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MG1962A
2006-Oct-09, 09:05 AM
I keep getting told that the sun produced about 75% less energy around 3 billion years ago, than it does today.

I can't find anything on the net. And it doesn't really fit with anything I understand about stella evolution.

So is someone spinning me a story, or isa there new research that may not have hit the net yet?

antoniseb
2006-Oct-09, 10:02 AM
I'd be interested in knowing more about the source for this information. It is true that stars generally increase their energy output as they evolve from the main sequence, but the if the Sun produced only one quarter of the energy then that it does now, it would have been pretty difficult for Early life to form here, since the Earth would have been only slightly warmer than Jupiter's moon Ganymede is now.

MG1962A
2006-Oct-09, 10:15 AM
Yeah - I have been trying to pin down the source - But sounds like you have the same opinion as I do. The information is incorrect

hhEb09'1
2006-Oct-09, 10:20 AM
The information is incorrectWhere are you getting it? You said you keep getting told that?

Jeff Root
2006-Oct-09, 10:27 AM
My extremely vague understanding is that the Sun, when it was
just a toddler, was a T-Tauri type star, which is very bright and
hot and puts out a lot of solar wind. The wind blows away
the gas and dust that has not yet been consolidated into the
Sun, planets, or smaller bodies, which is about half the original
mass of the protoplanetary disk.

-- Jeff, in Minneapolis

StupendousMan
2006-Oct-09, 01:37 PM
I keep getting told that the sun produced about 75% less energy around 3 billion years ago, than it does today.

I can't find anything on the net. And it doesn't really fit with anything I understand about stella evolution.

So is someone spinning me a story, or isa there new research that may not have hit the net yet?

There are plenty of groups who model stellar evolution. Many have created nice websites which show the evolution of stars in their models. Some even let you provide input data and give you the results of the models when you click a button. For example, look at the web site of the BaSTi project:

http://www.te.astro.it/BASTI/index.php

If you play with their models a bit, you can find out for yourself just how much typical solar models might change their luminosity over time. I spent about one minute making a very few test runs, and saw one model increase in luminosity from about 0.75 to 1.0 solar luminosities as it aged from 500 Myr to 5000 Myr.

Perhaps the figure you saw meant "the Sun increased its luminosity from 75 percent of its current value 3 billion years ago ...." instead of "the Sun increased its luminosity by 75 percent since 3 billion years ago ..."

Ken G
2006-Oct-09, 01:57 PM
Yeah, I think StupendousMan (who was that masked man?) has it right. It is natural for stars to increase brightness while they are still on the main sequence (the jargon there is they start at the "zero age main sequence", or ZAMS, and brighten until they reach the "terminal age main sequence", or TAMS), independently from any issues about T Tauri stars or red giants. Just how much they brighten I don't know, that link sounds very good. Nevertheless, not all the problems are solved by going from '75% less' to '75% as much'. There is still a bit of a conundrum for early life, which is that normal evolution models still suggest that Earth would be too cold for life to appear on the surface without including additional factors. One possibility is that the evolution models don't work for the Sun, but the more mainstream explanation is that the Earth must have had a stronger greenhouse effect in the past to keep it warm. If that's true, then the concept of "habitable zone" is seen to be a lot slipperier than you might think-- the Earth would have needed a lot of greenhouse gases in the past to allow life to appear, and as the Sun got brighter, the greenhouse gases would have needed to be reduced to keep it from getting too hot. You begin to see where thinking like the "Gaia hypothesis" begins to come in, where life on Earth can have a regulating effect on the temperature. I don't know if this is viewed as just a coincidental evolution of the greenhouse gases on Earth, or if there really is a feedback mechanism at work, but you can certainly see that the current "global warming" issue can be seen against a very longstanding backdrop. The irony if it is caused by human-made CO2 emissions is that we would have a system of life successfully regulating its environment for billions of years, and the appearance of intelligence rapidly messing up that balance. Kind of the opposite of the science fiction approach to things, isn't it? (Of course, the amount that it is being messed with at the moment is quite small compared to the vast extinctions of the past, so I'm being a bit colorful.)

max8166
2006-Oct-09, 03:02 PM
The theoretical models do point to an ever increasing output from the sun, until it's death as a red giant. I think these pages sum up what Ken G is saying.

