanation must have deep roots, because I've heard and read it across many media (print, electronic, radio, TV) for a long time. That's for sure, it gets copied from place to place until there is a mountain of error being mistaken as a mountain of independent evidence! It reminds me a little of the "Paper Towns" effect (pointed out in a book of that name), where maps sometimes included completely fallacious information (in the form of towns that did not exist, "paper" towns), so that if any other maps were found to have those towns, they would know the other maps were simply being copied. Imagine how much easier it is to copy a map than to actually do the geographical research yourself! In the case of textbooks and online notes, we can certainly forgive the authors for not researching personally every argument they use, but this is what can happen when they do that.

Ken G
2016-Aug-28, 01:25 PM
I said that gravitational compression heating got the star hot in the first place, and that fusion induced by the internal heat keeps it hot for far longer than could be explained any other way. If the textbooks would at least say that, the situation would be greatly improved. If enough people know it, it must start appearing in more places.


How can a novice reader tell whether or not Ken G is correct here? I think there is not a way, which is the main problem here. The novice reader has to depend to a large degree on the expertise of the authors of the material, they just don't have the tools to figure it out for themself. But there is a relatively easy way to see that part of the usual explanation is wrong-- one can look at the results of stellar interior models. Of course even that is not so easy for a novice to do, to get access to models and be able to interpret what they say.

There are really two main wrong arguments that are often seen, and both seem intuitively correct but only one is subtle and hard to check. The easier one to check is the claim that higher-mass main-sequence stars have stronger gravity and this leads to higher pressure and temperature in their cores. We know that mass is not enough by itself to tell us the gravity, so we also have to know the radius (that's why we can have low-mass black holes, of course), and thus we should be suspicious of any argument that only refers to mass. But as a novice, we might not know the virial theorem so we might not have any way to tell the radius, but if we look at models, we will see easily that higher mass main-sequence stars have lower gravity and lower core pressure. So that argument is easy to identify as baloney. The more subtle one is that the higher luminosity is caused by the higher fusion rate, which also seems right because the luminosity does in fact equal the fusion rate. I don't know how a novice could correctly disentangle the logic there, except by having it introduced to them in the way you did to the 12-year-old. If the thinking patterns start out following the right path, they might stay that way.

The argument that the luminosity of a primarily radiatively diffusing ball of hot gas is not at all sensitive to the core temperature is the one that no novice could get access to, and unfortunately can rarely be found in textbooks (though it is in Wikipedia, by the way).

Arneb
2016-Aug-28, 08:02 PM
Last night at a public observing session I touched on this topic when answering questions for an inquisitive 12-year-old boy. I did not get into the quantitative details of gravitational heating, heat flow as a function of density, the gas laws, etc. but I did explain that physicists had predicted how bright a star should be long before fusion was contemplated, let alone confirmed. I said that gravitational compression heating got the star hot in the first place, and that fusion induced by the internal heat keeps it hot for far longer than could be explained any other way. A complete explanation of the mass/luminosity relationship and the pressure and density in the core probably would have been over this kid's head, but still is only undergraduate stuff.

How can a novice reader tell whether or not Ken G is correct here? I confirmed his arguments by crunching the gas laws and integrating the gravitational forces inside a spherical body, having learned how to do so in college physics.

If it's a consolation to anyone here, that is the way I explained it to my son, having read the threads by Ken G on the issue. So it's not all for nought! :)

Ken G
2016-Aug-28, 08:38 PM
Excellent!

Hornblower
2016-Aug-28, 09:46 PM
My sanity check started with noting that main sequence stars with 10 times the Sun's mass also have about 10 times its radius, for whatever reason. I made the reasonable assumption that in gravitational equilibrium they would have similar density patterns from the center out, based on what I know about gravitationally bound atmospheres. Then I did a rough and dirty integration by dividing the two stars into equal numbers of layers. On the large star each layer thus has 10 times the mass of its counterpart in the small star, but at 10 times the radius its gravitational weight is only 1/10 as much. Thus the lower pressure in the center of the large star, which a novice could easily find to be counterintuitive. From the gas law equation PV = nRT, it follows that the internal temperature is about the same for both stars. This is in line with the findings of Eddington et. al. as reported by Ken G, whose explanation about why the large star stabilized at that radius completes the picture. The fusion is a low-intensity heat source that gives the observed yield only because of the sheer volume involved, so I would expect it to cause little if any difference in the overall pattern from what we get without it. Of course the core of the large star will have to stabilize hotter to induce the necessary higher fusion rate, but not by an awful lot because of the extreme sensitivity of the fusion rate to temperature. That's why Eddington's findings were as good as they were in the absence of any knowledge about fusion.

Perhaps the writers who originated the wrong explanation were confused by the case of evolved red giants, in which the core is indeed more compact and denser than it was during the main sequence, as well as much hotter. This is because of the layering that happens from lack of mixing of the hydrogen-depleted core with the envelope in solar mass and larger stars, and is a more complex process. In any case it appears that their successors assumed everything was correct instead of doing a sanity check by reading the original research papers.

Ken G
2016-Aug-28, 09:57 PM
Of course the core of the large star will have to stabilize hotter to induce the necessary higher fusion rate, but not by an awful lot because of the extreme sensitivity of the fusion rate to temperature. Exactly, and what is so ironic about this sensitivity is that it is generally cited as the reason that the fusion rate sets the luminosity, when in fact it is the reason the luminosity sets the fusion rate. In a way it's odd that the correct logic is so often reversed, because we all have experience with an analogous system-- a thermostat in a house in Winter. You can't get any more temperature sensitivity than a thermostat, as soon as the temperature drops below the thermostat reading, the heat kicks on. So the heating system in your house is very temperature sensitive, and fusion is very temperature sensitive, so if that makes fusion set the rate a star loses heat, then apparently your furnace sets the rate your house loses heat. Huh? Nobody thinks that, so why do they think it for stars? When you crack a window in Winter, your heating bill goes up, and when you add insulation, your heating bill goes down. So how does the rate you burn natural gas control the rate your house loses heat?

In any case it appears that their successors assumed everything was correct instead of doing a sanity check by reading the original research papers.Yes, the misconceptions are not present in research papers, and it's not in graduate level textbooks either, it's only in the introductory material-- exactly the material that is intended for people who can't check it.

Hornblower
2016-Aug-29, 11:36 AM
Exactly, and what is so ironic about this sensitivity is that it is generally cited as the reason that the fusion rate sets the luminosity, when in fact it is the reason the luminosity sets the fusion rate. In a way it's odd that the correct logic is so often reversed, because we all have experience with an analogous system-- a thermostat in a house in Winter. You can't get any more temperature sensitivity than a thermostat, as soon as the temperature drops below the thermostat reading, the heat kicks on. So the heating system in your house is very temperature sensitive, and fusion is very temperature sensitive, so if that makes fusion set the rate a star loses heat, then apparently your furnace sets the rate your house loses heat. Huh? Nobody thinks that, so why do they think it for stars? When you crack a window in Winter, your heating bill goes up, and when you add insulation, your heating bill goes down. So how does the rate you burn natural gas control the rate your house loses heat?
Yes, the misconceptions are not present in research papers, and it's not in graduate level textbooks either, it's only in the introductory material-- exactly the material that is intended for people who can't check it.

I am concerned that your presentation here is oversimplified and could confuse a novice, who could reasonably expect excessive heat loss from a star to cool the interior, which would reduce the fusion rate instead of increasing it. I would elaborate a bit and say that the excessive heat loss at the photosphere is at the expense of kinetic energy in the underlying material. This allows the star to continue contracting under its self gravitation, and the internal dynamics are such that the core temperature continues to rise in spite of the heat loss, thus inducing a higher fusion rate. I could consider this contraction to be the functional analogy to the movement of a bimetallic strip in a household thermostat.

Ken G
2016-Aug-29, 01:30 PM
I am concerned that your presentation here is oversimplified and could confuse a novice, who could reasonably expect excessive heat loss from a star to cool the interior, which would reduce the fusion rate instead of increasing it. I would elaborate a bit and say that the excessive heat loss at the photosphere is at the expense of kinetic energy in the underlying material. This allows the star to continue contracting under its self gravitation, and the internal dynamics are such that the core temperature continues to rise in spite of the heat loss, thus inducing a higher fusion rate. I could consider this contraction to be the functional analogy to the movement of a bimetallic strip in a household thermostat.
You are explaining the reason that fusion acts like a thermostat, but all I need to defeat the claims that the fusion rate sets the luminosity is the statement that it does act like a thermostat. The connection between fusion in a star, and the star's luminosity, is exactly like the connection between the rate the heater in a house pumps out heat, and the rate that the house leaks heat into the surrounding air. Yet in the latter case, we do not say that the rate your heater pumps out heat sets the rate your house loses heat to the outside air, given the presence of a thermostat at a given setting. All that is missing is why the thermostat setting is what it is, and why fusion has the thermostatic effect it does have, which is an important but different issue.

Hornblower
2016-Aug-29, 09:51 PM
You are explaining the reason that fusion acts like a thermostat, but all I need to defeat the claims that the fusion rate sets the luminosity is the statement that it does act like a thermostat. The connection between fusion in a star, and the star's luminosity, is exactly like the connection between the rate the heater in a house pumps out heat, and the rate that the house leaks heat into the surrounding air. Yet in the latter case, we do not say that the rate your heater pumps out heat sets the rate your house loses heat to the outside air, given the presence of a thermostat at a given setting. All that is missing is why the thermostat setting is what it is, and why fusion has the thermostatic effect it does have, which is an important but different issue.

Ken, I am sorry, but your latest post reinforces my misgivings about your previous one rather than resolving them. First of all, saying "fusion acts like a thermostat" is like saying "my furnace acts like a thermostat", with either one being absurd in my opinion. As I see it, the fusion in the core of a star and the furnace in my house are heat sources that are regulated by thermostats. I stand by my opinion that it is desirable to include the details of the action in the star as stated in my previous post. I think that boy at the observing session the other night would have followed me very well, as he knew about the compression heating that occurs in a diesel engine.

Ken G
2016-Aug-29, 10:54 PM
Ken, I am sorry, but your latest post reinforces my misgivings about your previous one rather than resolving them. First of all, saying "fusion acts like a thermostat" is like saying "my furnace acts like a thermostat", with either one being absurd in my opinion.My point is, I am not explaining why it is acting like a thermostat, I'm tracking the consequences of the fact that it is. The reason it acts like a thermostat is a whole different explanation, one that is usually correct-- there is a temperature at which fusion will replace the heat that leaks out, and if the temperature goes higher than that special mark, the star expands and turns its temperature down. If the temperature is lower than that special mark, the star contracts and raises the temperature. But again, that explanation is its own thing, it's not what is wrong in the Explore encyclopedia. What's wrong (among other things) is the claim that the fusion rate sets the luminosity, as if we should study the fusion process to understand the star's luminosity. That's exactly like studying how your house's heater works, in order to understand how much heat is leaking out your windows!


As I see it, the fusion in the core of a star and the furnace in my house are heat sources that are regulated by thermostats.Sure, that's fine, but it's that other explanation, not what is wrong.


I stand by my opinion that it is desirable to include the details of the action in the star as stated in my previous post. I think it's great to include the details, the more the merrier, but it's not the subject of what needs correcting and why it needs correcting. That only requires that there be a thermostat-- not how it works. There are many ways to build a thermostat, but all of them will produce a system where the rate that heat leaks out your window will set the rate that your house burns fuel, and none of them will make the rate your house burns fuel set the rate that heat leaks out your windows.


I think that boy at the observing session the other night would have followed me very well, as he knew about the compression heating that occurs in a diesel engine.I am not in any way suggesting you should not explain the thermostat, it's just not what I'm talking about here.

Reality Check
2016-Oct-19, 01:27 AM
A complete explanation of the mass/luminosity relationship and the pressure and density in the core probably would have been over this kid's head, but still is only undergraduate stuff.
The mass–luminosity relation (https://en.wikipedia.org/wiki/Mass%E2%80%93luminosity_relation) is that luminosity of main-sequence stars does increase with mass. For lighter stars L is proportional to M cubed, for heavier stars proportional to M. The Explore entry (currently unavailable) seems to be about main-sequence stars according to the URL and quoted text. So it looks like no correction is needed.
Perhaps clarification is needed, e.g.

This does not apply to off-sequence stars such as red giants or white dwarfs.
Emphasizing that the pressure increase with mass increase is at the core of the star where the fusion is happening.
The rate of nuclear reaction is related to density so a higher pressure at the core = a higher density = a higher rate of fusion.

Ken G
2016-Oct-19, 02:34 AM
The mass–luminosity relation (https://en.wikipedia.org/wiki/Mass%E2%80%93luminosity_relation) is that luminosity of main-sequence stars does increase with mass. For lighter stars L is proportional to M cubed, for heavier stars proportional to M. The Explore entry (currently unavailable) seems to be about main-sequence stars according to the URL and quoted text. So it looks like no correction is needed.So let us try to follow your logic here. Although you have not read the explanation, you feel it needs no fixing, on the grounds that it concludes by saying that higher mass stars are more luminous. All I can guess is that you are invoking a postulate that any explanation that leads to the conclusion that higher mass stars are more luminous, must be a correct explanation. Baffling logic, that.


Perhaps clarification is needed, e.g.

This does not apply to off-sequence stars such as red giants or white dwarfs.It is crystal clear that the topic is main-sequence stars, so no, there's no need to clarify that.

Emphasizing that the pressure increase with mass increase is at the core of the star where the fusion is happening.Let us not emphasize this false claim. That is indeed what it says in many places, but not any place that knows what it is talking about. Anyone with any clue about main-sequence stars knows that high-mass main-sequence stars have low pressure in their core. That is in fact what requires correction.


The rate of nuclear reaction is related to density so a higher pressure at the core = a higher density = a higher rate of fusion.
Totally wrong. The fusion depends almost exclusively on temperature, and the temperature simply self-regulates to replace the heat that is being lost. It has nothing to do with the pressure in the core being high, especially since the pressure goes the opposite way from that claim. But it's all in the thread above, simply read it.

Ken G
2016-Oct-19, 02:36 AM
Not sure what happened with that post, but it won't let me edit it at the moment.

Hornblower
2016-Oct-19, 02:41 AM
The mass–luminosity relation (https://en.wikipedia.org/wiki/Mass%E2%80%93luminosity_relation) is that luminosity of main-sequence stars does increase with mass. For lighter stars L is proportional to M cubed, for heavier stars proportional to M. The Explore entry (currently unavailable) seems to be about main-sequence stars according to the URL and quoted text. So it looks like no correction is needed.
Perhaps clarification is needed, e.g.

This does not apply to off-sequence stars such as red giants or white dwarfs.
Emphasizing that the pressure increase with mass increase is at the core of the star where the fusion is happening.
The rate of nuclear reaction is related to density so a higher pressure at the core = a higher density = a higher rate of fusion.


I'm sorry, but I feel confident that Ken is correct on this issue. Please review the whole thread, including my posts, and look for Ken's detailed references to Arthur Eddington's work about 1915, long before nuclear fusion was envisioned, let alone confirmed. I checked up on my own by applying the gas laws and a correct integration of the gravitational weight of the stellar envelope. To find the previous thread, go to Advanced Search, enter Ken G as user and Eddington as a key word. That should return a thread in the fall of 2005, even with this clunky search function.

As I think I understand it, we don't need higher density and pressure at the center to induce plenty of fusion to stabilize the high mass main sequence star, as long as the core gets hot enough. The high sensitivity of the fusion rate to temperature means only a modest increase in temperature is needed for a big increase in the fusion rate, and the dynamics of the star are such that it gets hot enough. To review, Eddington concluded that a 10-solar-mass star would be roughly the same temperature inside as the Sun, and is much hotter at the photosphere because in its more rarified state the heat leaks out faster. Now that we know about fusion, we can conclude that the Sun would achieve fusion-aided stability at a somewhat lower core temperature.

My misgivings recently in this thread were that what I thought were oversimplified explanations of the thermostat action in a star might confuse a novice. I remain confident that Ken is on the right track.

Reality Check
2016-Oct-19, 09:22 PM
I'm sorry, but I feel confident that Ken is correct on this issue.
I have read the thread but the physics history does not matter. The current physics is that luminosity increases as the mass of main-sequence stars increases: mass–luminosity relation (https://en.wikipedia.org/wiki/Mass%E2%80%93luminosity_relation)

Deriving a theoretically exact mass/luminosity relation requires finding the energy generation equation and building a thermodynamic model of the inside of a star. However, the basic relation L ∝ M3 can be derived using some basic physics and simplifying assumptions.[5] The first such derivation was performed by astrophysicist Arthur Eddington in 1924.[6]
Followed by the derivation of that basic relation.

ETA: The physics seems clear enough to me.
Having a higher mass means that gravity increases. That causes bigger pressures at the core of the star. That causes a higher density of matter. That causes fusion rates to go up. More photons are emitted. More photons escape the star and the star increases in luminosity.

Ken G
2016-Oct-19, 10:15 PM
The physics seems clear enough to me.One of the first rules of science is that what "seems" is often not what is.

Having a higher mass means that gravity increases.That might be true had gravity depended only on mass, but it does not. It also depends on radius.

That causes bigger pressures at the core of the star.Certainly not, anyone who knows essentially anything about main-sequence stars knows that higher-mass main-sequence stars have lower core pressures. The reasons are spelled out above.


That causes a higher density of matter. That causes fusion rates to go up. More photons are emitted. More photons escape the star and the star increases in luminosity.Also wrong. The luminosity controls the fusion rate, not the other way around. That's what it means to say that fusion is "self-regulated." What's so odd is that almost all sources will mention the stable way in which fusion self-regulates, but they usually fail to notice what that means. It means the luminosity controls the fusion rate, just as opening cracks in your windows in Winter will control the rate your house burns fuel. This is all so obvious, that I don't even regard it as "against the mainstream" to point out that the textbooks very often get this totally muddled. There's a difference between a common mistake in mainstream sources, and some non-mainstream theory!

slang
2016-Oct-19, 10:18 PM
To find the previous thread, go to Advanced Search, enter Ken G as user and Eddington as a key word. That should return a thread in the fall of 2005, even with this clunky search function.

This one (https://forum.cosmoquest.org/showthread.php?34341-Why-are-high-mass-stars-are-so-luminous)? Use google with "site:cosmoquest.org" to bypass any clunkyness from builtin functions. Some experts posting there that sadly haven't been seen here in ages :/

Hornblower
2016-Oct-19, 10:43 PM
This one (https://forum.cosmoquest.org/showthread.php?34341-Why-are-high-mass-stars-are-so-luminous)? Use google with "site:cosmoquest.org" to bypass any clunkyness from builtin functions. Some experts posting there that sadly haven't been seen here in ages :/

Yes, that's it. Thanks for the search tip.

Ken G
2016-Oct-19, 11:28 PM
That thread was more than a decade ago. Just for fun, let's try the google search again, and see if anything has changed. I'm not optimistic! I will google "explanation of the mass-luminosity relation" and see what I get. (Wikipedia always had it essentially right, so I'm going to skip that one, and consider every other one, in order, that I find that actually does offer an explanation and not just an assertion of the relation):
1) http://www.astronomynotes.com/starsun/s8.htm
"Massive stars have greater gravitational compression in their cores because of the larger weight of the overlying layers than that found in low-mass stars. The massive stars need greater thermal and radiation pressure pushing outward to balance the greater gravitational compression. The greater thermal pressure is provided by the higher temperatures in the massive star's core than those found in low-mass stars. Massive stars need higher core temperatures to be stable!"

Nope, strike one. I don't think this one has changed at all from 10 years go. What's wrong just stays wrong, apparently. Continuing:

2) https://www.e-education.psu.edu/astro801/content/l7_p3.html
"Since higher mass means a larger gravitational force, higher mass must also mean that higher pressure is required to maintain equilibrium. If you increase the pressure inside a star, the temperature will also increase. So, the cores of massive stars have significantly higher temperatures than the cores of Sun-like stars. At higher temperatures, the nuclear fusion reactions generate energy much faster, so the hotter the core, the more luminous the star."
Yuck, strike two.

Actually it's hard to find a third one, I had to go to the third page and there was an advanced astronomy course from Cambridge that did a careful calculation and is going to be correct. But if I search instead on "why are high mass stars so luminous", I quickly find:

3)http://www.astronomy.ohio-state.edu/~ryden/ast162_4/notes14.html
"Consider taking a star and increasing its mass by pouring a little extra hydrogen gas onto it.

Higher mass leads to
Higher compression, which leads to
Higher central density and temperature, which leads to
MUCH faster fusion, which leads to
MUCH higher luminosity."

And that's a strikeout. So little improvement in ten years. Heck, I couldn't even get them to fix the Explore encyclopedia. People just seem a lot more willing to write an explanation, than they are committed to checking it!

Reality Check
2016-Oct-19, 11:38 PM
Certainly not, ...!
I am certainly not going to believe in a stream of unsupported assertions form an unknown forum poster!

