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View Full Version : Persistent astrophysical error about massive main sequence stars.



Hornblower
2017-Nov-06, 05:03 PM
The following link is copied from a recent thread about star colors in Q&A.

http://faculty.wcas.northwestern.edu/~infocom/The%20Website/evolution.html

Once again I have encountered what appears to be a common fundamental error in accounting for the mass-luminosity relationship for main sequence stars. It has been discussed at length in this forum, but newer members may not have seen it.

The author asserts that a greater mass results in higher pressure in the core, which jacks up the fusion rate and makes the star disproportionately more luminous. In a thread about 12 years ago our friend Ken G, a physicist if I am not mistaken, insisted that in a more massive star that for whatever reason has stabilized at a radius proportional to its mass, the pressure at the center will be lower than in the lower mass star, though still plenty to induce fusion if it is hot enough. He referred to the work of Sir Arthur Eddington and colleagues a century ago, before fusion was known or even thought of, in which they found pretty good agreement between theory and observation, based on the properties of ideal gases along with the increase in opacity and consequent decrease in escaping heat as the protostar contracts out of a primordial nebula. Subsequent studies show that when reaching a quasi-stable state predicted by Eddington, the star induces enough fusion to keep itself stable for a very long time, and functions as its own thermostat. This fusion is a low-intensity action, just a few watts per ton for the Sun, and initially does not make a major change as it ramps up.

I did an exercise in calculus as a sanity check and concluded that Ken is right, and that someone garbled something in the meantime. We don’t know when or where or why that happened, but it appears that people who should know better are either blindly repeating that garble or are not bothering to speak up and correct it. My hunch is that someone confused the dynamics in a main sequence star with an evolved giant of the same total mass, in which the star has become stratified, and the core is indeed much more compressed and much hotter, and is jacking up the fusion rate of overlying hydrogen.

Mr. Taylor at Northwestern University says in his website that he teaches physics, but he does not say at what level. For all I know he could be an instructor in entry level physics for liberal arts majors, and as such not be active in nuclear physics or the astrophysics of star interiors. Even so, a simple exercise with the gas laws on a ball of gas of uniform composition, as is the case at zero-age main sequence, should raise a red flag.

Ken’s thread can be found by Googling “site:cosmoquest.org ken g eddington”. That works better than the clunky search function that is built into this forum.

George
2017-Nov-06, 09:55 PM
His degree (PhD) seems to be in physics education (Maryland, '83). I found that "Dr. Taylor is especially interested in teaching physics to nonscience majors and to the lay public." [my bold] Perhaps this goes to the heart of the lack of accuracy.

He starts off correctly by stating for stars that, "the great majority can be characterized by just two parameters: their mass and their age."

His side page on star color (http://faculty.wcas.northwestern.edu/~infocom/The%20Website/plates/not%20red.pdf) needs some changes. He has the Sun as yellow-white in the main page, then white on the color page.

He states, "Except perhaps for a very few, very bloated stars known as carbon stars (because they have so much raw carbon – that is, soot – in their atmospheres), red stars only seem red when viewed through a spectroscope. To the naked human eye, they would look quite white." I would hope he could get a refund on that spectroscope. *wink*

The weaknesses in the claims seem to be in trying to present an oversimplified model. I think his pressure and temperature views are likely fine if he was restricting his point to protostars prior to hydrostatic equilibrium, but he is specifically misapplying it to main sequence stars. He fails to mention the importance of Ken's key points about opacity and luminosity leaking.

Hornblower
2017-Nov-07, 03:34 PM
When Dr. Taylor and others characterize the Sun as yellowish white, I would cut them some slack because that is how it looks to me, even near the zenith in a clear sky. Likewise with any incandescent light that is so bright that it saturates my color vision. Under such conditions I see yellowish white.