ETA: I will believe what astronomers teach at university, e.g. Mass-Luminosity Relation Explained (http://www.astronomynotes.com/starsun/s8.htm)

Reality Check
2016-Oct-19, 11:48 PM
Credible sources:
The Mass-Luminosity Relationship by John A Dutton, Penn State University (https://www.e-education.psu.edu/astro801/content/l7_p3.html)

Given our theory for the structure of stars, you can understand where this relationship comes from. Stars on the Main Sequence must be using the energy generated via nuclear fusion in their cores to create hydrostatic equilibrium. The condition of hydrostatic equilibrium is that the pressure is balancing gravity. Since higher mass means a larger gravitational force, higher mass must also mean that higher pressure is required to maintain equilibrium. If you increase the pressure inside a star, the temperature will also increase. So, the cores of massive stars have significantly higher temperatures than the cores of Sun-like stars. At higher temperatures, the nuclear fusion reactions generate energy much faster, so the hotter the core, the more luminous the star.

THE MAIN SEQUENCE - Astronomy 162: Professor Barbara Ryden - Lecture notes (http://www.astronomy.ohio-state.edu/~ryden/ast162_4/notes14.html)

(1) A main sequence star is powered by fusion of hydrogen into helium in its core.
Consider taking a star and increasing its mass by pouring a little extra hydrogen gas onto it.
• Higher mass leads to
• Higher compression, which leads to
• Higher central density and temperature, which leads to
• MUCH faster fusion, which leads to
• MUCH higher luminosity.
Because of the extremely sensitive dependence of the fusion rate on temperature, a small change in mass leads to a small change in the central temperature, but a very large change in the luminosity.


Back to Basics: The Mass – Luminosity Relation in Main Sequence Stars (https://tallbloke.wordpress.com/2012/05/20/back-to-basics-the-mass-luminosity-relation-in-main-sequence-stars/) emphasizes that this is also a empirical relationship, .e. supported by observations.

Given our theory for the structure of stars, you can understand where this relationship comes from. Stars on the Main Sequence must be using the energy generated via nuclear fusion in their cores to create hydrostatic equilibrium. The condition of hydrostatic equilibrium is that the pressure is balancing gravity. Since higher mass means a larger gravitational force, higher mass must also mean that higher pressure is required to maintain equilibrium. If you increase the pressure inside a star, the temperature will also increase. So, the cores of massive stars have significantly higher temperatures than the cores of Sun-like stars. At higher temperatures, the nuclear fusion reactions generate energy much faster, so the hotter the core, the more luminous the star.

Ken G
2016-Oct-20, 12:26 AM
I am certainly not going to believe in a stream of unsupported assertions form an unknown forum poster!

ETA: I will believe what astronomers teach at university, e.g. Mass-Luminosity Relation Explained (http://www.astronomynotes.com/starsun/s8.htm)Well, are you willing to do the teeny bit of research necessary to understand the virial theorem? Or, the teeny bit of research necessary to read this thread? Because it's all elementary physics. It might please you to imagine it is "unsupported assertions", but so is anything if you refuse to read.

As for the sources you just quoted, perhaps you missed the entire point of the thread: they are wrong. This is not even controversial, more advanced sources don't make those silly mistakes. I suppose there is a kind of sense that if an explanation is being given to non-science students who are probably not going to understand it anyway, then it doesn't matter what baloney you tell them, but I think one can give a simplified explanation without completely replacing it with hooey.

Reality Check
2016-Oct-20, 02:53 AM
Well, are you willing to do the teeny bit of research necessary to understand the virial theorem?
Did that about 30 years ago and refreshed my memory many times since then.

Are you willing to try to read and understand the Mass-Luminosity Relation and its derivation (https://en.wikipedia.org/wiki/Mass%E2%80%93luminosity_relation)? Because the derivation is all elementary physics.+

Are you willing to cite the scientific literature that shows that the sources are wrong?
The Mass-Luminosity Relationship by John A Dutton, Penn State University (https://www.e-education.psu.edu/astro801/content/l7_p3.html)
THE MAIN SEQUENCE - Astronomy 162: Professor Barbara Ryden - Lecture notes (http://www.astronomy.ohio-state.edu/~ryden/ast162_4/notes14.html)
Back to Basics: The Mass – Luminosity Relation in Main Sequence Stars (https://tallbloke.wordpress.com/2012/05/20/back-to-basics-the-mass-luminosity-relation-in-main-sequence-stars/)

Reality Check
2016-Oct-20, 03:03 AM
An interesting post from Tim Thompson in the other mass/luminosity thread (https://forum.cosmoquest.org/showthread.php?34341-Why-are-high-mass-stars-are-so-luminous/page2) in 2005:

This obviously has to be true, and as fate would have it, it is true. Massive stars have enormous central pressures, as high as 100,000 times the central pressure of the sun, but only after evolving off the main sequence (which happens more quickly for higher mass). Indeed the central pressure for main sequence massive stars is much lower than I expected, although I'm supposed to know better.

A zero age main sequences (ZAMS) 15 solar mass star has a central temperature about 34,000,000 Kelvins, only about twice that of the sun (15,600,000 Kelvins), and a central density of only 6.3 gm/cm3, far less than the sun (150 gm/cm3). Since the pressure is directly proportional to the density in this case, it will actually be somewhat lower than the sun's central pressure.

However, let that 15 solar mass star hang around for about 10,000,000 years (and remember our sun is about 5,000,000,000 years old), and it starts it's journey off the main sequence. It will take about 2,000,000 years to complete that journey, during which time the density will skyrocket to over 106 gm/cm3, indeed over 107 near the end (Eid, Meyer & The, 2004). That would make the central pressure ~10,000 - 100,000 times the solar central pressure, but with a central temperature above 109 Kelvins, it's no surprise that the pressure has to be that high, to prevent expansion & cooling of the core. But the pressure will not be directly proportional to the density, either, but either to (density)5/3 for degenerate matter, or (density)4/3 for relativistically degenerate matter (An Introduction to the Theory of Stellar Structure and Evolution, Dina Prialnik, Cambridge University Press, 2000, ch. 7).

It was this high temperature, non main sequence case, that I had in mind originally (it did not occur to me that you were talking about main sequencee stars). I also refer the reader to an excellent review of the evolution of high mass stars: The evolution and explosion of massive stars (http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2002RvMP...74.1015W&db_key=AST&d ata_type=HTML&format=&high=4366fa465106188), Reviews of Modern Physics 74: 1015-1071, October 2002. Woosley is especially into massive stars, and a search of the ADS on his name as author will reveal quite a bit of work on massive stars. The RMP paper goes as high as 75 solar masses. Eid, Mayer & The stop at 30 solar masses. Prialnik's discussion of density & pressure is easier to follow than some other sources.
Still leaves the question whether the core pressure of main-sequence stars increases with mass open though.

Ken G
2016-Oct-20, 03:18 AM
Still leaves the question whether the core pressure of main-sequence stars increases with mass open though.
Ya think? Because I can do simple multiplication, so I can see that the post you cited gives us the wherewithal to compute the core pressure! That very post says the core density is some 25 times lower, with a T only about a factor of 2 higher, so when it says the core pressure is "somewhat lower", it really means it is lower by more than an order of magnitude! Now, everyone remotely connected with stellar astronomy research knows that high-mass main-sequence stars have low core pressure. It's a silly mistake in those sources you (and I, above) cited, this is not the least bit controversial. You should have listened to Hornblower, he tried to save you from this futile line of inquiry. The arguments in those websites are complete bunk, and obviously so.

Should we be hard on those teachers? No, no one can be expected to research everything they say, especially if they are simply repeating it from some other respected source. Which was exactly my reason for trying to get some of those respected sources fixed. Did I succeed? No, I had a direct email exchange with the author of the Explore encyclopedia but that person was too busy with other projects to effect the change. Disappointing, but understandable-- no one is paying him to update the encyclopedia, nor did I offer to do so. I'm sure I've taught wrong things before myself, all we can do is try to be made aware when we are wrong, so we can get it right in future. This turns out to be harder in practice than one might hope.

Reality Check
2016-Oct-20, 03:40 AM
..., everyone remotely connected with stellar astronomy research knows that high-mass main-sequence stars have low core pressure.
Everyone remotely connected with stellar astronomy research (like me!) can understand that this has nothing to do with any variation of core pressure of main-sequence stars with mass.
The interesting post by Tim Thompson (https://forum.cosmoquest.org/showthread.php?34341-Why-are-high-mass-stars-are-so-luminous/page2) was that high-mass main-sequence stars when they form have a core pressure that is "somewhat lower" than in the Sun. 10 billion years they start to leave the main sequence and have an unstated core pressure. After they leave the main sequence, that pressure grows to "~10,000 - 100,000 times the solar central pressure".

Thus: Still leaves the question whether the core pressure of main-sequence stars increases with mass open though.

And you did not answer my question so:
20 October 2016 Ken G: Please cite the scientific literature that shows that the sources are wrong with their "more mass = more core pressure/temperature/density = more fusion = more photons = higher luminosity" chain of physics.

Ken G
2016-Oct-20, 03:52 AM
Everyone remotely connected with stellar astronomy research (like me!) can understand that this has nothing to do with any variation of core pressure of main-sequence stars with mass.If you do research involving stars, I'd say it's high time that you learned some very basic truths about them. Starting with the fact that high-mass main-sequence stars are low density, low pressure objects. Goodness, how can you think you understand the first thing about how they evolve if you don't even know that?

The interesting post by Tim Thompson (https://forum.cosmoquest.org/showthread.php?34341-Why-are-high-mass-stars-are-so-luminous/page2) was that high-mass main-sequence stars when they form have a core pressure that is "somewhat lower" than in the Sun.Now try plugging the numbers in, as I did just above, rather than relying on a vague sense of what it means to be "somewhat lower"!


20 October 2016 Ken G: Please cite the scientific literature that shows that the sources are wrong with their "more mass = more core pressure/temperature/density = more fusion = more photons = higher luminosity" chain of physics.Even the Wikipedia entry on main-sequence stars describes that quite clearly. Or any randomly chosen graduate-level stellar interiors text.

slang
2016-Oct-20, 11:04 AM
Not sure what happened with that post, but it won't let me edit it at the moment.

It seems there is a problem in vBulleting when mixing LIST and QUOTE tags, you quotes a LIST structure posted by mr. Check, and broke up the list tag with quote start and quote end tags. Apparently the software doesnt like it when there happen to be LIST items in there. I think I fixed your post correctly, at least you should be able to edit it again if I made any mistakes in attributing quotes.

Ken G
2016-Oct-20, 12:36 PM
It seems there is a problem in vBulleting when mixing LIST and QUOTE tags, you quotes a LIST structure posted by mr. Check, and broke up the list tag with quote start and quote end tags. Apparently the software doesnt like it when there happen to be LIST items in there. I think I fixed your post correctly, at least you should be able to edit it again if I made any mistakes in attributing quotes.
Yes, you fixed it, thanks!

Swift
2016-Oct-20, 05:06 PM
I'm wondering what is the method for correcting errors in the "Explore" encylopedia that this forum links to? There are a number of misconceptions about stars that are propagated there (some really blatant, such as it claims that the pressure inside stars increases as the mass of a main-sequence star increases, and that light pressure is what balances gravity). Is there some Wiki-like mechanism for fixing those?
Given that this thread has long morphed from its original intent (quoted above) to a debate about the astronomy itself, it is moved from Feedback to Astronomy.

I also suggest that the participants back off from some of the snippy comments I've seen. Snippiness leads to anger, anger leads to rudeness, rudeness leads to infractions.

Hornblower
2016-Oct-20, 05:11 PM
Ya think? Because I can do simple multiplication, so I can see that the post you cited gives us the wherewithal to compute the core pressure! That very post says the core density is some 25 times lower, with a T only about a factor of 2 higher, so when it says the core pressure is "somewhat lower", it really means it is lower by more than an order of magnitude! Now, everyone remotely connected with stellar astronomy research knows that high-mass main-sequence stars have low core pressure. It's a silly mistake in those sources you (and I, above) cited, this is not the least bit controversial. You should have listened to Hornblower, he tried to save you from this futile line of inquiry. The arguments in those websites are complete bunk, and obviously so.

Should we be hard on those teachers? No, no one can be expected to research everything they say, especially if they are simply repeating it from some other respected source. Which was exactly my reason for trying to get some of those respected sources fixed. Did I succeed? No, I had a direct email exchange with the author of the Explore encyclopedia but that person was too busy with other projects to effect the change. Disappointing, but understandable-- no one is paying him to update the encyclopedia, nor did I offer to do so. I'm sure I've taught wrong things before myself, all we can do is try to be made aware when we are wrong, so we can get it right in future. This turns out to be harder in practice than one might hope.

Those who say the greater mass means greater gravitational weight and thus greater internal pressure are missing the effect of the greater radius of the high-mass star. I just did my sanity check again and I stand by my concurrence about lower internal density and pressure in a more massive main sequence star.

For simplicity, let's go back to Eddington's studies that came before hydrogen fusion was even envisioned, let alone confirmed. He knew from observation that a main sequence star with 10 times the Sun's mass also had about 10 times its radius. Let's consider the gravitational weight of, say, the top 1% of the Sun's radius. That weight is determined by the total mass of that layer and the total mass at all lower elevations, with the latter acting on the surface layer as if it were concentrated at the center. The pressure exerted by that top layer is found by dividing the weight by the surface area. That contribution to the internal pressure is transmitted throughout the Sun. The contribution from successive layers below there can be determined accordingly, and a rough-and-dirty integration gives us the pressure at the core.

Now let us increase the mass tenfold while keeping the radius the same, doing hypothetically whatever is needed to keep it stable. It is still virtually an ideal gas, so I expect the density and pressure gradient to be unchanged. Now the top 1% will have 10 times the mass and be acted on by the gravitational action of 10 times as much interior mass, giving us a 100-fold increase in gravitational weight and thus pressure. Integrating to the center will give us 100 times as much center pressure.

So far, so good. Now let's expand that heavyweight by a factor of 10, again changing whatever parameter is needed to stabilize it. The top 1% still has 10 times the mass of the Sun's corresponding layer, but at 10 times the distance from the center the gravitational weight is down 100-fold, and is spread out over 100 times the area. Thus that contribution to the pressure is down 10,000-fold, or 1/100 of the corresponding component in the Sun.

There we have it. Eddington's model of the 10 solar mass star has 10 times the radius, 1,000 times the volume, and thus 1/100 of the density of the Sun at any given percentage of the distance from the center to the photosphere. We just showed that the corresponding pressure is also down by a factor of 100. From the gas law equation it follows that the internal temperature should be about the same in the two stars. The much higher surface temperature and vastly greater luminosity are the result of the faster heat loss through the more tenuous envelope, and reportedly is in good agreement with what Eddington calculated for gases at various densities. Ken G described the process of reaching a quasi-stable equilibrium at length in the old thread, so I will not bother with it here. When we add fusion to the mix, we are just adding a low intensity heating action that should not affect the internal density profile much but will balance the heat loss and keep the star really stable for a very long time.

Suppose the high mass star had just formed and the fusion rate for the moment was no greater than in the Sun. That would not yet balance the rapid heat loss in the more rarefied envelope. We see that heat loss as high luminosity. That heat loss temporarily keeps the interior temperature and thus pressure lower than is needed for stability at that radius. Thus the gravitational contraction continues, the temperature rises despite the heat loss which slows down as the envelope becomes more opaque, and eventually the fusion is fired up enough to stabilize things. That is what Ken G means in his simplified statement "the fusion rate is a consequence of the luminosity." The dynamics of the star are such that it eases into a steady state instead of pulsating the way a home heating system does when operated by a conventional thermostat. The star is its own ideal thermostat.

Ken G
2016-Oct-20, 05:16 PM
Yup, you got it, hands down. Now that you know, beware-- you will have a hard time reading a lot of introductory "explanations" about how main-sequence stars work!

Hornblower
2016-Oct-20, 06:55 PM
Addendum: I assumed that the density and pressure gradients are the same percentage-wise in the two stars as we go from the surface to the center. With ideal gases of uniform composition, from what little bit I know about the virial theorem I think I am on the right track there.

My guess is that the popular media and low-level textbook writers were confused by evolved giants, in which astrophysicists have inferred enormously denser and hotter cores. The internal dynamics are much more complicated here, and are the result of lack of convection in the inner parts of a solar mass star, resulting in exhaustion of hydrogen in the center while there is still plenty in the surrounding layers. Here is what I imagine as happening. With no more fusion in the innermost core, gravitational contraction resumes, raising the temperature sharply. This causes the envelope to expand and also jacks up the fusion which is still happening in the outer parts of the core. The envelope becomes more leaky, raising the luminosity drastically. When the contracting inner core gets hot enough, helium fusion sets in, restoring the stability and stopping the production of heat from contraction. This lets the envelope contract and become less luminous though still more so than in the main sequence stage.

In an M type such as Proxima Centauri, astrophysicists have concluded that the star is convective throughout because of the greater opacity of its dense envelope. The helium "ash" is mixed throughout the star instead of remaining at the center. As a result, the star will never go through an evolving giant stage, but rather will gradually contract while becoming hotter and more luminous at the photosphere as its mass is concentrated into fewer and fewer atoms. When the hydrogen is exhausted the contraction will continue a while longer until electron degeneracy is reached throughout, with the result being a low mass white dwarf. Ref. Sky and Telescope, Nov. 1997, p. 20.

Ken G
2016-Oct-20, 07:20 PM
Addendum: I assumed that the density and pressure gradients are the same percentage-wise in the two stars as we go from the surface to the center. With ideal gases of uniform composition, from what little bit I know about the virial theorem I think I am on the right track there. Yes, that is a common tactic used in physics, called a "scaling argument", or more technically, "homology classes." We treat a set of objects with some controlled difference, in this case mass, as if they were homologous structures, only differing by an overall scale factor. If the physics of the object fundamentally changes as we vary the control parameter, this won't work, but we do it an awful lot in physics, because we find that oftentimes, there is not a fundamental change in the physics with scale-- at least not to a level of approximation useful for pedagogical understanding. In this example, it amounts to treating a main-sequence star as "all one thing", with a mass M and radius R and core temperature T, and everything just tracks the scale changes as one varies M. In actual practice, we have things like varying degrees of convection, relative core size, gradual depletion of hydrogen, and other possible effects like rotation and magnetic fields that could vary as well, but since our goal is simple understanding, we set aside those details and just focus on the scaling arguments. This is routine in all elementary explanations of anything.


My guess is that the popular media and low-level textbook writers were confused by evolved giants, in which astrophysicists have inferred enormously denser and hotter cores. I wouldn't be so generous-- they must know that giants have degenerate cores, and are nothing at all like main-sequence stars. For one thing, a giant star is a case where you definitely cannot get away with imagining the object is "all one thing"-- it is very clearly two very different things, a degenerate core living inside a convective envelope, separated by a shell of fusion. The degenerate core and the fusion shell surrounding it determine the properties of the convective envelope, producing the red giant phenomenon in ways that are vastly different from a main-sequence star. In fact, it's best to think of a red giant as being like a white dwarf living inside a bloated protostar, where the luminosity of the protostar is not set by its history of contraction and gravitational energy release, but rather by that all-important fusion engine buried so deeply inside it. But that's another thread and another myth (the myth that red giants are not straightforward to understand).


With no more fusion in the innermost core, gravitational contraction resumes, raising the temperature sharply. This causes the envelope to expand and also jacks up the fusion which is still happening in the outer parts of the core.Yes.

The envelope becomes more leaky, raising the luminosity drastically. Again correct, the only additional important factor is that the fusion in the core self-regulates the structure of the envelope to set the luminosity, whereas in main-sequence stars the luminosity is already set because the star is not undergoing the huge puffing out of a giant. The giant puffs out until its luminosity matches what the shell produces, as the production by the shell is reduced by the lowering of the weight of the bloating envelope. They reach a meeting of the ways-- the shell fusion starts out insanely high, producing plenty of heat to puff out the envelope, but as the envelope puffs out, it dials down the fusion rate until the fusion rate balances the luminosity that is escaping the shell. The envelope is very efficient at convecting away heat, so its size is set at first by its need to take weight off the shell, and later by its need to be fully convective and reach a surface temperature similar to fully convective protostars (i.e., "red").


When the contracting inner core gets hot enough, helium fusion sets in, restoring the stability and stopping the production of heat from contraction. This lets the envelope contract and become less luminous though still more so than in the main sequence stage.Yes, and what separates those behaviors is the short-lived unstable "helium flash." But that's another thread, and yes, another myth!


In an M type such as Proxima Centauri, astrophysicists have concluded that the star is convective throughout because of the greater opacity of its dense envelope. The helium "ash" is mixed throughout the star instead of remaining at the center. As a result, the star will never go through an evolving giant stage, but rather will gradually contract while becoming hotter and more luminous at the photosphere as its mass is concentrated into fewer and fewer atoms. When the hydrogen is exhausted the contraction will continue a while longer until electron degeneracy is reached throughout, with the result being a low mass white dwarf. Ref. Sky and Telescope, Nov. 1997, p. 20.Exactly correct. So when the mass is low enough that degeneracy is important, and the surface temperature is cool enough that convection dominates, we really have a rather different animal, and that's why stars of this type do not go through a pre-main-sequence phase of evolution at constant luminosity as they contract toward the main sequence. They really can't be lumped into the rest of the main sequence stars when you want to understand their luminosity, just as you also cannot include very high-mass main-sequence stars because their structure is regulated by radiation pressure. So this thread is about the bulk of the main sequence, say from 0.5 to 50 solar masses.

Reality Check
2016-Oct-20, 10:51 PM
Even the Wikipedia entry on main-sequence stars describes that quite clearly. Or any randomly chosen graduate-level stellar interiors text.
The Main sequence (https://en.wikipedia.org/wiki/Main_sequence) article does not look in detail at the physics behind the mass-luminosity relation - it just describes it. These is a paragraph about how opacity changes the exponent in the relation.
20 October 2016 Ken G: Please cite the scientific literature that shows that the sources are wrong with their "more mass = more core pressure/temperature/density = more fusion = more photons = higher luminosity" chain of physics (for the mass-luminosity relation). (https://forum.cosmoquest.org/showthread.php?154582-Correcting-errors-in-the-quot-Explore-quot-encyclopedia&p=2374655#post2374655)
Or cite an accessible graduate-level stellar interiors text.

Reality Check
2016-Oct-20, 11:12 PM
My guess is that the popular media and low-level textbook writers were confused by evolved giants, in which astrophysicists have inferred enormously denser and hotter cores.
The popular media and low-level textbooks that I have seen use the mass–luminosity relation (https://en.wikipedia.org/wiki/Mass%E2%80%93luminosity_relation) for main-sequence stars. I suspect they know that evolved giants are not main sequence stars.

When an astronomer writes lecture notes such as (http://www.astronomy.ohio-state.edu/~ryden/ast162_4/notes14.html)

Consider taking a star and increasing its mass by pouring a little extra hydrogen gas onto it.
• Higher mass leads to
• Higher compression, which leads to
• Higher central density and temperature, which leads to
• MUCH faster fusion, which leads to
• MUCH higher luminosity.
Because of the extremely sensitive dependence of the fusion rate on temperature, a small change in mass leads to a small change in the central temperature, but a very large change in the luminosity.
we can trust that they have the physics correct even if simplified.

Reality Check
2016-Oct-20, 11:25 PM
He knew from observation that a main sequence star with 10 times the Sun's mass also had about 10 times its radius...
You need to check this number, Hornblower. That may have been the observation 80 or so years ago but the Main sequence (https://en.wikipedia.org/wiki/Main_sequence#Sample_parameters) (Ken G made me look at it) article lists that a main sequence star with 6.5 times the Sun's mass has about 3.8 times the Sun's radius with an error of 20–30%. The value is 7.4 for 18 solar masses. That suggests a radius of roughly 5 solar radii for a 10 solar mass star.

Ken G
2016-Oct-20, 11:34 PM
The Main sequence (https://en.wikipedia.org/wiki/Main_sequence) article does not look in detail at the physics behind the mass-luminosity relation - it just describes it.Here's how Wikipedia works. If you want to learn about the luminosity of main-sequence stars, you start reading their article about main-sequence stars. Then when they start talking about the luminosity, if they don't give you the information you want, you have to click on the live links that do. In this case, you would actually need to click on the live link called "mass-luminosity relation", since you want to know about mass-luminosity relation.


Or cite an accessible graduate-level stellar interiors text.
Kippenhahn and Wiegert has a nice book, it's very clearly spelled out there. But it's in the Wiki too, as I said.

Ken G
2016-Oct-20, 11:36 PM
You need to check this number, Hornblower. That may have been the observation 80 or so years ago but the Main sequence (https://en.wikipedia.org/wiki/Main_sequence#Sample_parameters) (Ken G made me look at it) article lists that a main sequence star with 6.5 times the Sun's mass has about 3.8 times the Sun's radius with an error of 20–30%. The value is 7.4 for 18 solar masses. That suggests a radius of roughly 5 solar radii for a 10 solar mass star.That's the thing about simple explanations-- they sometimes only get the answer right to a factor of 2, as here. But still, they get the important ideas right, as here. But at least you are starting to look at some numbers, it can't be too long before you realize that high-mass main-sequence stars have low pressure, showing the argument you gave above (which comes from mistaken intro sources) is absolutely wrong. It's a no-brainer. But when something as easy as this is the error, and still has such a hard time being exposed and accepted, one can see the problem with subtler issues.

Reality Check
2016-Oct-20, 11:41 PM
That's the thing about simple explanations-- they sometimes only get the answer right to a factor of 2, as here.
The problem is rather relying on uncited 80 year old observations - they are sometimes wrong and sometimes inaccurate.
That "high-mass main-sequence stars have low pressure" compared to the Sun is irrelevant. What is relevant is that the mainstream position is that the core pressure of stars increases with mass.

Reality Check
2016-Oct-20, 11:49 PM
Kippenhahn and Wiegert has a nice book, it's very clearly spelled out there. But it's in the Wiki too, as I said.
An accessible link to that Kippenhahn and Wiegert book with a citation to where they state that the ""more mass = more core pressure/temperature/density = more fusion = more photons = higher luminosity" chain of physics for the mass-luminosity relation" is wrong?

Where in the Wiki?
No "more mass = more core pressure/temperature/density = more fusion = more photons = higher luminosity" chain of physics for the mass-luminosity relation" in Main sequence (https://en.wikipedia.org/wiki/Main_sequence).
No "more mass = more core pressure/temperature/density = more fusion = more photons = higher luminosity" chain of physics for the mass-luminosity relation" in Mass–luminosity relation (https://en.wikipedia.org/wiki/Mass%E2%80%93luminosity_relation) - not even the word fusion!

Ken G
2016-Oct-21, 12:06 AM
That "high-mass main-sequence stars have low pressure" compared to the Sun is irrelevant. What is relevant is that the mainstream position is that the core pressure of stars increases with mass.I was referring to the characteristic pressure of the star as a whole, which is essentially the same thing as the core pressure if you look at how homology relations (scaling laws) work. There's just too much to explain to you, I have to assume you know some basic physics or it will just take too long. It sounds like you are talking about surface pressure, but no one cares about that. Surface pressure is totally different physics, its scale is given by g/kappa, where g is the surface gravity and kappa is the opacity. That's also low for high-mass stars, but again, not what we are talking about.
Where in the Wiki?To repeat, click on "mass-luminosity relation." You then have to actually look at the mathematical argument there. In it, you will find that P ~ GM2/R4, that gets used in their derivation of the luminosity. To connect R and M, you will note they use the simplified approximation R ~ M, it's right there. The point is, they show how the luminosity is determined, and it has all to do with radiative diffusion, and nothing about fusion. Certainly nothing about the pressure being high! Again: everyone who knows anything about high-mass main-sequence stars knows they have low core pressure.

StupendousMan
2016-Oct-21, 01:32 AM
One good source for information on stellar interiors is a website run by Lionel Siess, a stellar astronomer at the Institute of Astronomy and Astrophysics at the Université Libre de Bruxelles. Here's his main home page's address:

http://www.astro.ulb.ac.be/~siess

Since Dr. Siess has published some 30+ papers in the technical literature as first author, in addition to many as co-author, I think we can accept his work as authoritative. Again, his research area is stellar interiors and evolution.

Now, he provides many very handy tools on his website that visitors can use to generate models of stars of various ages, masses, and chemical compositions. I used this one

http://www.astro.ulb.ac.be/~siess/pmwiki/pmwiki.php/WWWTools/Isochrones

to generate models of stars with various masses (expressed in solar units) on the zero-age main sequence. Here's one portion of the output:



Mass Tc roc etac Menv Renv/R Tenv roenv Lnuc Lgrav k2conv k2rad flag
0.500 8.740E+06 8.238E+01 -0.97 0.3165 0.55869 4.367E+06 1.552E+01 0.6421 0.3572 0.11900 0.06326 0
1.000 1.260E+07 7.180E+01 -1.72 0.9657 0.69330 2.635E+06 3.325E-01 0.6446 0.3552 0.00000 0.08278 0
2.000 1.780E+07 5.072E+01 -2.62 2.0000 0.99779 2.088E+04 1.015E-08 0.5281 0.4719 0.00000 0.03357 0
4.000 2.144E+07 1.933E+01 -3.88 4.0000 0.99631 1.764E+04 1.812E-09 0.5465 0.4535 0.00000 0.04255 0
7.000 2.482E+07 9.680E+00 -4.80 7.0000 0.99226 4.798E+04 1.173E-08 0.6288 0.3714 0.00000 0.05051 0


The important columns are the first three: mass (in solar units), central temperature (Kelvin) and central density (grams per cubic centimeter). Since the central material in these stars is roughly an ideal gas, one can compute the central pressure in an approximate manner by calculating

(central pressure) is proportional to (central temperature) * (central density)

Note that as the mass of a star increases from 0.5 to 7 solar masses, the central temperature goes UP by a factor of about 3, but the central density goes DOWN by a factor of about 8. The result is that the central pressure decreases with mass.

Many thanks to Lionel Siess for providing these tools for all of us, in addition to his many papers!

Ken G
2016-Oct-21, 01:49 AM
Note that as the mass of a star increases from 0.5 to 7 solar masses, the central temperature goes UP by a factor of about 3, but the central density goes DOWN by a factor of about 8. The result is that the central pressure decreases with mass.Yes, and when you go all the way down to 0.5 solar masses, you are starting to get into fully convective stars, which changes the situation because the stellar radius decouples from the central pressure (the star tries to get to a red surface temperature, it's something convection does). So the simple arguments start to break down around that mass (and indeed the core pressure is actually lower for 0.5 solar masses than for the Sun). But if you look from 1 to 7 solar masses, you find the core pressure drops by a factor of almost 5. So claims that 7 solar mass stars are some 500 times more luminous than the Sun because their mass compresses their core to higher pressure is obvious bunk. Yet that is still the argument you will see in most intro sources that give any argument at all, ten years after I first pointed out here just how wrong that is.

Hornblower
2016-Oct-21, 03:13 PM
The popular media and low-level textbooks that I have seen use the mass–luminosity relation (https://en.wikipedia.org/wiki/Mass%E2%80%93luminosity_relation) for main-sequence stars. I suspect they know that evolved giants are not main sequence stars.

When an astronomer writes lecture notes such as (http://www.astronomy.ohio-state.edu/~ryden/ast162_4/notes14.html)

we can trust that they have the physics correct even if simplified.The lecture in question looks like something in a college freshman level course, and in my opinion is incomplete. The lack of any detailed demonstration of the calculus that is needed to calculate the density and pressure gradient in a state of hydrostatic equilibrium makes me infer the low level of the course. In the hypothetical case of piling some more hydrogen onto a star there will initially be higher pressure and compression heating, thus jacking up the fusion rate far higher than it was, but it does not necessarily follow that the star will stay in that higher pressure state. I have concluded from all I have read in this thread and the one from 11 years ago that the star would puff up, core and envelope alike, and after some initial fireworks it would stabilize in an expanded form with lower density and pressure throughout. Radiation from the interior would leak out faster than before, and the star would stabilize at a core temperature that would enable the faster fusion that would balance that heat flow and luminosity.

It is not unheard of for a professor to make mistakes on relatively elementary details when teaching a freshman course. I witnessed it myself when the department chairman, a nuclear physics researcher, appeared to have forgotten some details of billiard ball ballistics in a classical mechanics demonstration. It could happen to anybody.

Ken G
2016-Oct-21, 08:27 PM
It's a lot worse than incomplete, it's pure baloney. Not the whole notes, just this part:
"Consider taking a star and increasing its mass by pouring a little extra hydrogen gas onto it.

Higher mass leads to
Higher compression, which leads to
Higher central density and temperature, which leads to
MUCH faster fusion, which leads to
MUCH higher luminosity."
That's wrong. As you said, if you add mass to the Sun, it will ultimately expand slightly and lower its pressure, but the luminosity will indeed go up.

StupendousMan
2016-Oct-22, 12:36 PM
Have you considered writing to Barbara to point out the mistake in her notes? I appreciate it when people let me know I've made an error -- it allows me to fix it for the next time I teach the course.

It's easy enough to fix: just remove the phrase "central density and", so that the third line reads "Higher temperature, which leads to".

The benefits are several:
- it reflects reality accurately
- students have one fewer link in a chain of reasoning to memorize for the test

Ken G
2016-Oct-22, 02:29 PM
Have you considered writing to Barbara to point out the mistake in her notes? I appreciate it when people let me know I've made an error -- it allows me to fix it for the next time I teach the course.I was hoping to put out a paper that corrected it, so I wouldn't have to write to every author. I've seen the wrong argument in a dozen books and a dozen online course notes!


It's easy enough to fix: just remove the phrase "central density and", so that the third line reads "Higher temperature, which leads to".That wouldn't fix it, there are many other parts of that argument that are wrong. Certainly the "more compression" has to go too, because that is not the reason the temperature would end up higher. If you added mass to the Sun, you'd get some compression early on, but this would not matter at all in how things ultimately shake out. The initial compression would lead to too high of a temperature, causing too much fusion, causing the star to expand even more than it compressed. There's no way to know whether the core will end up with higher or lower temperature until you look at the radiative diffusion through the lower density, larger radius star, and only when you look at the radiative diffusion can you understand that the higher mass must lead to higher luminosity. The core temperature responds to that, which is the only reason it ends up higher-- it has nothing to do with "more compression," so that part has to go also.

We do want to keep things as simple as possible, but we must retain the core truth of the situation! What is much closer to the truth is that the core heats up because the star as a whole expands. Any explanation missing that crucial element promotes incorrect intuition about stars. A main-sequence star is a big leaky bucket of light, and its luminosity depends only how how big and leaky is that bucket. If one is missing radiative diffusion in the explanation, one has missed the explanation. Fusion physics is almost irrelevant, so deserves no place in the simplest explanation!

StupendousMan
2016-Oct-22, 10:57 PM
You hand me a main-sequence star of mass M and luminosity L. I'll dump a small amount of mass dm onto it. I maintain that after a few tens of thousands of years, we'll end up with a main sequence star of higher mass (M + dm) [yes, I know that a tiny fraction of this will be turned into radiation and emitted by the star; so we can pick dm large enough to make the final mass still larger than the initial mass], and the final star will have

a) a higher central temperature
b) a higher luminosity

Do we disagree on these points?

Ken G
2016-Oct-22, 11:24 PM
No disagreement there, as that much is given by the mass-luminosity relation itself. But what we seek is the proper explanation for it. The point is that it will not be "more compressed," it will be less compressed. So the rise in core T has nothing to do with compression, the T rise comes from the fusion self-regulation to replace the rise in the luminosity that comes from more light diffusing out of the bigger leakier bucket. There is not even a hint of this correct explanation in the story given in the various books and websites being critiqued, such as the account by Ryden.

To see this, it is informative to consider what would have happened had we added that dm prior to fusion onset in the first place. Take the Sun back in time, just prior to fusion, and then add dm. Notice first of all that the luminosity of that Sun is quite similar to the current Sun-- fusion onset has little effect on luminosity, it only causes a small restructuring of the star and a small change in luminosity as a result. Also, the effect on L of adding dm will also be quite similar. So we can understand both versions of dL/dm in the same stroke-- all that is happening is, adding mass converts the Sun into a bucket that leaks more light (remarkably, the rate the bucket leaks light has almost no dependence on its core temperature!). Either way, when you add dm, whether you get a short-term expansion or contraction depends on if you add the dm very cold or very hot, so the initial behavior is of no consequence. What matters is the ultimate force balance and the radiative diffusion it supports, and in either case that will make for a similar increase dL. Ergo, a correct explanation for dL/dm is all about radiative diffusion, and doesn't even mention fusion. Fusion only matters if you want to know the self-regulated core temperature that will result, so dT/dm, which also has nothing to do with compression because there will actually be expansion there. The Ryden account strongly suggests that the energy needed for the dT in the core comes from compression work, but that is also wrong-- the needed energy comes from fusion, and some of it goes into expansion work! It just couldn't be more wrong, it is being judged purely on getting a positive dL/dm, but that's not good enough to count in scientific logic.

Reality Check
2016-Oct-25, 08:11 PM
One good source for information on stellar interiors is a website run by Lionel Siess, a stellar astronomer at the Institute of Astronomy and Astrophysics at the Université Libre de Bruxelles. Here's his main home page's address:

http://www.astro.ulb.ac.be/~siess

Thanks for the source, StupendousMan.
So it looks like sources that attribute increased luminosity to just increased pressure are stating "lies to children (https://en.wikipedia.org/wiki/Lie-to-children)" when it should be temperature and density.
THE MAIN SEQUENCE - Astronomy 162: Professor Barbara Ryden (http://www.astronomy.ohio-state.edu/~ryden/ast162_4/notes14.html) says "Higher central density and temperature".

The Mass-Luminosity Relationship by John A Dutton, Penn State University (https://www.e-education.psu.edu/astro801/content/l7_p3.html) and Back to Basics: The Mass – Luminosity Relation in Main Sequence Stars (https://tallbloke.wordpress.com/2012/05/20/back-to-basics-the-mass-luminosity-relation-in-main-sequence-stars/) have the same text attributing the increase in fusion to temperature increase.

Reality Check
2016-Oct-25, 08:18 PM
The lecture in question looks like something in a college freshman level course, and in my opinion is incomplete.
Of course it is incomplete - they are lecture notes for undergraduate students :D! The details will be in the lecture itself and the recommended textbooks. But the notes are correct in that higher mass leads to "Higher central density and temperature" thus more fusion and higher luminosity.

Reality Check
2016-Oct-25, 08:37 PM
That's wrong. As you said, if you add mass to the Sun, it will ultimately expand slightly and lower its pressure, but the luminosity will indeed go up
That is correct physics incorrectly stated as shown by StupendousMan's source. Run stellar modes for higher mass and:

Higher mass leads to
Higher [gravity] compression, which leads to
Higher central density and temperature, which leads to

Emphasize that the compression is not thermal pressure, remove density. Then nuclear physics gives us

MUCH faster fusion, which leads to
MUCH higher luminosity

since the rate of nuclear fusion is sensitive to temperature: Astronomy notes: Hydrostatic Equilibrium Controls the Reaction Rates (http://www.astronomynotes.com/starsun/s3.htm)

Hydrostatic equilibrium is the balance between the thermal pressures from the heat source pushing outwards and gravity trying to make the star collapse to the very center. I will discuss hydrostatic equilibrium in more depth (no pun intended) in a later section. The nuclear fusion rate is very sensitive to temperature. It increases as roughly temperature4 for the proton-proton chain and even more sharply (temperature15) for the Carbon-Nitrogen-Oxygen chain. So a slight increase in the temperature causes the fusion rate to increase by a large amount and a slight decrease in the temperature causes a large decrease in the fusion rate.
Now suppose the nuclear fusion rate speeds up for some reason. Then the following sequence of events would happen: 1) the thermal pressure would increase causing the star to expand; 2) the star would expand to a new point where gravity would balance the thermal pressure; 3) but the expansion would lower the temperature in the core---the nuclear fusion rate would slow down; 4) the thermal pressure would then drop and the star would shrink; 5) the temperature would rise again and the nuclear fusion rate would increase. Stability would be re-established between the nuclear reaction rates and the gravity compression.


ETA: Astronomy notes: Mass-Luminosity Relation Explained (http://www.astronomynotes.com/starsun/s8.htm) has the physics stated correctly (gravity compression -> higher temperature-> more fusion-> higher luminosity).

Ken G
2016-Oct-26, 03:31 AM
Ok, this is just one more time for those who can actually understand it: the explanation for why the Sun's luminosity would ultimately rise if mass were added to it has nothing, zilch, squat to do with compression. In fact, there would not even be compression, there would be expansion. There is not a single shred of that explanation you just gave that is even remotely correct. It's not even true that the luminosity rises because the core temperature goes up, what is true is that the core temperature goes up because the luminosity rises (and fusion self-regulates, a well-known aspect of fusion). Yes I know that surprises you, that's the point, physics can be interesting. It's all in the very simple mathematical arguments presented above-- nothing beyond sophomore physics.

What's a bit more subtle is that the increase in luminosity has almost nothing to do with fusion, only the self-regulation of the core temperature depends on fusion. That luminosity increase does not depend on fusion is obvious from the fact that Eddington, Henyey, and Russell all would have had no trouble understanding why adding mass to the Sun would increase its luminosity-- before any of them even knew there was any such thing as fusion. That is a fact, like it or not. So a correct explanation mentions neither compression, nor fusion. I strongly suspect you will not understand this, but I cannot make you understand because all I know how to use is the actual laws of physics, not misinformed websites that make blatant errors I can prove wrong in two lines of mathematics.

Reality Check
2016-Oct-27, 09:46 PM
Ok, this is just one more time for those who can actually understand it: the explanation for why the Sun's luminosity would ultimately rise if mass were added to it has nothing, zilch, squat to do with compression. ...
Obviously wrong

Without gravity compressing the Sun's plasma the Sun would not exist :D!
The photons and thus luminosity of stars comes from fusion.
Thus any increase in luminosity has to come from an increase in fusion - with some modification because of optical opacity.
That people did not know that luminosity originates with fusion before fusion was discovered is irrelevant.
Luminosity cannot increase just because you say that it increases.
There has to be a physical reason for the increase.

The explanation in the lecture notes was a bit wrong. Add mass to a star and

The additional mass leads to more gravitational compression.
More gravitational compression leads to higher central temperature.
Higher central temperature leads to more fusion.
More fusion = higher luminosity.

See Astronomy notes: Mass-Luminosity Relation Explained (http://www.astronomynotes.com/starsun/s8.htm)

Massive stars have greater gravitational compression in their cores because of the larger weight of the overlying layers than that found in low-mass stars. The massive stars need greater thermal and radiation pressure pushing outward to balance the greater gravitational compression. The greater thermal pressure is provided by the higher temperatures in the massive star's core than those found in low-mass stars. Massive stars need higher core temperatures to be stable!