To return to my topic of choice involving the interiors of massive main-sequence stars, I find it perplexing that there appear to be two populations of writers who do not appear to communicate with one another. One includes Eddington and his successors who have done the actual research and calculations, and have written papers that are not widely seen by the general public. The other consists of authors of popular textbooks who appear to have repeated a mistake over so many generations that it has become something resembling common knowledge to those (most of us) who have not done the exercise in calculus. What I am wondering now is what is typically encountered in the type of college freshman astronomy course that is a prerequisite for a major in astronomy.

George
2017-Nov-07, 04:25 PM
When Dr. Taylor and others characterize the Sun as yellowish white, I would cut them some slack because that is how it looks to me, even near the zenith in a clear sky. Likewise with any incandescent light that is so bright that it saturates my color vision. Under such conditions I see yellowish white. Right, "under those conditions". You are at least qualifying the Sun's color. But normally context is not included and, worse, the Sun, even in textbooks, is graphically portrayed as an extended object in space, and without being 10,000x beyond our photopic limit (when we look up at it) or as a sunset view of it.


The other consists of authors of popular textbooks who appear to have repeated a mistake over so many generations that it has become something resembling common knowledge to those (most of us) who have not done the exercise in calculus. What I am wondering now is what is typically encountered in the type of college freshman astronomy course that is a prerequisite for a major in astronomy.
I think the color ambiguity should serve to help make your point about articles that perpetuate erroneous information. It is why I raised the yellow Sun error, or ambiguity if you prefer. The problem is that the context is rarely presented and, if it is, it often doesn't remove the confusion, which is what has happened in his presentation for star colors. We all learned that it is a yellow dwarf G2V star and we need not be bothered with facts, unless the facts will somehow make a real difference to science, perhaps.

Similarly, though I could be confused, his thermodynamic description is correct in the context of a protostar. Am I correct in this? But he states it is for a star in hydrostatic equilibrium, so he, as you note, is repeating erroneous views that need correcting.

Hornblower
2017-Nov-07, 05:34 PM
Similarly, though I could be confused, his thermodynamic description is correct in the context of a protostar. Am I correct in this? But he states it is for a star in hydrostatic equilibrium, so he, as you note, is repeating erroneous views that need correcting.
My bold. I doubt it. My hunch is that the more massive protostar will have a density and pressure curve throughout the early contraction that is similar to that of the stabilized main sequence state, for the same reasons. That curve would be the density as a function of the elevation from the center as a percentage of the overall radius. I would have to yield to the real experts to have my hunch evaluated. As I understood it from the old thread, the more massive body gets just as hot inside at a much more rarefied state than that of the less massive one, and I would expect that heat to resist any tendency for the core to become disproportionately dense during the protostar stage, just as it does in the stabilized main sequence state.

Hornblower
2017-Nov-08, 01:23 PM
In my opinion the color terminology issue is a very minor semantic grievance. What we have here is a modest shift of the commonly used color names toward the red end of the spectrum and not explicitly stating just how pastel these tints are. To me this is far less bothersome than the terms early and late for spectral types, or the practice of referring to all elements heavier than helium as metals. These do not bother me all that much because they are one-word terms for which technically superior substitutes mean more verbal clutter. All of this is jargon that has evolved over modern astronomical history. I consider it a far cry from the major physics blunder of getting the mass/core-density relationship backward for main sequence stars.

George
2017-Nov-09, 03:57 PM
My bold. I doubt it. My hunch is that the more massive protostar will have a density and pressure curve throughout the early contraction that is similar to that of the stabilized main sequence state, for the same reasons. That curve would be the density as a function of the elevation from the center as a percentage of the overall radius. I would have to yield to the real experts to have my hunch evaluated. I'm unclear about a lot of things in stellar formation, but it seems that what you are saying is not that different than what he (Taylor) and I am saying. I'm, however, restricting it to the very earliest period for the proto-star, on or before the Class 0 period. His application of it to main sequence stars, of course, is the problem you present.