ETA: Mass–luminosity relation (https://en.wikipedia.org/wiki/Mass%E2%80%93luminosity_relation) has a derivation that it says is similar to Eddington's. This starts with assuming that stars are black body radiators, i.e. there is a relationship between L and T no matter what the source of T is. We could have a absurdly unphysical scenario where stars burn coal and still be able to use that relationship. In the real world T comes from fusion.

Ken G
2016-Oct-28, 12:32 AM
Obviously wrongWhat part of this true statement:
Adding mass to the Sun would ultimately cause every layer in the Sun to expand
are you not getting? There cannot be any doubt the statement is true, that's what the models quoted above were supposed to be telling you.
Without gravity compressing the Sun's plasma the Sun would not exist Oh I see the problem, you don't understand the difference between the words "gravity" and "compression." When people refer to "gravity", they mean that which is responsible for the past compression of the Sun, but when they say adding mass will cause "greater compression", that means they are claiming the volume of the Sun will drop, or at least the density will rise-- that's what "greater compression" actually means, but neither happens here. "Gravity", on the other hand, does not require that the volume of the Sun must drop when mass is added-- it just doesn't mean that, but one does have to understand the equations of physics. So when I said the explanation has nothing to do with compression, I did not say it had nothing to do with gravity. If you cannot parse the difference in the meanings of those two words, of course you will not understand. Hence, my explanation is only designed for people who do understand that a system can expand, yet still experience gravity, and that this is different from a system that compresses, and experiences gravity.
The explanation in the lecture notes was a bit wrong. Add mass to a star and
The additional mass leads to more gravitational compression.
More gravitational compression leads to higher central temperature.
Higher central temperature leads to more fusion.
More fusion = higher luminosity.Again, this is to those people who understand the meaning of words like "gravity" and "more compression":
Let there be no doubt, the above explanation is completely and utterly false. There is not one step in the logic that is actually correct. First, it is wrong to say that additional mass leads to compression. Whether it initially leads to compression or expansion depends on the temperature of the mass that is added, which is, quite fortunately, completely irrelevant to what will ultimately happen to the star that has had mass added to it. The explanation we desire is about what will ultimately happen to the Sun, once it reaches a new thermal equilibrium, after mass has been added to it, and the answer is that the Sun will have expanded, and its gravity will be lower. This is just a fact. I completely understand why this is true, how it involves fusion, and why the luminosity of the Sun would rise whether it was undergoing fusion or not. The completely wrong explanation you just gave, by contrast, implies the following falsehoods:
1) adding mass will ultimately cause "more compression" of the Sun (wrong, it will ultimately cause expansion)
2) gravitational energy release will be responsible for raising the core temperature (wrong, fusion will do that, gravity will eat up some of the energy)
3) the higher fusion rate from the higher core temperature results in a higher luminosity (wrong, the higher luminosity has nothing to do with fusion, it comes from radiative diffusion, which is what Eddington also understood. The higher fusion rate is a result of the higher luminosity, not the other way around.)

So the wrong explanation contains no less that three completely false implications, in only four lines, which is a pretty impressive standard of baloney. This comes down to whether or not the reader wishes to actually understand stars. I think most want that, and hopefully most now do understand. But as long as they think any shred of that wrong explanation is actually a correct way to understand the mass-luminosity relation, then they cannot understand even the first thing about how stars work. Pity that this misinformation is so widespread, but you will only find that wrong explanation in introductory textbooks intended for non-astronomers. Any graduate-level text will get it right, you won't see anything like that wrong explanation in a real book about stars. Trust me, this is just a fact, though you are of course welcome to look for yourself if you do have access to any real books about stars.

Ken G
2016-Oct-28, 03:16 AM
This in particular is worthy of additional lambasting, not for Reality Check who is merely the messenger of false tidings here, but for the original website:

See Astronomy notes: Mass-Luminosity Relation Explained (www.astronomynotes.com/starsun/s8.htm):
"Massive stars have greater gravitational compression in their cores because of the larger weight of the overlying layers than that found in low-mass stars. The massive stars need greater thermal and radiation pressure pushing outward to balance the greater gravitational compression. "
What unadulterated baloney, this is the point I'm making-- this type of information is just complete garbage. I hope no one is paying "astronomynotes.com" for drivel like this! It's obviously wrong, one only needs first-year physics for this one. But for those who don't want to follow the physics derivation, simply consult the Seiss models above, and notice that it is just completely wrong to claim that high-mass stars have envelopes with greater weight. If that were true, their core pressures would be higher, but they are lower. So when I say "wrong", I mean "the opposite of right"!

These are not idle details, there are physics lessons here. One of the most important things to know about weight is that it does not depend only on mass, but also on radius. High-mass main-sequence stars have larger radii, and are low-density, weak-gravity, and lighter envelope objects! The simple physical reason for this is they do not need to compress as much to reach fusion temperatures, owing to their higher mass, so you should think of them as low compression objects, not high compression objects! Sheesh, you really have to step carefully through the minefields of poor information out there. Now, should cosmoquest call it "against the mainstream" for us to require that the "mainstream" actually hold true to simple first-year physics? I think not, and I'm glad the moderators appear to agree.

Hornblower
2016-Oct-28, 03:29 PM
Reality Check can keep repeating his argument and referring to bad sources until doomsday and it will not shake my confidence in my opinion that Ken G is on the right track, or in my own sanity checks. Having said that, in all fairness to Reality Check and any lurkers out there, I still find some of Ken's simplified presentations to be potentially problematical, as opposed to his more detailed work in this thread and in the old one from 11 years ago. To be specific:

1. Fusion rate is a consequence of luminosity, not vice versa.

A novice could ask, "How could that be? The high luminosity means more radiant energy going out, not in. How does that heat the core and cause more fusion?" I understand the causality chain that appears in a more detailed explanation, but a college freshman with just some entry level physics at that point might be lost initially.

2. This has nothing to do with compression.

If in a thought experiment we pile some more hydrogen onto a previously stable star, the initial heating is very much caused by what I would call compression. The added weight squeezes what is under it and raises the temperature by doing work on the gas molecules. The fact that the star would stabilize in a more rarefied state than that it was in before adding the mass does not mean that no compression ever took place.

I would say that we need the detailed explanations to do a satisfactory job of debunking the bad sources.

Ken G
2016-Oct-28, 04:01 PM
Yes, one must marvel at a form of logic that responds to "isn't it amazing that all these websites have it wrong, and here's why they have it wrong," with "you are wrong, here's a bunch of websites that you are contradicting."

Ken G
2016-Oct-28, 11:56 PM
If in a thought experiment we pile some more hydrogen onto a previously stable star, the initial heating is very much caused by what I would call compression.Ah, but that's not at all necessary, you are making assumptions about both the temperature of the gas being added (that it is lower than the average temperature of the gas in the Sun now), and about the rate that it is being added (suddenly, rather than gradually). If I suddenly add mass at a temperature of 100 million K to the core of the Sun, you can be sure there will be no compression at all, there will only be expansion. But the net result will still be just the same-- the star will settle down to the same expanded state, regardless of the temperature I added. It's only that final state we are trying to understand, not the arbitrary intermediate states that lead there, which we cannot even know without saying more about how the mass is added. What's more, if the mass is added gradually, say by a real accretion process, there would also never be any compression-- only steady expansion. So compression is a total red herring, it should never be mentioned at all.

The fact that the star would stabilize in a more rarefied state than that it was in before adding the mass does not mean that no compression ever took place.More to the point, it also doesn't mean there ever needed to be any compression! Ergo, it deserves no place in the explanation of the result. Explanations are about what is required to happen, not what might or might not happen in irrelevant transient phases of certain special versions of the story. Worse, saying that the luminosity grows due to compression carries utterly wrong implications, as you know, and that's the real problem there. We are trying to use the explanation to train correct intuition, not ruin any chance of correct intuition, which is the result we have seen on Reality Check. His participation in the thread is crucial-- it demonstrates the harm.

Hornblower
2016-Oct-29, 03:03 AM
I see your point now. With a trickle of accreting gas as in a mass-exchanging binary such as Algol, the gravitationally acquired kinetic energy of the infalling gas becomes heat, with the dynamics being such that expansion occurs throughout the star.

AFJ
2016-Oct-30, 06:30 PM
I have no substantial contribution to add to this discussion. But just wondering that if all this is well-known, why aren't there a lot of links to references in this and the other thread to evince this? Even one for that matter? Might make the discussion quite a bit shorter.

Or is it so well-known among relevant scientists it just isn't described anywhere?

Ken G
2016-Oct-30, 10:04 PM
I have no substantial contribution to add to this discussion. But just wondering that if all this is well-known, why aren't there a lot of links to references in this and the other thread to evince this? Even one for that matter? Might make the discussion quite a bit shorter.I did give a link to Wikipedia, right from the start, which gets it right. But it doesn't spell it out very clearly. Graduate-level textbooks and course notes always get this right, but they're too advanced for most. The whole point of the thread is that you cannot find intro websites that get this right! There's nothing controversial about this, everyone who knows anything about stars knows this.


Or is it so well-known among relevant scientists it just isn't described anywhere?Experts on stars know it. Textbook writers are usually not experts.

Reality Check
2016-Oct-31, 03:32 AM
What part of this true statement:
Adding mass to the Sun would ultimately cause every layer in the Sun to expand
are you not getting?
I get that.
I get that insulting me does not make a rational argument.
I know what gravity is.
I know what compression is.
I know that a higher mass will initially compress the Sun because that is what gravity does - compress gases.
I know that leads to higher temperatures at the core that will ultimately expand the Sun and reduce temperatures. The Sun will then have a higher luminosity because luminosity increases with mass.

Reality Check
2016-Oct-31, 03:34 AM
What unadulterated baloney, ....
Just repeating "unadulterated baloney" without any science is not impressive, nor is insulting the authors of astronomy notes.

Reality Check
2016-Oct-31, 03:45 AM
Reality Check can keep repeating his argument and referring to bad sources until doomsday and it will not shake my confidence in my opinion that Ken G is on the right track, or in my own sanity checks
How do you know that these source written by astronomers are bad, Hornblower?
On the one hand you list your doubts about Ken G's assertions and yet you believe him over astronomers?

As for Ken G being "on the right track" - that web pages emphasizing pressure in the mass-luminosity relation are wrong was established by StupendousMan on 21 October 2016 (https://forum.cosmoquest.org/showthread.php?154582-Correcting-errors-in-the-quot-Explore-quot-encyclopedia&p=2374763#post2374763) with his link to Lionel Siess Homepage (http://www.astro.ulb.ac.be/~siess/) and his isochrone calculation tool (http://www.astro.ulb.ac.be/~siess/pmwiki/pmwiki.php/WWWTools/Isochrones).
Note that this thread started on 29 November 2014 and there are no citations of astrophysics on this topic by Ken G.

Ken G
2016-Oct-31, 04:26 AM
I know that a higher mass will initially compress the Sun because that is what gravity does - compress gases.No, you don't know any such thing! I already covered this just above-- you are making two assumptions:
1) the mass is not added at high temperature, and
2) the mass is added suddenly.
If the mass is added at very high temperature into the core of the star, there would not be any "initial compression" at all. Also, as I just said above, and Hornblower underscored for you, if the mass is accreted gradually, there will also never be any compression, there will just be gradual expansion. Yet there will still be a need for explaining the rising luminosity! So what is obvious from this reasoning is that compression plays no role at all in explaining the mass-luminosity relation of radiatively diffusing stars (such as main-sequence stars from about 0.5 to 50 solar masses).

The Sun will then have a higher luminosity because luminosity increases with mass.
And the reason for that is what we wish to explain! Get: the explanation has nothing at all to do with transient behavior like "initial compression", which may be there in some scenarios but not others, and has nothing to do with what is always there: the mass-luminosity relation we are trying to understand. Transient behaviors that don't even have to be there at all deserve no place in an explanation of a pervasive effect, I would really hope we could all see that.

Ken G
2016-Oct-31, 04:47 AM
Just repeating "unadulterated baloney" without any science is not impressive, nor is insulting the authors of astronomy notes.You can be sure that when I see baloney, I will point it out, labeled as such. For example, in one sentence you just said two things that are baloney: you said that I am not offering "any science" with my claims, which is patently absurd given the meticulous scientific logic I include with everything I say, and you said I insulted authors, which is totally false. Please don't make wild claims with zero evidence. Instead, just read.

Hornblower
2016-Oct-31, 04:15 PM
I'm sorry Ken G, but some of your remarks in your simplified presentations continue to trouble me, and could be giving some other posters excuses to blow you off. I will address the compression issue after having thought about it for a few days. Let's look at mass transfer in an evolving binary again, where gas is accreting in a trickle onto a star. As any given portion of this gas approaches the star while being gravitationally accelerated, it is being packed into a smaller volume than it previously occupied after being blown off the other star. This action causes the acquired kinetic energy to become heat. I consider this action to be compression, and the fact that in a slow steady state process the star otherwise expands throughout its volume as this accretion heats it does not change what I call the action in the accretion disk.

My above misgivings do not change my opinion that you are spot on about the aforementioned errors in describing the cores of main sequence stars of various masses.


How do you know that these source written by astronomers are bad, Hornblower?
On the one hand you list your doubts about Ken G's assertions and yet you believe him over astronomers?If by astronomers you mean the writers who keep getting it wrong when writing low-level textbooks, I think we are seeing the same sort of herd mentality as with the commercial map publishers and GPS programmers who have been getting my street wrong for over 30 years and making it hard for visitors to find my place. Ken has consistently said that astrophysicists who do research in this field get it right. I read his detailed presentations in the original thread and did sanity checks of my own, based on what I had learned in sophomore-level college physics courses about gas dynamics.

Ken G
2016-Oct-31, 09:30 PM
I'm sorry Ken G, but some of your remarks in your simplified presentations continue to trouble me, and could be giving some other posters excuses to blow you off. It all depends on if they want to simply understand the mass-luminosity relation, or if they don't. The arguments I'm giving are correct, they are the simple understanding of that relation, as per the understanding that Eddington would have had.

Let's look at mass transfer in an evolving binary again, where gas is accreting in a trickle onto a star. Sure, we can take the Algol binary as a classic example. There, you have a 3.2 solar mass main-sequence star that had to start out with less than 2 solar masses, so has to have accreted (and is still accreting) more than 1 solar mass of gas. So we have a main-sequence star having its mass go from something like 1 solar mass, to something like 3 solar masses, due to accretion.
As any given portion of this gas approaches the star while being gravitationally accelerated, it is being packed into a smaller volume than it previously occupied after being blown off the other star. What that density of the gas was as it crossed between stars is of no consequence (was it clumpy? Did it happen smoothly or in bursts? Who cares! We are trying to understand the mass-luminosity relation of the accreting star, not the accretion process!), because it will not have anything to do with the mass-luminosity relation that we are trying to understand. Go back to Algol, and just ask yourself these two questions:

1) did the main-sequence star obey the mass-luminosity relation throughout the period that it was accreting?
(answer: yes, ignoring any sudden "burps" that might have happened during unstable phases of mass transfer during which the star might not have obeyed that relation as it thermally readjusted, but we don't care about because we are trying to understand the mass-luminosity relation not the burps)

2) did the density in the fusing core of that star, where misinformed people are saying we can understand the mass-luminosity relation by claiming it is undergoing compression, ever actually undergo compression in that process?
(answer: no, not during smooth accretion, the star simply went through a smooth sequence of those Seiss models, which is why we have those models in the first place.)

That's it, done-- the mass-luminosity relation that the main-sequence star in Algol obeys, and that we are trying to explain why it obeys, has squat, zilch, nada to do with compression. It's just that simple. Transient effects occuring during adding mass have nothing to do with the mass-luminosity relation we are trying to understand, and they could be done a thousand different ways in a thousand different systems, all obeying a single mass-luminosity relation. So they would be terrible things to want to include in an explanation of the mass-luminosity relation, that should be very clear.

Reality Check
2016-Nov-08, 12:41 AM
No, you don't know any such thing!...
I know that fantasies about teleporting hot matter into the center of stars are irrelevant. Which leaves the basic physics of the example of adding mass to the Sun:

Adding mass to the Sun gives a higher mass :eek:!
The higher mass will initially compress the Sun because that is what gravity does - compress gases.
That leads to higher temperatures at the core and a higher rate of fusion.
That will ultimately expand the Sun and reduce the core temperature.
But not to what it was before because we observe that luminosity increases with mass.

Compression thus plays an essential role in explaining the mass-luminosity relation (https://en.wikipedia.org/wiki/Mass%E2%80%93luminosity_relation). No compression = no increase in temperature = no increase in the rate of fusion = no increase in luminosity :doh:!

Usually the "initial compression" comes during stellar formation. I suspect that stars that are gaining mass by accretion will have a luminosity that reflects a past point of hydrostatic equilibrium, e.g. the mass that they had 10,000 or 100,000 or a million years ago.

If you want to know why core temperature in stars do not remain constant or even decrease when mass increases then ask an astronomer or read an astrophysics textbook. Or just look at the real world where luminosity (thus fusion thus temperature) is observed to increase with mass.

Reality Check
2016-Nov-08, 01:14 AM
If by astronomers you mean the writers who keep getting it wrong when writing low-level textbooks, ...
I mean the authors and professional astronomers that you are relying on Ken G's personal opinion of "keep getting it wrong". Ken G has not quoted what he thinks are errors in any textbooks at all in this thread.
This thread has been about

A now inaccessible entry in "Explore" encyclopedia when the thread started 2 years ago. What he quoted has the error that core pressures increase with mass.

Why does luminosity depend so strongly on mass? A modest increase in mass corresponds to a star with a substantially higher pressure and temperature in the core. Since the rate of nuclear reactions depends sensitively on temperature, more massive stars have much larger rates of nuclear fusion. This in turn leads to a much higher luminosity.

More massive stars have greater gravity that creates higher pressure in the stellar interior. The higher pressure results in higher temperature that causes higher energy output by the fusion process, giving both higher luminosity and higher surface temperature.
The Wikipedia article on star and their age (https://en.wikipedia.org/wiki/Star#Age).
Three web pages:
THE MAIN SEQUENCE - Astronomy 162: Professor Barbara Ryden - Lecture notes (http://www.astronomy.ohio-state.edu/~ryden/ast162_4/notes14.html)
The Mass-Luminosity Relationship by John A Dutton, Penn State University (https://www.e-education.psu.edu/astro801/content/l7_p3.html)
Back to Basics: The Mass – Luminosity Relation in Main Sequence Stars (https://tallbloke.wordpress.com/2012/05/20/back-to-basics-the-mass-luminosity-relation-in-main-sequence-stars/)

We have science to show that the web pages are wrong because stellar models actually show that core pressures decrease with mass (https://forum.cosmoquest.org/showthread.php?154582-Correcting-errors-in-the-quot-Explore-quot-encyclopedia&p=2374763#post2374763). This science was supplied by StupendousMan.

That is my main nitpick with the thread. Starting the thread with an unsupported assertion that an online encyclopedia entry is wrong without citing the correct science makes this a personal opinion thread. We had to wait almost 2 years for your back of the envelope calculation and then the results of stellar models.

ETA: The Wrong answers to why high-mass main-sequence stars have such high luminosity (https://forum.cosmoquest.org/showthread.php?155506-Wrong-answers-to-why-high-mass-main-sequence-stars-have-such-high-luminosity)thread also does not quote textbooks.

Ken G
2016-Nov-08, 03:58 AM
I know that fantasies about teleporting hot matter into the center of stars are irrelevant.I have no interest in your opinions about effective pedagogical devices. People who actually teach use devices like this all the time, in the real world in which I live.

The higher mass will initially compress the Sun because that is what gravity does - compress gases.I already told you why this claim is baseless. It depends on how the mass is added. There are many ways to add mass where we would only get expansion. I also gave you a classic example of that: gradual mass transfer in a binary. When mass gradually transfers between stars, the mass gaining star simply moves through a sequence of higher and higher mass models, with higher and higher luminosity, all of which have lower and lower density. So there's no "initial expansion" associated with that mass gain, it's just plain wrong. But also irrelevant to this thread, it's grabbing at straws to vainly try to justify the concept of "compression" when the physics involved in the mass-luminosity relation is actually all about expansion. If you cannot understand that, then you just won't understand stars. My efforts are for those who actually do want to understand why a star gaining mass has a rising luminosity, and it sure has nothing to do with compression. So my remarks are for those who can understand, and don't need to try to force the square peg of compression into the round hole of expansion that is at the heart of the mass-luminosity relation for main-sequence stars.

tusenfem
2016-Nov-08, 06:10 AM
Okay and that is enough, take it to ATM.
Thread closed.

tusenfem
2016-Nov-10, 02:10 PM
After looking through the last pages of the thread, I noticed that I made a mistake here, about the ongoing discussion, where I somehow had gotten the impression that this was discussing degeneracy pressure as in the ATM thread. Thread re-opened.

Ken G
2016-Nov-10, 03:16 PM
OK, then the current status of the conversation is this:
It has been demonstrated that, if we consider main-sequence stars from mass about 0.5 to 50 solar masses (which are the ones where energy transport is primarily via radiative diffusion), then the higher luminosity with higher mass (widely called the "mass-luminosity relation") has nothing to do with compression. This has been shown quite conclusively by looking at two crucial facts:
1) models of higher-mass versions of these stars have everywhere lower density and pressure than lower-mass ones, and
2) in a binary, where one of these stars is receiving mass gradually from its companion, all that would happen is the star would move slowly through a sequence of these models, which implies that its luminosity would be constantly rising with mass in keeping with the mass-luminositya relation we are trying to explain, while constantly undergoing nothing but expansion-- no compression is relevant anywhere in the explanation.

These points, which no one has successfully disputed, together refute totally any generally true and conceptually insightful explanation of the mass-luminosity relation that relies anywhere on the concept of "compression." Sadly, you will indeed find reference to compression in many botched attempts to explain the mass-luminosity relation in otherwise credible sources, and even some members of this forum appear to have fallen into using this false explanation. The purpose of this thread has been to reveal this problem, in hopes of helping fix it. It is, of course, only useful for those people who actually want their explanations to satisfy basic physics.

Reality Check
2016-Nov-10, 09:28 PM
It has been demonstrated that, if we consider main-sequence stars from mass about 0.5 to 50 solar masses (which are the ones where energy transport is primarily via radiative diffusion), then the higher luminosity with higher mass (widely called the "mass-luminosity relation") has nothing to do with compression. .
The highlighting is a bit misleading about the error.
What has been demonstrated is that there some (five) web pages that attribute increases in luminosity with mass to increases in core pressure and density. But as you state stellar models actually show that central density and pressure decreases with mass (https://forum.cosmoquest.org/showthread.php?154582-Correcting-errors-in-the-quot-Explore-quot-encyclopedia&p=2374763#post2374763) so those 5 web pages are wrong.

Gravitational compression has to increase with mass which looks like the source of one web page's error: THE MAIN SEQUENCE - Astronomy 162: Professor Barbara Ryden - Lecture notes (http://www.astronomy.ohio-state.edu/~ryden/ast162_4/notes14.html) goes from increasing compression to increasing core density and pressure. It has something to do with the increasing luminosity but not via increasing core density and pressure.

Ken G
2016-Nov-10, 11:23 PM
What has been demonstrated is that there some (five) web pages that attribute increases in luminosity with mass to increases in core pressure and density. Nope, it's in every elementary textbook I've ever seen that gives any explanation at all. The websites and books often don't give any explanation, they just cite it as an empirical relationship, so they don't count as trying to understand it. The real question is, how many actually give the correct reasoning? The answer there is simple: very few indeed, until you go to more advanced sites and books. If your position is going to be that this error is not widespread among the subset that offer any explanation at all, give it up now, you're wrong. But at least it's progress-- for the first time you have recognized that it is indeed an error! So now you are saying, you were wrong all this time, but remarkably, you can still pretend you were right, if you can just assert (without evidence) that the error is not found widely in the explanation of the mass-luminosity relation. That's not going to be any better an argument than when you claimed it wasn't an error at all.

Hornblower
2016-Nov-10, 11:42 PM
When I mentioned the occurrence of compression in an earlier post, I did not intend to imply that I expected the core of a star experiencing accretion to be increasing in density. I fully expect it to be in virtually the same state as that of a fully stabilized star of the same mass after a trickle of accreting gas has stopped. I was envisioning compression of the gas that is forming the accretion disk as a source of heat for heating the star. Of course, with fusion in the core, we do not need such a heat source to drive the evolution that leads to expansion and reduced density and pressure, along with increasing luminosity, as the accretion process progresses. I realize that we can safely ignore initial transient effects when calculating the slow, long term evolution of the state of the star, but I would wish to discuss the transients if a youngster asks me what happens when the evolving companion star initially overflows its Roche lobe and starts pouring matter onto the main sequence star.

Ken G
2016-Nov-10, 11:58 PM
When I mentioned the occurrence of compression in an earlier post, I did not intend to imply that I expected the core of a star experiencing accretion to be increasing in density. I fully expect it to be in virtually the same state as that of a fully stabilized star of the same mass after a trickle of accreting gas has stopped. I was envisioning compression of the gas that is forming the accretion disk as a source of heat for heating the star.Yes, but of course the key is that fusion is self-regulating, so it is happy to provide whatever heat is needed to both replace the light leaking out, and create whatever expansion is required to maintain force balance. Fusion is a very ready source of an (almost) limitless capacity of heat, whatever is necessary. That's why compression is of no importance to the mass-luminosity relation anywhere in the star, the internal structure is controlled by the heat released by fusion, which in turn is controlled by the rate that light is leaking out, and that depends only on the mass-- that's the mass-luminosity relation for radiatively diffusive stars (which unfortunately is often called the mass-luminosity relation for main-sequence stars, but that can mix in different physics at the very low and very high mass ends, so should really be considered a different animal unless one wishes only the empirical result with no conceptual content).


Of course, with fusion in the core, we do not need such a heat source to drive the evolution that leads to expansion and reduced density and pressure, along with increasing luminosity, as the accretion process progresses. Exactly, fusion does it.


I realize that we can safely ignore initial transient effects when calculating the slow, long term evolution of the state of the star, but I would wish to discuss the transients if a youngster asks me what happens when the evolving companion star initially overflows its Roche lobe and starts pouring matter onto the main sequence star.Certainly the behavior of transients have their place-- but not in the mass-luminosity relation, for that we only want elements that have to be there, without which we couldn't understand the relation.

StupendousMan
2016-Nov-11, 12:17 AM
Ken, I believe the issue here may be simply the attempt by some to answer the question "Why is the temperature of the core higher in high-mass main sequence stars than low-mass main sequence stars?" Students learn in introductory physics courses that there is a simple relationship between pressure, volume, density and temperature for ideal gases (ordinary gases at everyday temperatures -- which are not undergoing fusion). They do homework problems, and some perform experiments, which show that, in general, if you compress a gas, its temperature increases. Some students perform lab experiments in which they add weights to the top of a piston; as the piston sinks into a cylinder of gas, the temperature rises.

So, students are primed with this information when they take an introductory astronomy course. The topic of stellar structure comes up, usually to be covered in just one or two hour-long lectures. Stellar properties on the main sequence change with mass -- that HAS to be described. One facet involves the properties of the core and fusion therein. High-mass stars have higher temperatures. High-mass stars have more mass.

I can see how it would be very easy for an instructor to say to himself, "I want to help the students remember that higher-mass stars have higher internal core temperatures. How can I cause this idea to stick in their brains?" One option is to start talking about the opacity of gas at different layers of the star, which will take a considerable time to explain, and which is a completely new idea to most of the students, and which involves some complicated physics. Another option is to realize that "more mass compresses the gas, so it gets hotter" will get the message across in 30 seconds, and probably make sense to many students.

It involves telling a small lie in the service of a larger truth. Some may see it as the proper course of action. I have very likely used similar techniques, glossing over a complicated subject in favor of a simple-to-grasp idea, in my own classes.

Reality Check
2016-Nov-11, 01:41 AM
Nope, it's in every elementary textbook I've ever seen that gives any explanation at all.
Without citations and quotes we cannot know that whether that assertion is true. We have to rely on the evidence that has been given which is 5 web pages.

We know that elementary textbooks state things in elementary terms because they are addressing students who have not done intermediate or advanced physics. I would not be surprised if elementary textbooks contain "lies to children (https://en.wikipedia.org/wiki/Lie-to-children)".

Ken G
2016-Nov-11, 03:13 AM
Ken, I believe the issue here may be simply the attempt by some to answer the question "Why is the temperature of the core higher in high-mass main sequence stars than low-mass main sequence stars?"Yes, I know, and they invariably get the answer totally wrong. They say all kinds of nonsense, like that the higher mass star has a stronger gravity, so needs a higher core pressure (wrong). They say the higher mass causes compression, raising the core temperature (wrong). I mean, these are not just a little off, they are the opposite of right-- the gravity is weaker, the core pressure is lower, and there is expansion not compression when going from one model to a higher mass one, as in a binary star receiving mass transfer.

Students learn in introductory physics courses that there is a simple relationship between pressure, volume, density and temperature for ideal gases (ordinary gases at everyday temperatures -- which are not undergoing fusion). They do homework problems, and some perform experiments, which show that, in general, if you compress a gas, its temperature increases.Sure, but that only intensifies the mistake-- by tying it to common intuition in a wrong way, it only cements the false logic. That's why it's in so many places, even though it is so wrong-- it's truthy.


The topic of stellar structure comes up, usually to be covered in just one or two hour-long lectures. Stellar properties on the main sequence change with mass -- that HAS to be described. One facet involves the properties of the core and fusion therein. High-mass stars have higher temperatures. High-mass stars have more mass. Right, so the connections jump right out at you. But one thing I always stress to my students about science is that it is the one pursuit that doesn't stop when you think you have it right-- you keep digging. And when you do, you often find you didn't get it right, so you try again. The self-correcting aspect of science-- if we stop when it "sounds right", we have forgotten everything that matters about scientific thinking. If science were about getting a warm fuzzy feeling of understanding, we could have stopped at the Greek models, and saved a whole lot of effort.


It involves telling a small lie in the service of a larger truth.No, no, it's not a "small lie", it is completely the opposite of the truth. As soon as the scientist says "this is totally the opposite of right, but it will sound reasonable to my students, so who cares?", they should turn in their educator credentials on the spot. I don't mean an honest mistake in believing something that is wrong, we all do that, I mean not caring when you know it's wrong! Of course we simplify, of course we leave out important details if our students can't handle the full truth, but we never, never, purposely tell them something that is just completely wrong at every level. The very idea of settling for that is appalling-- with a little effort, it is always possible to find an explanation that actually does ring true, at least at a qualitative level. This is true even if it is a high school class.

I'll give you an example. This is how I would explain the mass-luminosity relation to a high school class. I'd say that when you look up at the stars, each one is basically a giant leaky bucket of light. There is light in there because gravity made the star very hot in its deep interior, much hotter than what you see on the surface, and all that huge amount of light slowly leaks out, like water through a sieve. But deep inside there is a fusion engine, which responds by self-regulating to replace the light that leaks out. A more massive star is simply a bigger leakier bucket of light, so more light leaks out and the star is much brighter, so the fusion burns faster, just like the furnace in Winter in a larger house with more windows. This requires a small increase in core temperature to accomplish that.

That's it, that's why the core temperature is higher, that's the beating heart of it. It's not complicated at all, it uses quite familiar ideas, and it is a whole lot closer to the truth than the complete baloney that the more massive star is compressed, or has a higher pressure, or that any of those things are leading to a higher core temperature and a higher fusion rate. The very idea of telling students that the fusion rate sets the luminosity is wrong, the fusion would have absolutely no idea how fast to proceed if it wasn't being told how fast the light is leaking out. (If you surrounded a star with a mirror, the star would not just keep heating up until it exploded, it would simply cease fusing.) You can see this very easily, a little above the Sun on the main sequence, the physics of fusion changes almost totally. It goes from proton-proton fusion to fusion that is catalyzed by the CNO cycle, which gives it a completely different dependence on temperature and composition. Yet you will notice nary a hitch in the slope of the main sequence in an H-R diagram, the stellar structure clearly doesn't care a whit that its fusion physics has changed drastically.


Some may see it as the proper course of action. I have very likely used similar techniques, glossing over a complicated subject in favor of a simple-to-grasp idea, in my own classes.We have all glossed over details, it's essential. But that's a whole lot different from giving an answer that is basically what Calvin's dad gives in Calvin and Hobbes! (You should appreciate that.) If it only sounds plausible, but on closer inspection is seen to be totally wrong, you would be far better not telling them anything at all. Untrained intuition is better than intuition that is poisoned by "truthiness," that's much harder to undo later (as this thread shows quite clearly!).

Ken G
2016-Nov-11, 03:39 AM
Without citations and quotes we cannot know that whether that assertion is true. That's why I started the thread with a very simple google experiment, just read that again. There's not much point in quoting half a dozen intro textbooks that you can't look up, but if by now, in this thread, you haven't gained a certain degree of confidence in what I'm saying, you are a hard case indeed.


We have to rely on the evidence that has been given which is 5 web pages.Oh it's much better than that, look at that google experiment again. It's not just 5 selected websites, it's the first 5 that give explanations, other than the Wiki (which tends to be more advanced and more reliable than intro courses and textbooks).


We know that elementary textbooks state things in elementary terms because they are addressing students who have not done intermediate or advanced physics. I would not be surprised if elementary textbooks contain "lies to children (https://en.wikipedia.org/wiki/Lie-to-children)".Read what I said to StupendousMan, I don't want to say it all again!

StupendousMan
2016-Nov-11, 04:33 AM
This is how I would explain the mass-luminosity relation to a high school class. I'd say that when you look up at the stars, each one is basically a giant leaky bucket of light. There is light in there because gravity made the star very hot in its deep interior, much hotter than what you see on the surface, and all that huge amount of light slowly leaks out, like water through a sieve. But deep inside there is a fusion engine, which responds by self-regulating to replace the light that leaks out. A more massive star is simply a bigger leakier bucket of light, so more light leaks out and the star is much brighter, so the fusion burns faster, just like the furnace in Winter in a larger house with more windows. This requires a small increase in core temperature to accomplish that.

As I see it, this is the crux of the issue. A student raises his hand and says, "Dr. G, what is the physical mechanism causing the increase in core temperature? In my house, when more heat leaks out, the temperature drops ... but then a thermostat senses the decrease in temperature and turns the furnace on. Is there a thermostat inside the star's core? How does it work?"

The typical explanation is "if the envelope becomes more transparent and so more energy leaks out, the temperature of the core drops slightly. This causes the outer core layers to contract, which in turn raises the pressure and density and temperature of the core slightly -- until the rising and now hotter-than-it-was-originally core fuses hydrogen at a higher rate than before, producing enough extra heat to keep the outer layers from contracting any further."

If I understand you correctly (and if I've misunderstood your objection, my apologies), you'd like to change this explanation. Could you tell us how you would answer the student's question?

Ken G
2016-Nov-11, 09:19 AM
As I see it, this is the crux of the issue. A student raises his hand and says, "Dr. G, what is the physical mechanism causing the increase in core temperature? In my house, when more heat leaks out, the temperature drops ... but then a thermostat senses the decrease in temperature and turns the furnace on. Is there a thermostat inside the star's core? How does it work?"Yes, that's the right question to ask, and it has a very straightforward answer. The first thing you need to do is convey the concept of heat capacity-- how much heat do you have to remove to get the temperature to drop a certain amount. Then you have to convey what happens when the temperature drops-- gas pressure drops (so they need the ideal gas law, a common high school topic). Then you say that when pressure drops, gravity wins, and the core contracts. Then you must make them understand what happens when you compress air, say in a bicycle pump-- the temperature rises. These are all common high school topics, I know that's where I learned them. Finally, you say that fusion is very sensitive to temperature, a small rise produces a big jump in fusion rate. That fixes the original problem you started with-- that the fusion rate was lower than the rate light is leaking out.

So that's the key mechanism in there-- all you need is a furnace that works by burning more slowly any time the temperature drops even a teensy bit. The interesting thing is that this sounds like it would be the opposite of what you want, but that's because you forgot about what happens when the gas contracts-- its temperature rises. So if you build a furnace that turns itself down when the temperature drops, and the temperature does drop, it causes the temperature to bounce right back again, when the under-pressured gas contracts under gravity. (OK it's a weird house-- it's self-gravitating, that's another key element and it is the reason this won't work for real houses.)

So it's the role of gravity that is crucial to the stability, that's the surprising part the student must understand. We say that a stellar core has an effectively negative specific heat (this is called "gravothermal specific heat, but they don't need that). Meaning, if you remove heat, the response ends up raising the temperature, and then fusion replaces the deficit.

So that's the key concept. It's not simple, but there's nothing there a high school student cannot get a feel for. And above all, it's right-- it's what is actually happening. There's just no way to understand main-sequence stars without understanding this, no shortcuts or other routes to get there. Those pretend routes are just completely wrong-- the student has to understand what you and I can call the negative gravothermal specific heat o fa stellar core. That's the answer to the question, "the physical mechanism causing the increase in core temperature?" Questions like that have answers, we must not shy away from them and give them complete baloney in its place. If we don't know the answer, the teacher must say "good question, I don't really understand that myself," and this invites the student to be a scientist and do more research. Or, if you do know the answer, and can't make it clear, then try harder-- there is an answer, it can be understood.

So what I'm saying is, there are two kinds of "lies to children," one which goes like "here's what's basically happening, though I'm not going to get into details I would need for a quantitatively accurate simulation,' which is a "good" lie, but another goes like "I don't want to bother trying to give you a working understanding, so I'll be like Calvin's dad and just make something up that will sound good to you and you can regurgitate it on an exam." That's a bad lie, worse than just wrong-- it's the opposite of how science actually works. Science is not about satisfying ourselves, it's about challenging ourselves, attacking our understanding with questions like "why is the pressure in the core of a high-mass star lower rather than higher, if compression is what raises the core temperature?" Try that question, if one uses the wrong explanation!


The typical explanation is "if the envelope becomes more transparent and so more energy leaks out, the temperature of the core drops slightly. This causes the outer core layers to contract, which in turn raises the pressure and density and temperature of the core slightly -- until the rising and now hotter-than-it-was-originally core fuses hydrogen at a higher rate than before, producing enough extra heat to keep the outer layers from contracting any further."Yup, that's the negative gravothermal specific heat, right there-- removing heat causes the temperature to ultimately rise, it would work perfectly well as a thermostat in your house (if your house was self-gravitating!) The temperature you get is whatever is the stable temperature, but you already know what that temperature is, it's the temperature where fusion initiates. This is a good understanding of stars like the Sun-- their core temperature is tightly constrained by fusion physics, but the luminosity just comes from the leak rate, and fusion self-regulates with teeny T changes.


If I understand you correctly (and if I've misunderstood your objection, my apologies), you'd like to change this explanation. Could you tell us how you would answer the student's question?I wouldn't like to change that at all, that's completely right, as the argument for the stability. But that's no argument for the mass-luminosity relation, it's missing its guts: the rate that light leaks out, that big leaky bucket idea. Also, this is not at all the explanation you will find in the sources I am talking about (basically, all of them, that offer any explanation and are at a more elementary level than Wiki), those that actually attempt to explain why the luminosity rises with mass. See the beginning of the thread for examples of how they actually explain what is going on.

What's ironic in the wrong explanations is, they often do give just the explanation you did when they answer "why is it stable," but not "why is the luminosity what it is." So they get the self-regulation right if they do it at all, but then they botch the mass-luminosity relation, as if that had some totally different answer that is internally inconsistent with the self-regulation issue. The common botched explanation goes, a higher mass star has a stronger gravity, so contracts, which raises the core temperature, which raises the fusion rate, which raises the luminosity. Note several points:
1) this is completely wrong, the gravity and pressure are lower, and the star is expanded not contracted, and
2) how could a self-regulated fusion, whose whole raison d'etre is to replace the rate that light is leaking out, be used to set the rate that light leaks out? It makes absolutely no sense, which is why it's wrong. You must already know the rate the light leaks out, or you have no idea why the luminosity changes in the way it does when you add mass. If a clever student detects the swindle, they will be confused, and lose all hope of understanding stars unless they simply reject the wrong stuff they are being told. A less clever student just buys it hook line and sinker, and again loses all hope of actually understanding. We can do much better than that-- the explanation for the mass-luminosity relation must, at the very least, be consistent with the stable self-regulation argument! It's all about combining knowledge of how big and leaky is the bucket, with how fusion self-regulates via that negative effective specific heat. Without those two pillars, we would be kidding ourselves that we are conveying anything even resembling a correct understanding, and we can do better.

Reality Check
2016-Nov-14, 08:31 PM
That's why I started the thread with a very simple google experiment, just read that again.
Which says nothing about elementary textbooks or even how common the error is. You googled "explanation of the mass-luminosity relation" in post #67 and you listed 3 pages out of 1,250,000 results. The first page suggests that most of the results are statements of the relation, not a full explanation.

Without actual quotes from these elementary textbooks you are talking about we cannot even be sure that they contain the error.
I read what you said to StupendousMan and it seems to be the idea that post graduate astrophysics should be taught to undergraduate students. But what about high school science students - should they be also taught post graduate astrophysics :eek:? In the practical world of education are simplified to match the level of the students and the time allowed to teach them.

The common correct explanation using basic physics is that a higher mass star has a stronger gravity, so contracts, which raises the core temperature, which causes expansion lowering the temperature again and establishing a new balance between gravitational pressure and thermal pressure. The small increase in temperature raises the fusion rate. Luminosity increases for the simple reason that more photons are emitted.

The "lie to children" would include not explaining why there is that small increase in temperature, not covering the effect of opacity (changes a 3.33 power to 3 (https://en.wikipedia.org/wiki/Mass%E2%80%93luminosity_relation)) or composition changes with mass.

Ken G
2016-Nov-15, 01:51 AM
Which says nothing about elementary textbooks or even how common the error is.That is correct. It is not my job to tromp you through the dozens of intro textbooks I have seen, and not one of them got it right. About half gave no explanation, the other half the wrong explanation that mentions either stronger gravity, higher pressure, or compression, all wrong. Textbooks are no better than the websites. I don't care if you believe me, you can live on in whatever state of ignorance you like. Why should you know the truth? You can go on choosing to believe whatever you like. Maybe I just made the whole thing up, for fun. Yeah, that's real likely.



The common correct explanation using basic physics is that a higher mass star has a stronger gravity,Already wrong. Seriously, haven't you gotten to this point yet? Did you look at any of those Seiss models? Everyone who knows the first thing about high-mass main-sequence stars knows they have weak gravity throughout, compared to lower mass stars like the Sun. I'm embarrassed for you, you have a chance to learn something about stars but you won't even look up a simple fact.