As I understood it from the old thread, the more massive body gets just as hot inside at a much more rarefied state than that of the less massive one, and I would expect that heat to resist any tendency for the core to become disproportionately dense during the protostar stage, just as it does in the stabilized main sequence state. That is also what I recall from Ken's diligent posts, but my grip is slippery.

I would love to see a step 1 - 12, or whatever, of stellar formation; from cloud fragment to protostar to PMS to MS. I would also hope it would include the microscopic description of each because we have hydrogen disassociation and not long after, ionization. These greatly impact opacity and goes to the heart of Ken's points. In a cursory look at one Harvard paper on Eddington, it seems that Eddington tackled the question of how a star maintains luminosity and saw the importance of opacity.

Another thing that would be helpful to learn in order for me is to understand how it is that the error remains so attractive that it hides itself from highly educated folks?

Look at the equation Taylor presents:

L = C R2 T4

Using my old rusty math techniques, I would want to know temperature for a given radius so that I could derive L. Isn't that the normal approach to any equation like this? But I think, and I could easily be mistaken, that Ken's point is that this is putting the cart before the horse. The key variable isn't temperature or pressure (Taylor) but luminosity. It doesn't change the equation but the equation would be better stated where the variable to be determined is T. Is this a fair analysis? If so, it may help explain why the error persists in explanations.

George
2017-Nov-09, 05:02 PM
In my opinion the color terminology issue is a very minor semantic grievance. What we have here is a modest shift of the commonly used color names toward the red end of the spectrum and not explicitly stating just how pastel these tints are. I agree with that whenever color is being associated with the spectrum (or a point-source solar analog or twin). But if one, however, takes a pure white object and calls it yellow in the context that that is its color without hint of a spectral reference, it looks silly. If a teacher of a pomology course continually states an orange is green, over and over and over and over, shouldn't something be said at some point? The teacher could argue, correctly, that an orange is actually green before it ripens, but that hardly mitigates the error unless the context is explicitly about the un-ripe orange.

I mention color mainly because of its analogy to the regurgitation of the erroneous explanation for MS star structures, and secondarily because he gets color wrong as well. I seriously doubt any high altitude Sun projection would ever look yellow or even yellowish-white; it will look "pure white", as Newton once called sunlight. The very flat photon sp. irr. distribution for an AM0 or AM1 Sun may be the ideal choice for a "pure white" definition, though none exists that I'm aware. Using a yellow term doesn't eschew obfuscation and could make some folks look -- the one thing anathema to science -- silly. Is it a big deal, no, because we both agree it won't advance actual science, but why let it drag on?


To me this is far less bothersome than the terms early and late for spectral types, or the practice of referring to all elements heavier than helium as metals.Yet the oddity of the astronomical definition for metals is understandable given that they are so scarce in the universe, and its use isn't ambiguous or erroneous like a yellow Sun (unless color context is stated).


All of this is jargon that has evolved over modern astronomical history. Yes, and reading and learning about astronomical history is nothing short of wonderful. The yellow sun history is yet another curious set of circumstances that are valid and invalid, which can serve to demonstrate how science advances because it helps explain how science works and astronomy, in particular, is all about what we see, which involves color to some extent. Have you noticed how more and more textbooks today are using the white adjective for the sun and not yellow? Unfortunately, perhaps > 80% of the color graphics for a Sun in space still choose to make it more, well, colorful. My personal involvement is perhaps too deep into it because a yellow sun (without any spectral context) is a lot like a green orange for me. I think it is a big enough issue for someone to do a scientific paper on it and get the astronomical community and graphics departments corrected, though trivial enough for no one to have already done this, but why let this continue when "silly" is a potential label for any that accidentally, or intentionally, chose to present the extended Sun as we draw it in space with color accurate neighbors as anything other than white?


I consider it a far cry from the major physics blunder of getting the mass/core-density relationship backward for main sequence stars. Yes, otherwise, the color issue would have easily been corrected long ago since a white Sun is no new discovery.

But, again, I didn't want to distract from your important OP, though I thought the analogy worth mentioning. So, I will try and stay on your main topic from this point.