Ken G
2016-Nov-15, 02:13 AM
I read what you said to StupendousMan and it seems to be the idea that post graduate astrophysics should be taught to undergraduate students. But what about high school science students - should they be also taught post graduate astrophysics? In the practical world of education are simplified to match the level of the students and the time allowed to teach them.This is worthy of further comment. It seems likely that in the US, going forward, there will be considerable question as to what is the purpose of science. Is science just a kind of "mode of justification", whereby we already know what will happen, so given that we know the answer, we reverse engineer our "science" to seem to provide the answer we "already know"? That's a perfect prescription for you-know-what. But it's precisely what you just said: tell them lies, because you know the answer, so how you got there doesn't matter. Excuse me while I find a place to throw up!

No. Science is not a set of answers, justifed by reverse engineering of internally inconsistent arguments! A thousand times no. Science is a way of thinking, it says you keep asking questions, you are never satisfied that you understand. Most people are satisfied that they think they understand that the phases of the Moon are caused by the shadow of the Earth. That's a "lie to children," but it sure isn't science.

So what does the scientific thinker actually do? Simple: they question. If someone says that high-mass main-sequence stars are more luminous because they have stronger gravity, you question if that is true. You go out and observe such stars, model what you see, and infer their gravity. You discover their gravity is low, not high. The explanation was the opposite of correct.

Someone else says they are more luminous because their core pressure is higher. Do you think "ah, that explains it"? Not if you are a scientific thinker who wants to actually know what causes the phases of the Moon, or the mass-luminosity relation. You observe, model, and discover that their core pressure is low, not high. Again the explanation was the opposite of correct.

This is science. So we do not skirt our duty as scientists: we seek to explain it in a way that is correct, or at least not the opposite of correct. Does this mean we need to treat the student like they have a Ph.D.? Certainly not, that would be skirting our duties as educators. We need to do the hard work of making the correct explanation accessible. Is it really too much to ask, or should we just let people use science to justify what they already think is true, even when the argument they are citing is obviously wrong? If you will settle for wrong explanations because it "doesn't matter", you have forgotten what separates science from non-science.

Hornblower
2016-Nov-15, 02:26 PM
Let's make sure we clarify what we mean when we say "stronger gravity" or "weaker gravity". Reality Check said stronger gravity for the more massive star is correct, and Ken G disagreed. As I see it, a stable 10 solar mass main sequence star, with a radius several times that of the Sun, has stronger gravity at all places within it than the proto-Sun did when the latter was still at that larger radius. That greater gravitational action generated the greater amount of heat that pressurized and stabilized the star at that large radius, in spite of the leakier envelope. The proto-Sun, not being heated as much, kept contracting until it finally stabilized at a smaller radius. At this point the smaller radius more than offsets the smaller mass and makes the gravity at any given percentage of the way from the center to the photosphere stronger than in the more massive star.

In making this presentation to children and other novices who do not yet have the necessary mathematical skills for a full quantitative analysis, of course we must leave out some of the details and ask them to trust our judgment. That does not mean we must say anything which is false. In a court of law, a witness is obliged to tell the truth, the whole truth, and nothing but the truth. In presenting science to novices, we can omit some parts of the whole truth as needed, but still keep everything which we do not omit as true.

Ken G
2016-Nov-15, 03:00 PM
Let's make sure we clarify what we mean when we say "stronger gravity" or "weaker gravity". Reality Check said stronger gravity for the more massive star is correct, and Ken G disagreed. As I see it, a stable 10 solar mass main sequence star, with a radius several times that of the Sun, has stronger gravity at all places within it than the proto-Sun did when the latter was still at that larger radius. Yes, and of course this entire thread is about main-sequence stars, so no other phase of evolution is relevant. The central point, that intro textbooks should be ashamed of themselves for omitting because it's basic bad astronomy, is that gravity does not just depend on mass, it depends on mass and radius. So no one can never use the baseless claim "more mass means stronger gravity,", one must say what is happening to radius as well. That's what we do when we say we have main-sequence stars, we have a mass-radius connection. To a rough accuracy, radius is proportional to mass since the core T is similar. To better approximations, radius does not increase as fast as mass. But it always increases enough that the gravity is weaker for higher mass stars, except for convective red dwarfs that are really a rather different animal and probably shouldn't be counted in the same mass-luminosity relation in the first place.


That greater gravitational action generated the greater amount of heat that pressurized and stabilized the star at that large radius, in spite of the leakier envelope. The proto-Sun, not being heated as much, kept contracting until it finally stabilized at a smaller radius. At this point the smaller radius more than offsets the smaller mass and makes the gravity at any given percentage of the way from the center to the photosphere stronger than in the more massive star.Yes, higher mass main-sequence stars simply don't have to contract as much to reach fusion temperatures, so they are less contracted, weaker gravity, lower density, and lower pressure objects. These facts are probably the single most important things to know about main-sequence stars, so imagine how horrendous is an explanation for their mass-luminosity relation that causes us to expect the exact opposite! I was quite shocked to find how widespread in intro texts was such an awful explanation (one book even went so far as to say that the mass-luminosity relation was the single most important thing to understand, and went right on to give the totally wrong explanation for it!), though the ones that offered no explanation at all were certainly missing an opportunity to convey this kind of understanding as well. It's just a lost opportunity, either way.

In presenting science to novices, we can omit some parts of the whole truth as needed, but still keep everything which we do not omit as true.Exactly, we must not make the mistake of saying "well, I can't tell them everything, so it doesn't matter if I just make up some hooey. They can't tell the difference anyway, so where's the harm?" Just watch what happens now in American education, if you think there's no need for self-consistent, albeit simplified, logic leading to our scientific conclusions. "The end justifies the means" has to be about the most opposite possible attitude from what is a scientific approach, and if we can't hold firmly to that fact here, on a science forum, there's certainly no hope anywhere else.

George
2016-Nov-16, 08:47 PM
I'm probably indicative of the students who would get this wrong, and maybe my fresh view will help.

At this point, I think it would be nice to have a different word for internal gravity, but not igravity. It is obvious for all that greater mass means greater gravity affecting surrounding space, but this isn't the gravity being discussed since we are now in the star, which has no direct experience since no night expedition has been attempted as of yet. It would seem intuitive that more mass => more gravity => more pulling together => more pressure, even internally, and this is true, I think, until core temperatures get cranking, near main sequence.

Baking this cake from scratch makes good sense; Hornblower's start with a more massive protostar settling in toward main sequence helps the thought process.


Yes, higher mass main-sequence stars simply don't have to contract as much to reach fusion temperatures, so they are less contracted, weaker gravity, lower density, and lower pressure objects. This is the tricky part.

There are several dozen extra cool things in astronomy y'all have taught me. [A special thread probably should address these since they are somewhat amazing.] One is that if you add mass (even a lot) to a Jupiter-sized object, it will not increase in size much. I've assumed it is the extra gravity (due to extra mass) that squeezes it in tighter, and not that volume increases as the cube of the radius thing, or other explanation. Thus, for a non-star, with greater mass we increase both density and pressure, right?

But, ignoring brown and red dwarfs, once the mass level produces a nuclear and stable core, something special has already happened -- the pressure and density has dropped, but what flipped the intuitive Jupiter scenario? As the core has been heating, it expanded because no one has confined the star within a box. It's a gas, but that doesn't necessarily mean pressure has dropped. And now begins the really interesting part, IMO, of this dance in getting all the variables (p, V, T, opacity, gi) a waltzin'. Ken, as Dick Smothers would tell Tommy, "Take it!".

CJSF
2016-Nov-16, 09:04 PM
(some of us need to take a really big step back for these ideas)
When you say "gas" here you mean "plasma" right?

CJSF

Reality Check
2016-Nov-16, 10:14 PM
This is worthy of further comment. ....
Unfortunately your further comment is mostly irrelevant to the subject of my post - how to educate students about science.
Should we expect high school students to learn post graduate science? Or do we take the more practical approach of teaching them science that they are able to learn, even if the coverage is incomplete or even incorrect?
Ditto for undergraduate students.

That is education, not science.

Hornblower
2016-Nov-16, 10:44 PM
Unfortunately your further comment is mostly irrelevant to the subject of my post - how to educate students about science.
Should we expect high school students to learn post graduate science? Or do we take the more practical approach of teaching them science that they are able to learn, even if the coverage is incomplete or even incorrect?
Ditto for undergraduate students.

That is education, not science.

My bold. Good heavens, no! To knowingly give youngsters an incorrect explanation is dishonest, and it could force them to have to unlearn something at a later time should they wish to advance to professional levels. An explanation that is simplified to the point of being incomplete but is correct as far as it goes is fine, because the youngsters can learn more of the details as they gain the mathematical tools and it will all fit together in a logical manner.

DALeffler
2016-Nov-16, 11:47 PM
My bold. Good heavens, no! To knowingly give youngsters an incorrect explanation is dishonest, and it could force them to have to unlearn something at a later time should they wish to advance to professional levels. An explanation that is simplified to the point of being incomplete but is correct as far as it goes is fine, because the youngsters can learn more of the details as they gain the mathematical tools and it will all fit together in a logical manner.

Especially of what an explanation that was taught in school and found later by a students own investigation to be incorrect can say to the student.

After reading this thread and understanding what Ken G is saying, I kind of feel like I've been lied to by all the astronomy books I paid good money for...

Reality Check
2016-Nov-17, 12:43 AM
My bold. Good heavens, no!
Good heavens yes. This is not incorrect as in physically wrong. This is incorrect as in "there is a better theory to explain it". Explanations of gravity are incorrect until students learn GR. Explanations of QM are incorrect until students learn quantum field theory.

DALeffler
2016-Nov-17, 01:21 AM
Good heavens yes. This is not incorrect as in physically wrong. This is incorrect as in "there is a better theory to explain it". Explanations of gravity are incorrect until students learn GR. Explanations of QM are incorrect until students learn quantum field theory.

Then we should be able to teach math this way?

Ken G
2016-Nov-17, 02:14 AM
At this point, I think it would be nice to have a different word for internal gravity, but not igravity. It is obvious for all that greater mass means greater gravity affecting surrounding space, but this isn't the gravity being discussed since we are now in the star, which has no direct experience since no night expedition has been attempted as of yet.Yet the same issue applies at the surface, and indeed the simplest measure of the "strength of the gravity" of a star is the gravitational acceleration at its surface, often called g. Adding mass to the Sun would cause its g to drop, not rise. Of course this is because of changes in the stellar radius.


It would seem intuitive that more mass => more gravity => more pulling together => more pressure, even internally, and this is true, I think, until core temperatures get cranking, near main sequence. Ah, you are asking an interesting question, what happens to g, and the central pressure P (another important benchmark) if you add mass to a pre-main-sequence star? The answer is, it depends on how much internal energy that mass has when you add it. If you add it at a temperature that is hotter than the general average of the star you are adding it to, the star will expand and the g could drop. If you add it at very low temperature, the star will contract and g will rise. So even then, there is no general rule that says adding mass causes contraction, it's simply wrong. But more to the point, you are noticing that the main-sequence situation is very different, because we have fusion, so then it doesn't matter the internal energy of the mass we add, we always get expansion as a net result.

Thus, for a non-star, with greater mass we increase both density and pressure, right?Yes, there are three simple cases to analyze. The simplest is constant density, like a rocky planet. Then there's gas like a star, for which you can use the virial theorem to connect mass to the radius if you know the temperature. And then there's degenerate matter, which has a radius that scales like mass to the -1/3 power, so actually contracts when you add mass. Jupiter is most like that third case, so the density scales like M2, and the pressure scales like M10/3. So yes, big increase in both density and pressure, with mass.

But, ignoring brown and red dwarfs, once the mass level produces a nuclear and stable core, something special has already happened -- the pressure and density has dropped, but what flipped the intuitive Jupiter scenario? Ideal gas behavior, coupled with the necessary temperature for fusion. But if you just wait long enough, you'll be through all the nuclear fuel, and the star will eventually be back to the Jupiter scenario, that's a white dwarf.

Ken G
2016-Nov-17, 02:17 AM
When you say "gas" here you mean "plasma" right?
Yes, you bring up a "dirty little secret" that permeates astronomy: in most situations, plasmas behave exactly like a neutral gas would. The charges only insure that the various species stay tightly coupled, which collisions can enforce anyway.

Ken G
2016-Nov-17, 02:21 AM
Good heavens yes. This is not incorrect as in physically wrong. This is incorrect as in "there is a better theory to explain it".Nope, it certainly is incorrect as in physically wrong. It doesn't get much more physically wrong to tell a student that a star has a higher core temperature due to compression, when the star that has a higher core temperature has expanded. This is the fact of the main sequence. And it doesn't get much more physically wrong to tell a student that compression has yielded a higher core pressure, when in fact the core pressure has dropped. Yet these very falsehoods are precisely what you will find in intro textbooks, and in the wrong explanations you've given in this very thread. It's just totally, completely, and utterly the opposite of true. There's a good term for that: "physically wrong."


Explanations of gravity are incorrect until students learn GR.You need a more sophisticated understanding of the word "incorrect," your current usage is unworkable in science. If the naive thinker maintains that "incorrect" means "does not yield exactly true results", then obviously all of science is incorrect. That's why the usage is so silly.

Ken G
2016-Nov-17, 02:56 PM
After reading this thread and understanding what Ken G is saying, I kind of feel like I've been lied to by all the astronomy books I paid good money for...Remember that errors like this are relatively few, but that's why they are so important to correct. The logic we sometimes see seems to be along the lines of, "if the mistakes are few, then we can tolerate them and leave them be, nothing is perfect," but it's only if the mistakes are frequent that there's no point in fixing them. The rare mistake is the most important one to fix, for then one can strive to a truly authoritative account. What I find more surprising than the presence of simple mistakes like this is how widespread they become, and how resistant to change. The sources all reference each other, until at some point being part of the "standard dogma" becomes more important that being correct. Just look at how tightly some people on this very thread cling to the dogma, even after it has been exposed as wrong. They bend over backward to say it's not wrong, it's just not as right as it could have been. They may as well be saying that teaching 2+2=5 isn't wrong either, it's just not as right as it could have been, which I presume was your point as well.

Reality Check
2016-Nov-17, 08:14 PM
Nope, it certainly is incorrect as in physically wrong.
I was talking about education in general not an "it". We have a total of 1 physically wrong explanation in this thread: What has been demonstrated is that there some (five) web pages that attribute increases in luminosity with mass to increases in core pressure and density. (https://forum.cosmoquest.org/showthread.php?154582-Correcting-errors-in-the-quot-Explore-quot-encyclopedia&p=2377246#post2377246)

That is a "lie to children". If we taught high school children and undergraduates the details of stellar models and made them run a few then they would find that core pressure decreases with mass. Or the teacher could just assert it and the students would have to just believe it.

It is physically correct to tell a student that a higher mass star has a higher core temperature due to compression because more mass = more compression = higher temperatures. That would be incomplete since it does not mention hydrostatic equilibrium, e.g. the higher temperature cause more fusion which expands the star lowering temperatures to balance out the compression and thermal pressure. We have no evidence that this happens in science lessons or even in textbooks.

Every lesson about classic mechanics is incorrect because we know that classical mechanics is a low velocity approximation. It is appropriate to teach classical mechanics as a first step to learning this.
Every lesson about Newtonian gravity is incorrect because we know that Newtonian gravity is a low gravity and velocity approximation. It is appropriate to teach Newtonian gravity as a first step to learning this.
Teachers should mention that they are teaching an approximation.

Ken G
2016-Nov-17, 08:41 PM
We have a total of 1 physically wrong explanation in this thread: What has been demonstrated is that there some (five) web pages that attribute increases in luminosity with mass to increases in core pressure and density. (https://forum.cosmoquest.org/showthread.php?154582-Correcting-errors-in-the-quot-Explore-quot-encyclopedia&p=2377246#post2377246)What has actually been shown, using real physics equations even, is that there is not compression involved in the explanation of higher luminosities for larger masses, there is less compression involved. It's a simple error of forgetting that gravity also depends on radius, I just don't see how you don't get that. But what is also true, and you are of course welcome to test this or pretend it isn't true, that's up to you, is that it is also in every intro astro textbook you can find that offers any explanation at all. This is a fact, whether you know it or not. It is the reason for the thread. The intro material has totally dropped the ball on the mass-luminosity relation, one of the most fundamentally important relations in all of astronomy. Yup, just that. So we are not talking about children and bedtime stories, we are talking about college students trying to learn what scientific thinking is, and they need to be shown what it actually is. You just don't get it, what the rest of us are talking about here is an error, a mistake, a commonly repeated blunder-- not some intentional oversight. Any author exposed to this error should change it immediately, and they would of course do so, if they are doing an updated edition.

It is physically correct to tell a student that a higher mass star has a higher core temperature due to compression because more mass = more compression = higher temperatures.Totally wrong. You can lie to children, but don't try to lie to us, we are too savvy. I already gave you a perfectly normal physical situation that completely destructs your claim here-- the Algol binary. There, you have a main-sequence star gaining mass slowly, and obeying the mass-luminosity relation all the while. That star over time exhibits more mass and a higher core temperature-- but is always expanding, no compression anywhere. It's just bunk.

Now, you can hold any personal opinion you like. You can think it's fine to say that little fairies cause the mass-luminosity relation, and call it a "lie to children." But to people who want to understand the mass-luminosity relation, their first step is rejecting the wrong explanation that higher mass leads to stronger gravity, more compression, higher core pressure, higher core temperature, and faster fusion. Rejecting that should be easy once they understand these facts, all of which are quite well known to stellar experts:

The correct reasons that higher-mass main-sequence stars have much higher luminosity have essentially nothing to do with any of these, as long as we select from the range 0.5 to 50 solar masses:
1) fusion (this one does produce a small effect because of how it weakly feeds back onto the stellar structure, but this can be safely ignored, especially for CNO-cycle fusion)
2) stronger gravity (i.e., a higher g, this should be ignored because it's wrong)
3) compression (also wrong)
4) higher pressure (just plain wrong)

On the other hand, it has everything to do with these:
1) radiative diffusion
2) weaker gravity
3) expansion
4) lower pressure

Once that baloney is finally cleared up, discarding volumes of intro texts and websites on the way, someone who actually wants to understand the mass-luminosity relation can begin to assemble the key parts:
1) the rate that radiation leaks out of a star by diffusing out from great depth (here we must recognize that the mass-luminosity relation is poorly fit by stars of less than about 0.5 solar masses, or above about 50, which are convective).
2) the internal structure that determines what the radiation is diffusing through is set by force balance between gravity and gas pressure, which can be summarized by the virial theorem (here we must recognize that the mass-luminosity relation is poorly fit by stars of greater than about 50 solar masses, for whom radiation pressure dominates gas pressure).
3) combining these two key elements with some simplified treatment of the opacity in the star gives you the mass-luminosity relation without telling any lies at all, just a few simplifying idealizations. You hardly even need to know the radius, gravity, or temperature of the star-- the luminosity can be determined almost without any of those, depending on how rough of an opacity idealization you are willing to make!

The bottom line is, the physical reason main-sequence stars between about 0.5 and 50 solar masses obey a single simple mass-luminosity relation is because those stars are exactly the ones whose energy transport in their interior (the key to understanding their luminosity) is primarily by radiative diffusion. This means they are essentially "big leaky buckets of light." The rate the light leaks out gives the luminosity, and this turns out to depend only on the mass, and in a simple way, for reasons that are crucial to understand, if one is to understand the first thing about stars. Hint: don't look at intro textbooks, they don't have that understanding. Use more advanced books, or read this thread-- very carefully.

Hornblower
2016-Nov-18, 06:54 PM
My coldly logical mind says that astrophysicists who have it right are remiss in not challenging textbook writers who may be leading entry level college students astray. Another side of me acknowledges that I have not challenged the multitude of map publishers and GPS programmers who have made it hard for plumbers and electricians to find my house, so perhaps I should not complain about the astrophysicists.

Ken G
2016-Nov-18, 07:03 PM
There may be a parallel with map-making. It is said that maps sometimes include "paper towns", which are made-up landmarks that don't exist, placed on a map as a kind of trap for anyone who would copy that map without proper copyright privileges. Whoever first inserted the bogus explanation for the mass-luminosity relation, it seems to have served the same purpose-- it's poor physics, but it shows who copied who if you can find where it first appears!

Hornblower
2016-Nov-19, 02:53 PM
It might be an interesting research project to try to trace the paper trail back over the past century and find the smoking gun, that is, a book or paper that either misquotes an astrophysicist who had it right or else made up the wrong explanation out of thin air.

Ken G
2016-Nov-19, 03:29 PM
Indeed, it would be fascinating for a lot of reasons just to see what was in intro texts 50 years ago!

George
2016-Nov-20, 07:04 PM
It might be an interesting research project to try to trace the paper trail back over the past century and find the smoking gun, that is, a book or paper that either misquotes an astrophysicist who had it right or else made up the wrong explanation out of thin air. Funny you should mention that...

[I'm curious if my logic makes sense, so I will throw this out there in hopes I have a causal view of Ken's claims.]

"The Quiet Sun", 1973, Edward Gibson written to educate those going to Skylab with focus on the surprising temp gradient of the corona. It states:

P = NkT for a unit volume, no surprise, but notes that ionization doubles N for hydrogen. This implies pressure doubles, though he goes into mean atomic weights. But increasing pressure will cause expansion and, with ionization, lower opacity, further causing expansion. This, I think, would reduce density and move the tacholine zone (where recombination occurs and opacity increases) farther from the core.

Helium ionization triples the paticle count. It is unclear how the transmutation to He would affect density given all the variables, but, that aside, it looks like density would decrease due to the expansion since local gravity is reduced with expansion.

I haven't read enough of this fairly comprehensive book to be too critical, but I suspect it had the opportunity to address what seems would become misleading regaerding density, but ignored it.

My Jupiter case was to serve as the easy example one could hold for greater density with mass addition. Ionization, I think, makes the flip. [ I sure hope this is so because I'm wearing weak borrowed glasses typing poorly on an iPad.]

Hornblower
2016-Nov-20, 10:41 PM
Funny you should mention that...

[I'm curious if my logic makes sense, so I will throw this out there in hopes I have a causal view of Ken's claims.]

"The Quiet Sun", 1973, Edward Gibson written to educate those going to Skylab with focus on the surprising temp gradient of the corona. It states:

P = NkT for a unit volume, no surprise, but notes that ionization doubles N for hydrogen. This implies pressure doubles, though he goes into mean atomic weights. But increasing pressure will cause expansion and, with ionization, lower opacity, further causing expansion. This, I think, would reduce density and move the tacholine zone (where recombination occurs and opacity increases) farther from the core.

Helium ionization triples the paticle count. It is unclear how the transmutation to He would affect density given all the variables, but, that aside, it looks like density would decrease due to the expansion since local gravity is reduced with expansion.

I haven't read enough of this fairly comprehensive book to be too critical, but I suspect it had the opportunity to address what seems would become misleading regaerding density, but ignored it.

My Jupiter case was to serve as the easy example one could hold for greater density with mass addition. Ionization, I think, makes the flip. [ I sure hope this is so because I'm wearing weak borrowed glasses typing poorly on an iPad.]
My bold. Can you elaborate on this? As I see it, a Jupiter-sized ball of hydrogen and helium with several times Jupiter's mass is already many times more dense than the upper limit for having it in the form of normal neutral atoms in their ground state. It must be dissociated into a state with the electrons and nuclei buzzing around much more closely spaced. I would need someone better informed than myself to say whether or not this is considered ionized.

George
2016-Nov-21, 01:58 AM
Good point. Still shooting from the hip.., perhaps the ionization along a much greater radius (radiative zone and not so much the core region) from the very small core volume yields the doubling of particle count => increasing pressure => causing expansion and lowering opacity (from ionization) => decreasing local gravity => decreasing core density. I would guess the heat transfer from lower opacity would cause greater adjacent ionization as well. I am stumbling along, but it is an interesting adventure.

Hornblower
2016-Nov-21, 02:31 AM
Good point. Still shooting from the hip.., perhaps the ionization along a much greater radius (radiative zone and not so much the core region) from the very small core volume yields the doubling of particle count => increasing pressure => causing expansion and lowering opacity (from ionization) => decreasing local gravity => decreasing core density. I would guess the heat transfer from lower opacity would cause greater adjacent ionization as well. I am stumbling along, but it is an interesting adventure.

If I am not mistaken, a star is fully ionized throughout, except at and very near the photosphere. That makes high opacity and very slow radiative transfer of energy. In the more rarified envelope of a more massive star the transfer is faster but still a snail's pace compared with what it would be if we had neutral gas instead of plasma throughout the envelope at the same radius and density. If I am off here, I welcome help from Ken G or anyone else who can help.

Reality Check
2016-Nov-21, 02:51 AM
What has actually been shown,...
What has been actually shown in this thread is that for larger masses, there is less density and pressure as calculated in solar models.
21 October 2016 from StupendousMan: Note that as the mass of a star increases from 0.5 to 7 solar masses, the central temperature goes UP by a factor of about 3, but the central density goes DOWN by a factor of about 8. The result is that the central pressure decreases with mass. (https://forum.cosmoquest.org/showthread.php?154582-Correcting-errors-in-the-quot-Explore-quot-encyclopedia&p=2374763#post2374763)

What has been demonstrated is that there some (five) web pages that attribute increases in luminosity with mass to increases in core pressure and density. (https://forum.cosmoquest.org/showthread.php?154582-Correcting-errors-in-the-quot-Explore-quot-encyclopedia&p=2377246#post2377246)

It is physically correct to tell a student that a higher mass star (a star that has mass added to it) has a higher core temperature due to compression because more mass = more compression = higher temperatures because that is basic physics (compressed gases can heat up :eek:). It is not complete because it does not mention that higher temperatures = more fusion = more pressure = the star expands = temperatures decrease. It is especially not complete in undergraduate courses where the teacher may not go into the details of stellar modeling that shows that the resulting balance has the increase in temperature from compression + more fusion mostly canceled by the decrease in temperature caused by the star expanding.

The topic remains education where "lies to children" are used.

Unsupported assertions and an accusation of "baloney" in the mass-luminosity relation (https://en.wikipedia.org/wiki/Mass%E2%80%93luminosity_relation) has nothing to do with the teaching of undergraduate astronomy courses. The physical facts are that if you add mass to a star the star will react with

Stronger gravity (more mass :eek:!)
Compression.
Higher core pressure.
Higher core temperatures.
Greater rate of fusion.

What happens then is that hydrostatic equilibrium is reestablished resulting in the core pressure actually decreasing (see the first link above) possibly because the core stabilizes at a higher core temperature (Tc).
For that matter - do you realize the core temperatures go up in stellar models with mass (the Tc 21 October 2016 from StupendousMan (https://forum.cosmoquest.org/showthread.php?154582-Correcting-errors-in-the-quot-Explore-quot-encyclopedia&p=2374763#post2374763). And that fusion rates go up wit increasing temperature? And that means that there are more photons released and thus a higher luminosity?

OTOH, maybe we are getting into ATM territory - an ATM idea that an increasing rate of fusion does not make stars more luminous?

Ken G
2016-Nov-21, 03:17 PM
If I am not mistaken, a star is fully ionized throughout, except at and very near the photosphere. That makes high opacity and very slow radiative transfer of energy. In the more rarified envelope of a more massive star the transfer is faster but still a snail's pace compared with what it would be if we had neutral gas instead of plasma throughout the envelope at the same radius and density. If I am off here, I welcome help from Ken G or anyone else who can help.There's no question that ionization plays an important role, including doubling the number of particles and reducing the opacity. It also completely changes the ground state, because electrons are such a low-mass particle that they have a low momentum per kinetic energya, whereas neutral hydrogen is not even a fermion! If the question is being asked is, what would the Sun, or Jupiter, be like if we waved a magic wand and made them both neutral without changing their temperature, then they would indeed be a lot different. The Sun's radius would roughly double to maintain force balance at core fusion temperature, but Jupiter's ground state would be changed so completely it probably requires a very small radius to achieve it. So it's a question of when you are comparing the effects of de-ionization.

Or if you just de-ionize Jupiter right now, and don't wait, it will immediately have its temperature go way up because the heavy neutrals will start acting like an ideal gas, barring van der Waals forces and the like, but it still won't expand unless you include all that ionization energy. Did the ionization energy magically disappear when we magically de-ionized Jupiter, or is it still going to be in there? The reason it won't expand without the ionization energy being included is that monatomic nonrelativistic gas pressure is 2/3 the internal kinetic energy divided by the volume, so simply doubling the particles doesn't change either the internal energy or the volume, you just have half the kinetic energy per particle. So the overall question is complicated, one must say what one is comparing when one waves the magic wand. In the solar atmosphere, you can assume that conduction maintains something like a smooth temperature, so going from neutral to ionized does double the pressure if there is not expansion. What happens is the "scale height" roughly doubles as the gas becomes ionized, but there the comparison is at fixed temperature.

Ken G
2016-Nov-21, 03:20 PM
What has been actually shown in this thread is that for larger masses, there is less density and pressure as calculated in solar models.Nope, those are stellar models for zero-age main-sequence stars. I wouldn't highlight the wrong parts of your statements if I were you! And yes, I know the core pressure and density both drop with mass, that's what I've been telling you throughout.



It is physically correct to tell a student that a higher mass star (a star that has mass added to it) has a higher core temperature due to compression because more mass = more compression = higher temperatures because that is basic physics (compressed gases can heat up :eek:). Wrong. I already told you how wrong that claim would be for the Algol binary, right now. I have no idea what part of that you still aren't getting, but perhaps this challenge will help you think: let's say you just told a student that nonsense you quoted above, perhaps someone on this very forum. The student, being a scientific thinker, asks you "but then how come the main-sequence star in Algol is always obeying the mass-luminosity relation as its mass increases, yet the star is always only expanding, not contracting anywhere?" What say you to that student?

You see, a good question will always destroy a poor explanation, and the poor instructor simply hopes the students are not smart enough to ask that good question. The good instructor says, "my goodness, you're completely right, the explanation I've been handing out all these years is sheer nonsense." Yup, that's just what the good instructor must say, it's part of the job.

George
2016-Nov-23, 06:46 PM
If I am not mistaken, a star is fully ionized throughout, except at and very near the photosphere. I don't have that impression because isn't the main reason for convection at the tacholine recombination (even if partial), which increases opacity and creates hot cells that become buoyant? There is a critical luminosity that, if exceeded, causes convection, which may explain the massive star core convections, but may not, seemingly, apply to the sun-like stars.

Your much earlier post that shows how much greater in size are the massive stars (in ratio with their mass) would seem to be enough to verify Ken's arguments, but I am still curious about the cause, since ionization was a simpleton shot that fizzled....

Ken's reference to the Henyey track is interesting. But, the PMS (not main sequence admittedly) for this track reveals a decrease in size since temperatures increases and luminosity remains about the same, so radius must shrink and, therefore, density must increase. But this is with a star with a very low density to begin with, so I don't think this in any way counters your arguments, Ken. What stands out to me is that massive stars have [I]convective cores, thus greater heat transfer to the radiative zone, which, IMO (as an amateur), would simulate something like the red giant phase for a one solar mass star where fusion takes place farther from the original core radius. This should yield low density for massive stars even during their main sequence period.

Am I close? :)

Ken G
2016-Nov-23, 07:03 PM
I don't have that impression because isn't the main reason for convection at the tacholine recombination (even if partial), which increases opacity and creates hot cells that become buoyant? You are probably thinking about helium, which is not fully ionized throughout. But hydrogen is-- except near the surface.

There is a critical luminosity that, if exceeded, causes convection, which may explain the massive star core convections, but may not, seemingly, apply to the sun-like stars.Yes, very massive stars are convective over most of their interior.


Your much earlier post that shows how much greater in size are the massive stars (in ratio with their mass) would seem to be enough to verify Ken's arguments, but I am still curious about the cause, since ionization was a simpleton shot that fizzled....
The reason is simple-- stars contract until their cores are hot enough to fuse hydrogen. A more massive star doesn't have to contract as much to get there, so they are bigger and have lower density. It's a simple consequence of the core temperature being proportional to the gravitational potential energy per particle, which is proportional to M/R.


What stands out to me is that massive stars have [I]convective cores, thus greater heat transfer to the radiative zone, which, IMO (as an amateur), would simulate something like the red giant phase for a one solar mass star where fusion takes place farther from the original core radius.The fusion is still in the core, but you''re right that if the mass gets too big, there is too much convection, and the radiative diffuion argument breaks down. These tend to also be stars where radiation pressure is important, and they have their own mass-luminosity relation more like luminosity proportional to mass (this is also called "the Eddington luminosity").


This should yield low density for massive stars even during their main sequence period.

Just use T ~ M/R, that's the easy way to see that R is nearly proportional to M.

George
2016-Nov-24, 05:05 PM
You are probably thinking about helium, which is not fully ionized throughout. But hydrogen is-- except near the surface. Me thinks I too quickly jump onto causal explanations. Opacity increases exponentially with radius, and I imagined recombination as a big part of it.


The reason is simple-- stars contract until their cores are hot enough to fuse hydrogen. A more massive star doesn't have to contract as much to get there, so they are bigger and have lower density. But this happens when it is very close, or equal to, the same mass as any star that begins hydrogen fusion. So a more massive stars simply continues accretion, which changes things, creating the incorrect view you address.


It's a simple consequence of the core temperature being proportional to the gravitational potential energy per particle, which is proportional to M/R. But what does this look like in a physical explanation? If you don't mind another hip shot....if I understand the virial theorem, half the PE becomes heat, increasing temperature, increasing pressure. But pressure is free to do its thing -- push. So density would decrease as a result of the expansion. But by how much seems to be the crux (of the matter)? The ideal gas law doesn't tell us what happens to P & V as T increases. If P increases more than V increases, density increases, but the opposite would lower density. You are using other tools that reveal these degrees of change, which are still unclear to me, though I haven't read all your posts here, largely due to time constraints, even today.


Just use T ~ M/R, that's the easy way to see that R is nearly proportional to M. But even here one could say that R decreases when T increases, which increases density. That's not what happens, but why?

Happy Thanksgiving and I am thankful to one and all here, BTW.

Ken G
2016-Nov-24, 05:46 PM
Me thinks I too quickly jump onto causal explanations. Opacity increases exponentially with radius, and I imagined recombination as a big part of it.
When opacity comes into play, you need to consider "metals" too, so they do recombine.


But this happens when it is very close, or equal to, the same mass as any star that begins hydrogen fusion. So a more massive stars simply continues accretion, which changes things, creating the incorrect view you address.Not sure what you mean-- you only need 0.1 solar masses for fusion, so we are talking about stars with plenty of mass. The issue is more how much they need to contract before they can reach fusion temperature.


But what does this look like in a physical explanation? If you don't mind another hip shot....if I understand the virial theorem, half the PE becomes heat, increasing temperature, increasing pressure. But pressure is free to do its thing -- push. So density would decrease as a result of the expansion. Yes, no matter how you think of it, the virial theorem gives you that T ~ M/R, and that has density consequences.
But by how much seems to be the crux (of the matter)? The ideal gas law doesn't tell us what happens to P & V as T increases. You don't need the ideal gas law, you can just use P ~ GM2/R4 if you know M and R and want P. Then you get T ~ M/R from the virial theorem, but that does require the ideal gas law because of the reference to T.
You are using other tools that reveal these degrees of change, which are still unclear to me, though I haven't read all your posts here, largely due to time constraints, even today.The key tool is the virial theorem with the ideal gas law, giving T ~ M/R. The consequences for density follow.


But even here one could say that R decreases when T increases, which increases density. That's not what happens, but why?That is what happens if you fix M and consider higher T, you will be talking about more dense stars. As stars contract toward fusion temperature, their density increases.

Ken G
2018-Apr-15, 05:54 AM
Update: It looks like the author of the teachastronomy textbook this forum links to, Chris Impey, has made some important revisions, perhaps due to the comments in this thread (and/or an email discussion I had with him). At https://www.teachastronomy.com/textbook/Properties-of-Stars/Understanding-the-Main-Sequence/ it now says: "The luminosity of the star depends on the way radiation diffuses out from the hot central regions, subject to hydrostatic equilibrium at every point. The result of these calculations is a luminosity that depends strongly on temperature, and so on mass. Intriguingly, the energy generation mechanism does not feature prominently in this calculation." This is a vast improvement, correcting the problem I alluded to, and refuting claims by certain others that my position was "against the mainstream." No more. (It could be noted that the luminosity doesn't depend sensitively on internal temperature either, because as the star contracts, its temperature rises in such a way as to largely compensate for the rising density and retain a consistent total radiative diffusion rate, but this is kind of a detail that is not an essential correction. The main point is, the luminosity does not hinge on the fusion physics, but it does hinge on the radiative diffusion physics.)

grapes
2018-Apr-15, 09:56 AM
Update: It looks like the author of the teachastronomy textbook this forum links to, Chris Impey, has made some important revisions, perhaps due to the comments in this thread (and/or an email discussion I had with him).

Perhaps. But, success, you say


At https://www.teachastronomy.com/textbook/Properties-of-Stars/Understanding-the-Main-Sequence/ it now says: "The luminosity of the star depends on the way radiation diffuses out from the hot central regions, subject to hydrostatic equilibrium at every point. The result of these calculations is a luminosity that depends strongly on temperature, and so on mass. Intriguingly, the energy generation mechanism does not feature prominently in this calculation." This is a vast improvement, correcting the problem I alluded to, and refuting claims by certain others that my position was "against the mainstream." No more. (It could be noted that the luminosity doesn't depend sensitively on internal temperature either, because as the star contracts, its temperature rises in such a way as to largely compensate for the rising density and retain a consistent total radiative diffusion rate, but this is kind of a detail that is not an essential correction. The main point is, the luminosity does not hinge on the fusion physics, but it does hinge on the radiative diffusion physics.)

Ken G
2018-Apr-15, 01:59 PM
It helps restore my faith in the self-correcting nature of scientific thought.

Reality Check
2018-Apr-16, 12:36 AM
Update: It looks like the author of the teachastronomy textbook this forum links to, Chris Impey, has made some important revisions, perhaps due to the comments in this thread (and/or an email discussion I had with him). At https://www.teachastronomy.com/textbook/Properties-of-Stars/Understanding-the-Main-Sequence/ it now says: "The luminosity of the star depends on the way radiation diffuses out from the hot central regions, subject to hydrostatic equilibrium at every point. The result of these calculations is a luminosity that depends strongly on temperature, and so on mass. Intriguingly, the energy generation mechanism does not feature prominently in this calculation." This is a vast improvement, correcting the problem I alluded to, ...
A couple of years ago we had More massive stars have greater gravity that creates higher pressure in the stellar interior" (https://forum.cosmoquest.org/showthread.php?154582-Correcting-errors-in-the-quot-Explore-quot-encyclopedia&p=2268305#post2268305) and your unsupported assertion that was wrong. The scientific evidence in this thread that central pressure does go down with mass came 9 months later from StupendousMan (https://forum.cosmoquest.org/showthread.php?154582-Correcting-errors-in-the-quot-Explore-quot-encyclopedia&p=2374763#post2374763)

One good source for information on stellar interiors is a website run by Lionel Siess, a stellar astronomer at the Institute of Astronomy and Astrophysics at the Université Libre de Bruxelles. Here's his main home page's address:

http://www.astro.ulb.ac.be/~siess

Since Dr. Siess has published some 30+ papers in the technical literature as first author, in addition to many as co-author, I think we can accept his work as authoritative. Again, his research area is stellar interiors and evolution.

Now, he provides many very handy tools on his website that visitors can use to generate models of stars of various ages, masses, and chemical compositions. I used this one

http://www.astro.ulb.ac.be/~siess/pm...ols/Isochrones

...
Note that as the mass of a star increases from 0.5 to 7 solar masses, the central temperature goes UP by a factor of about 3, but the central density goes DOWN by a factor of about 8. The result is that the central pressure decreases with mass.

Many thanks to Lionel Siess for providing these tools for all of us, in addition to his many papers!
However the new text you quote does not actually say central pressure reduces with mass in stellar models.

Understanding the Main Sequence (https://www.teachastronomy.com/textbook/Properties-of-Stars/Understanding-the-Main-Sequence/)


Why does luminosity depend so strongly on mass? An increase in mass corresponds to a star with a substantially higher temperature in the core. The luminosity of the star depends on the way radiation diffuses out from the hot central regions, subject to hydrostatic equilibrium at every point. The result of these calculations is a luminosity that depends strongly on temperature, and so on mass. Intriguingly, the energy generation mechanism does not feature prominently in this calculation. That's why astrophysicists like Arthur Eddington were able to understand the main sequence even before the theory of the fusion process was developed!
The bit that may be included from your comments is that knowledge of fusion is not needed (if I remember correctly all Eddington needed was gravity + gas laws + entropy?).

Ken G
2018-Apr-16, 10:12 AM
A couple of years ago we had More massive stars have greater gravity that creates higher pressure in the stellar interior" (https://forum.cosmoquest.org/showthread.php?154582-Correcting-errors-in-the-quot-Explore-quot-encyclopedia&p=2268305#post2268305) and your unsupported assertion that was wrong. What are you even talking about? My assertions were all correct. Why are you bringing in this non sequitur to the issue that was corrected that I just pointed out? The error you just quoted was a different one that I also pointed out. But do you finally realize you were mistaken all along? Read the thread, you were.

The scientific evidence in this thread that central pressure does go down with mass came 9 months later from StupendousMan (https://forum.cosmoquest.org/showthread.php?154582-Correcting-errors-in-the-quot-Explore-quot-encyclopedia&p=2374763#post2374763)That may have been when you understood the situation. I did from the start, as that thread shows. Just read it again.


However the new text you quote does not actually say central pressure reduces with mass in stellar models.
Yes we call all read, I don't know if that different error appears somewhere else in the text or not, but it's not one I'm talking about here. Try to keep up, the corrected error was the one about the mass-luminosity relation hinging on fusion physics. That's what has been corrected, in contradiction to the many false claims you made above and seem to have conveniently forgotten about. The part I pointed to did not mention core pressure, and I don't know what it currently claims about that, but hopefully it is correct that the core pressure drops in more massive stars, as I knew all along. I also knew all along that fusion physics was not crucial to the mass-luminosity relation, which is what I'm actually talking about now because it has been corrected.


The bit that may be included from your comments is that knowledge of fusion is not needed (if I remember correctly all Eddington needed was gravity + gas laws + entropy?).The key is radiative diffusion. Read the thread, it's all spelled out quite clearly, a long time ago. Are you on board yet?

Reality Check
2018-Apr-17, 12:17 AM
What are you even talking about?...
I am talking about the documented facts in this thread as in my post:

A couple of years ago we had More massive stars have greater gravity that creates higher pressure in the stellar interior" (https://forum.cosmoquest.org/showthread.php?154582-Correcting-errors-in-the-quot-Explore-quot-encyclopedia&p=2268305#post2268305) and your unsupported assertion that was wrong. The scientific evidence in this thread that central pressure does go down with mass came 9 months later from StupendousMan (https://forum.cosmoquest.org/showthread.php?154582-Correcting-errors-in-the-quot-Explore-quot-encyclopedia&p=2374763#post2374763)

You made an unsupported assertion. StupendousMan supported your assertion. Thus your assertion were correct.

Ken G
2018-Apr-17, 12:27 AM
You made an unsupported assertion. StupendousMan supported your assertion. Thus your assertion were correct.
Well I'm very glad we could clear up that I made correct assertions. I try. But what you count as "support" is different from what I count as support-- I include arguments from basic laws of physics, you need authority to do it for you. The problem is, the authorities can disagree with each other, because graduate level textbooks can say one thing, and elementary intro texts another, as in this thread. But yes, I realize it is always a sticky situation when some of the "authorities" are wrong, but you must remember, elementary textbooks and course websites really aren't the kind of authorities that don't make easily exposed mistakes, they just don't make them often.

A basic physics argument always trumps a weak authority like that, in fact it's how science self-corrects. Citing advanced textbooks often takes the argument out of the sphere where non-experts can understand it, hence the need for simple basic physics arguments like those I provided above. The question of this thread is, what to do when the people providing the simple arguments have stated something that is the opposite of correct, and the people providing detailed arguments are not interested in making simple easily understood statements? Something of a gap is created there, and this thread is a beautiful case study in just exactly that. In my view, when such a gap exists, it's useful to have people who can provide simple physics arguments from basic principles, and that is how I have attempted to fill that gap here. You're welcome.

Hornblower
2018-Apr-17, 01:42 AM
I did a sanity check on my own and concluded that if a main sequence star of 10 solar masses also has about 10 times the diameter of the Sun, which I think is a pretty good estimate, the pressure throughout, including the center, will be a lot lower. It is easy to fall into the trap of thinking the greater mass means greater gravitational weight, and thus the need for higher pressure to support it. Someone in that trap has overlooked the fact that each increment of the star is 10 times as far out, greatly reducing its gravitational weight. I realize I did not do a rigorous calculation of the density profile, because I do not have all of the math knowhow that Eddington et. al. did, but I am confident I am on the right track.

My question: Why aren't the graduate level experts making a blistering denunciation of the underlings who are continually regurgitating the wrong stuff? Are they unaware that some astronomy majors may be having to unlearn mistakes as they head for graduate school?

Ken G
2018-Apr-17, 02:37 AM
I did a sanity check on my own and concluded that if a main sequence star of 10 solar masses also has about 10 times the diameter of the Sun, which I think is a pretty good estimate, the pressure throughout, including the center, will be a lot lower.Yup.
It is easy to fall into the trap of thinking the greater mass means greater gravitational weight, and thus the need for higher pressure to support it. Someone in that trap has overlooked the fact that each increment of the star is 10 times as far out, greatly reducing its gravitational weight.Precisely, weight involves more than mass, it also involves distance from the center. This is also why red giants puff out so much-- they need to reduce the weight of their envelope, or it presses down too hard and induces ghastly fusion rates. But note also that red giants cannot regulate their fusion the way regular stars do, so for red giants, fusion physics is actually quite important, unlike for main-sequence stars. The main point is, science is the one place where "truthy" is not supposed to be enough, we have to take the extra step to make sure it actually makes sense.


My question: Why aren't the graduate level experts making a blistering denunciation of the underlings who are continually regurgitating the wrong stuff? It's a good question. All I can tell you is that it is unbelievably difficult to try to correct basic textbooks, you face equal doses of skepticism from those who can't follow the argument, and apathy from those who can, but don't care what the textbooks say.


Are they unaware that some astronomy majors may be having to unlearn mistakes as they head for graduate school?And some never do, the myths die so hard.

George
2018-Apr-19, 05:51 PM
I did a sanity check on my own and concluded that if a main sequence star of 10 solar masses also has about 10 times the diameter of the Sun, which I think is a pretty good estimate, the pressure throughout, including the center, will be a lot lower.Yup.
Thanks, this is georgeeze stuff! To further this, here's a table that articulates y'all's points (I think)...

23167

This simply takes the ideal gas law as a general rule of thumb and using it for a list of main sequence stars from O6 to M8 (per Wiki's main sequence page).

Reality Check
2018-Apr-19, 10:09 PM
Well I'm very glad we could clear up that I made correct assertions. I try. But what you count as "support" is different from what I count as support-- I include arguments from basic laws of physics, you need authority to do it for you.
What we have cleared up is that you made unsupported assertions in this thread that someone else later researched and found to be correct. The point I am making is not whether you were correct or incorrect. The point is that you made another person do research to support your assertions when you should already have supporting sources to include in your posts. Or links to posts in another thread (see below). You had 9 months to do that - people produce babies in that time :).

Arguments from basic laws of physics would be stating those laws and deriving that your assertions were valid from them. If you had done that then the assertions would have been supported. I cannot find laws of physics stated in the posts here (maybe in the other thread that is mentioned early on?).

Hornblower
2018-Apr-19, 10:51 PM
What we have cleared up is that you made unsupported assertions in this thread that someone else later researched and found to be correct. The point I am making is not whether you were correct or incorrect. The point is that you made another person do research to support your assertions when you should already have supporting sources to include in your posts. Or links to posts in another thread (see below). You had 9 months to do that - people produce babies in that time :).

Arguments from basic laws of physics would be stating those laws and deriving that your assertions were valid from them. If you had done that then the assertions would have been supported. I cannot find laws of physics stated in the posts here (maybe in the other thread that is mentioned early on?).

He did the work about 12 years ago and posted it here back then.

Reality Check
2018-Apr-20, 12:15 AM
He did the work about 12 years ago and posted it here back then.
Which rather emphases my point - a link to that work in this thread would have short-circuited 9 months (with only a few posts though) of discussion here.

ETA: A thought - Is that work still on the forum? If not, then memories that it existed is not support for his assertions.
However the latest started thread link on profiles actually goes back 12 years so here it is: Why are high-mass stars are so luminous? (https://forum.cosmoquest.org/showthread.php?34341-Why-are-high-mass-stars-are-so-luminous&highlight=)

Swift
2018-Apr-20, 01:41 AM
You had 9 months to do that - people produce babies in that time :).

Reality Check,

You seem to have a general difficulty keeping the conversation polite; given that, it is best you leave out the smart-mouth comments, smilies or not.

Ken G
2018-Apr-20, 02:30 AM
Which rather emphases my point - a link to that work in this thread would have short-circuited 9 months (with only a few posts though) of discussion here.My style is simply to explain the physics as simply as possible without making it entirely wrong, rather than relying on elementary generic textbooks to quote truthy-sounding things on my behalf, without checking them. I know that elementary textbooks sometimes make mistakes that contradict more advanced texts, but the more advanced texts aren't as interested in giving simple explanations, creating the gap I try to fill. For many people, the simple explanations are what they want to know, and they are my target audience. Others, not so much, they just want to quote authorities like that's what science is about. But interesting in this context is Feynman's definition of science: "belief in the ignorance of experts." Ponder that. Although this forum requires rules to keep ATM discussions at bay, we don't have to completely forget the wisdom of Feynman in the process.

Besides, you are mistaken if you think the core pressure is the entire issue here, or that saying high-mass stars have high core pressure is the sole error made by the elementary textbooks. Some textbooks don't claim the core pressure is higher, they just claim the core temperature is higher, and that makes the fusion faster, and that makes the luminosity higher. Well, the core temperature is higher, and the fusion rate is faster, but both those things are true because the luminosity is higher-- not the other way around. This is obvious for several logical reasons I have given many times, but can repeat:
1) the luminosity of radiatively diffusing stars was understood prior to knowing anything about fusion.
2) the luminosity of radiatively diffusing stars is set in the pre-main-sequence (ponder that as long as it takes).
3) the same textbooks that botch the cause of the mass-luminosity relation often say the fusion rate self-regulates, and this keeps the star from exploding like an H bomb. They simply forget to notice the ramifications of having the fusion self-regulate: self-regulate to what? Answer: to the luminosity.
So no, I could not have made all this clear simply by posting core pressures, all that would do is prove what I already know, what Feynman knew, and what you really should too: elementary textbooks make mistakes, but nothing trumps a basic, well-reasoned physics argument. When the argument is wrong, its flaws can be teased out using basic logic. The google searches can help with that, but should never replace it, lest poor Feynman should roll over in his grave.

George
2018-Apr-20, 01:53 PM
So no, I could not have made all this clear simply by posting core pressures, all that would do is prove what I already know, what Feynman knew, and what you really should too: elementary textbooks make mistakes, but nothing trumps a basic, well-reasoned physics argument. When the argument is wrong, its flaws can be teased out using basic logic.
And astronomers provide the pudding for the "proof". [My pudding ingredients in the prior post were right, but not my cooking. This batch should be pretty tasty.]

The O6 data reveals a star with an overall density of 1% of the Sun, supporting Hornblower's (and prior ones as well, IIRC) claim.

23168

So how can a massive star put the squeeze on its core when its overall density is only 1% that of our little white Sun?

grant hutchison
2018-Apr-20, 02:02 PM
Which rather emphases my point - a link to that work in this thread would have short-circuited 9 months (with only a few posts though) of discussion here.

ETA: A thought - Is that work still on the forum? If not, then memories that it existed is not support for his assertions.
However the latest started thread link on profiles actually goes back 12 years so here it is: Why are high-mass stars are so luminous? (https://forum.cosmoquest.org/showthread.php?34341-Why-are-high-mass-stars-are-so-luminous&highlight=)That link was provided in post #65 (https://forum.cosmoquest.org/showthread.php?154582-Correcting-errors-in-the-quot-Explore-quot-encyclopedia&p=2374626#post2374626), a year and a half ago, after Hornblower gave you directions on how to find it in post #62 (https://forum.cosmoquest.org/showthread.php?154582-Correcting-errors-in-the-quot-Explore-quot-encyclopedia&p=2374568#post2374568).


I'm sorry, but I feel confident that Ken is correct on this issue. Please review the whole thread, including my posts, and look for Ken's detailed references to Arthur Eddington's work about 1915, long before nuclear fusion was envisioned, let alone confirmed. I checked up on my own by applying the gas laws and a correct integration of the gravitational weight of the stellar envelope. To find the previous thread, go to Advanced Search, enter Ken G as user and Eddington as a key word. That should return a thread in the fall of 2005, even with this clunky search function.


This one (https://forum.cosmoquest.org/showthread.php?34341-Why-are-high-mass-stars-are-so-luminous)? Use google with "site:cosmoquest.org" to bypass any clunkyness from builtin functions. Some experts posting there that sadly haven't been seen here in ages :/

Grant Hutchison

Hornblower
2018-Apr-20, 02:17 PM
And astronomers provide the pudding for the "proof". [My pudding ingredients in the prior post were right, but not my cooking. This batch should be pretty tasty.]

The O6 data reveals a star with an overall density of 1% of the Sun, supporting Hornblower's (and prior ones as well, IIRC) claim.

23168

So how can a massive star put the squeeze on its core when its overall density is only 1% that of our little white Sun?
Follow the links provided by Grant Hutchison and read posts 62 through 65. I explained my take on it there.

George
2018-Apr-20, 03:25 PM
Follow the links provided by Grant Hutchison and read posts 62 through 65. I explained my take on it there. Oops, I somehow had in my head that you had suggested 1% for an O class star. In looking over all those posts recommended, I don't see specific example cases. This table supports the physics stated. [It's also a subliminal color message for another error in some textbooks. :)]

Hornblower
2018-Apr-21, 12:09 PM
And astronomers provide the pudding for the "proof". [My pudding ingredients in the prior post were right, but not my cooking. This batch should be pretty tasty.]

The O6 data reveals a star with an overall density of 1% of the Sun, supporting Hornblower's (and prior ones as well, IIRC) claim.

23168

So how can a massive star put the squeeze on its core when its overall density is only 1% that of our little white Sun?

My bold. The same way the Sun does on its core. Gravity. The more massive star just doesn't squeeze as hard, but still plenty to induce as much fusion as is needed to stabilize the star.

Ken G
2018-Apr-21, 02:52 PM
Also, I would be careful with the term "stabilize." I know what you mean-- that fusion greatly slows the timescale for the star to undergo changes, and a star that changes only very very slowly has been "stabilized." The problem is, stability is a concept of its own, and has to do with the ability to maintain force balance without having catastrophic collapses (like core-collapse supernovae), and the ability to maintain an energy balance without fusion runaway (like type Ia supernovae). So the discovery of supernovae was the discovery that stars are not always stable, but in that more formal sense of the term, fusion is not required to "stabilize" stars, they are usually quite stable with or without fusion.

The reason I mention this, even though I know the meaning you are taking for the word, gets into another error you will sometimes find in elementary textbooks! They imply that without fusion, the star could not hold itself up (and sometimes even point to some erroneous role for the pressure of the radiation that fusion produces). But of course gas pressure is perfectly able to hold up lower-mass stars like the Sun with no help from radiation or fusion. Radiation pressure does essentially nothing in those stars, and fusion only keeps the star from changing for a much longer time than without it, but the star is still "stable" either way. It's just a question of the timescale for drastic change being, say, 10 million years (if there were no fusion), or 10 billion years (with fusion).

George
2018-Apr-21, 05:47 PM
My bold. The same way the Sun does on its core. Gravity. The more massive star just doesn't squeeze as hard, but still plenty to induce as much fusion as is needed to stabilize the star. Sorry, I was being rhetorical and arguing your point by expanding your O class example by extending it to actual stars across the classes.

Reality Check
2018-Apr-22, 11:40 PM
That link was provided in post #65 (https://forum.cosmoquest.org/showthread.php?154582-Correcting-errors-in-the-quot-Explore-quot-encyclopedia&p=2374626#post2374626), a year and a half ago, after Hornblower gave you directions on how to find it in post #62 (https://forum.cosmoquest.org/showthread.php?154582-Correcting-errors-in-the-quot-Explore-quot-encyclopedia&p=2374568#post2374568).
Thanks grant - I missed it because it was an answer to Hornblower. Still a minor nitpick that Ken G did not give the link but that is excusable for a 12 year old thread.

grant hutchison
2018-Apr-22, 11:59 PM
Thanks grant - I missed it because it was an answer to Hornblower. Still a minor nitpick that Ken G did not give the link but that is excusable for a 12 year old thread.See Ken's response to that link in post #67 (https://forum.cosmoquest.org/showthread.php?154582-Correcting-errors-in-the-quot-Explore-quot-encyclopedia&p=2374632#post2374632). Are you suggesting he had some duty to repeat the same link in one of his own posts? That seems a very minor nitpick.

And also seems likely that you didn't miss the link, at the time. You quoted it yourself in post #72 (https://forum.cosmoquest.org/showthread.php?154582-Correcting-errors-in-the-quot-Explore-quot-encyclopedia&p=2374652#post2374652):

An interesting post from Tim Thompson in the other mass/luminosity thread (https://forum.cosmoquest.org/showthread.php?34341-Why-are-high-mass-stars-are-so-luminous/page2) in 2005:

This obviously has to be true, and as fate would have it, it is true. Massive stars have enormous central pressures, as high as 100,000 times the central pressure of the sun, but only after evolving off the main sequence (which happens more quickly for higher mass). Indeed the central pressure for main sequence massive stars is much lower than I expected, although I'm supposed to know better.

A zero age main sequences (ZAMS) 15 solar mass star has a central temperature about 34,000,000 Kelvins, only about twice that of the sun (15,600,000 Kelvins), and a central density of only 6.3 gm/cm3, far less than the sun (150 gm/cm3). Since the pressure is directly proportional to the density in this case, it will actually be somewhat lower than the sun's central pressure.

However, let that 15 solar mass star hang around for about 10,000,000 years (and remember our sun is about 5,000,000,000 years old), and it starts it's journey off the main sequence. It will take about 2,000,000 years to complete that journey, during which time the density will skyrocket to over 106 gm/cm3, indeed over 107 near the end (Eid, Meyer & The, 2004). That would make the central pressure ~10,000 - 100,000 times the solar central pressure, but with a central temperature above 109 Kelvins, it's no surprise that the pressure has to be that high, to prevent expansion & cooling of the core. But the pressure will not be directly proportional to the density, either, but either to (density)5/3 for degenerate matter, or (density)4/3 for relativistically degenerate matter (An Introduction to the Theory of Stellar Structure and Evolution, Dina Prialnik, Cambridge University Press, 2000, ch. 7).

It was this high temperature, non main sequence case, that I had in mind originally (it did not occur to me that you were talking about main sequencee stars). I also refer the reader to an excellent review of the evolution of high mass stars: The evolution and explosion of massive stars (http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2002RvMP...74.1015W&db_key=AST&d ata_type=HTML&format=&high=4366fa465106188), Reviews of Modern Physics 74: 1015-1071, October 2002. Woosley is especially into massive stars, and a search of the ADS on his name as author will reveal quite a bit of work on massive stars. The RMP paper goes as high as 75 solar masses. Eid, Mayer & The stop at 30 solar masses. Prialnik's discussion of density & pressure is easier to follow than some other sources.
Still leaves the question whether the core pressure of main-sequence stars increases with mass open though.You seem to have read at least as far as post #53 (https://forum.cosmoquest.org/showthread.php?34341-Why-are-high-mass-stars-are-so-luminous&p=597344#post597344) in a 54-post thread.

Grant Hutchison

Reality Check
2018-Apr-23, 12:31 AM
See Ken's ...
I am saying that when starting a thread on a similar topic as an existing thread, it is good manners to link back to that thread, e.g. in the OP. Likewise when making assertions in a post using evidence in another thread, it is good manners to link to that thread in that post. But that was fixed by other posters later. So a minor or even very minor nitpick.

It seems that a couple of years ago I looked through the old thread but did not see the evidence from Ken G, e.g. the luminosity relation was established before fusion was known to power stars.

grant hutchison
2018-Apr-23, 12:54 AM
I am saying that when starting a thread on a similar topic as an existing thread, it is good manners to link back to that thread, e.g. in the OP. Likewise when making assertions in a post using evidence in another thread, it is good manners to link to that thread in that post.Good manners. I see. Thanks.

Grant Hutchison

Ken G
2018-Apr-23, 01:18 AM
I apologize for any and all bad manners I may have had in trying to help people understand how stars work. But if they understand now, I'm happy, all the same.

Hornblower
2018-Apr-23, 03:15 PM
Also, I would be careful with the term "stabilize." I know what you mean-- that fusion greatly slows the timescale for the star to undergo changes, and a star that changes only very very slowly has been "stabilized." The problem is, stability is a concept of its own, and has to do with the ability to maintain force balance without having catastrophic collapses (like core-collapse supernovae), and the ability to maintain an energy balance without fusion runaway (like type Ia supernovae). So the discovery of supernovae was the discovery that stars are not always stable, but in that more formal sense of the term, fusion is not required to "stabilize" stars, they are usually quite stable with or without fusion.

The reason I mention this, even though I know the meaning you are taking for the word, gets into another error you will sometimes find in elementary textbooks! They imply that without fusion, the star could not hold itself up (and sometimes even point to some erroneous role for the pressure of the radiation that fusion produces). But of course gas pressure is perfectly able to hold up lower-mass stars like the Sun with no help from radiation or fusion. Radiation pressure does essentially nothing in those stars, and fusion only keeps the star from changing for a much longer time than without it, but the star is still "stable" either way. It's just a question of the timescale for drastic change being, say, 10 million years (if there were no fusion), or 10 billion years (with fusion).

A more detailed answer to avoid oversimplification and possible misunderstandings about what I meant by stability:

A high-mass star puts the squeeze on its core in the same way the Sun does, by means of the pressure generated by the gravitational weight of the overlying material. It is more gentle in the sense of lower density and pressure at the center, but the dynamics are such that nevertheless there is plenty of heat and pressure to induce as much fusion as is needed to balance the greater outflow of heat through the more rarefied envelope and keep the star in its main sequence state for far longer than would be the case without the fusion. The thermodynamics are such that we have a stable equilibrium.

I was answering what I thought was a straightforward question, and I am baffled by George's response.

George
2018-Apr-23, 05:12 PM
I was answering what I thought was a straightforward question, and I am baffled by George's response. Why?

Your example case of a 10 solar mass star was a great way to argue the main point in this thread. A radius increase of a star by 10x makes it 1000x larger in volume, so with only a 10x increase in solar mass, it is obvious to an "Average Joe" that density must necessarily be much less and it's not difficult to extend this lower density idea into the core region as well. As the "Average Joe" around here, I enjoy pointing out, at times, the arguments that stand out as more significant to help students, and amateurs like me, understand the key points being made. Your example is one of those.

The table only reinforces what you said, right? The Wiki data was used for specific, and named, MS stars as examples in each stellar class, so I used this data to calculate a simple (average) density as shown in the last column (M/V). The O6 example, for instance, happens to match your value of 1% (10/1000) to affirm your point, but it also shows how the average density increases from there for the other classed stars.