http://en.wikipedia.org/wiki/Faint_young_sun_paradox

http://en.wikipedia.org/wiki/Sun#Faint_young_sun_problem

Spaceman Spiff
2006-Oct-09, 03:24 PM
According to modern models of stellar evolution, a star with the mass and bulk composition of our Sun reached the Zero Age Main Sequence (ZAMS) with luminosity of ~70% of its current value (i.e., L_ZAMS = L_now * 0.7). I've attached a small jpeg plot of the evolution of our Sun on the H-R diagram (first one), from the Basti website linked above. Stars do evolve while on the main sequence (MS), because changes in their core composition (increase in helium abundance with time) moves the pressure-gravity equilibrium point to conditions in which the core is both denser and hotter. The higher core temperatures especially increase the hydrogen fusion reaction rates and thus results in an increase in the power released from fusion while on the MS. In the plot, the MS evolution occurs in the lower left corner of the diagram, where you can see the hook up and then around the corner to the right, where (or when) hydrogen core exhaustion occurs. So in general, evolution in time is from lower left toward the upper right, with a loop back down and then up again representing the onset of core helium burning and exhaustion.

In the second plot, again from the same set of models, I have plotted the time evolution of our Sun's luminosity, roughly corresponding to the MS phase. Note that all units on both plots are on a log10 scale, so 0 = 1.0, 8 = 100 million, 9 = 1 billion, etc. Please also note that when log t = 9.66 (present time), the predicted luminosity is just a bit under the present solar value (log L/Lsun = 0.0), for a number of reasons that I needn't go into here.

Nereid
2006-Oct-10, 12:11 AM
Yeah, I think StupendousMan (who was that masked man?) has it right. It is natural for stars to increase brightness while they are still on the main sequence (the jargon there is they start at the "zero age main sequence", or ZAMS, and brighten until they reach the "terminal age main sequence", or TAMS), independently from any issues about T Tauri stars or red giants. Just how much they brighten I don't know, that link sounds very good. Nevertheless, not all the problems are solved by going from '75% less' to '75% as much'. There is still a bit of a conundrum for early life, which is that normal evolution models still suggest that Earth would be too cold for life to appear on the surface without including additional factors. One possibility is that the evolution models don't work for the Sun, but the more mainstream explanation is that the Earth must have had a stronger greenhouse effect in the past to keep it warm. If that's true, then the concept of "habitable zone" is seen to be a lot slipperier than you might think-- the Earth would have needed a lot of greenhouse gases in the past to allow life to appear, and as the Sun got brighter, the greenhouse gases would have needed to be reduced to keep it from getting too hot. You begin to see where thinking like the "Gaia hypothesis" begins to come in, where life on Earth can have a regulating effect on the temperature. I don't know if this is viewed as just a coincidental evolution of the greenhouse gases on Earth, or if there really is a feedback mechanism at work, but you can certainly see that the current "global warming" issue can be seen against a very longstanding backdrop. The irony if it is caused by human-made CO2 emissions is that we would have a system of life successfully regulating its environment for billions of years, and the appearance of intelligence rapidly messing up that balance. Kind of the opposite of the science fiction approach to things, isn't it? (Of course, the amount that it is being messed with at the moment is quite small compared to the vast extinctions of the past, so I'm being a bit colorful.)I'm curious to see if we can get some harder info on early life on Earth, and early surface temperatures.

For example, the basic biochemical machinery of all of today's life was in place ~3 billion years ago*, but as we are increasingly discovering, this machinery is very adaptable - the same basics work for hyper-saline, acidic, anaerobic, high temperature (etc) environments as the ones the cells of our bodies find nice and cosy.

And, since photosynthesis didn't get going until >2 billion years after the Sun formed, life didn't need the Sun as an energy source (just as the chemoautotrophs are able to do fine without it today).

*the 'only' things that happened since were the development of eukaryotic cells (~2 bya), of multicellularity (~1 bya), and body plans (some time later).

George
2006-Oct-10, 01:49 AM
It is interesting to guess what other factors may be contributors...

What about the possibility of the Earth being a little closer to a more massive sun, before the wind blew off?

Whatever the sun's radiation level was back then, the Earth would recive 30% more of it if the Earth were 14% closer.

What about greater internal heat from a greater radioactive decay rate, as well as, the greater molten state due to accretion and impacts?

More vents and volcanoes, maybe?

Ronald Brak
2006-Oct-10, 01:54 AM
The earth was closer to the sun in the past, however, I don't think the loss of mass of the sun over time has been enough to cause the earth to move a significant distance away.

Ken G
2006-Oct-10, 06:49 AM
I think the problem is that with 75% luminosity and the same greenhouse effect we have now, the Earth's temperature would drop by about 15-20 C, and that would make the oceans freeze (what that would do to the greenhouse effect I can only guess, but it doesn't appear to have happened much). What with ice ages and all, it seems the Earth self-regulates by some means to keep itself just above freezing. It couldn't have been measureably closer to the Sun (the Sun's mass loss rate is tiny), and heating from the interior, or volcanoes, or meteorites would not be significant enough. I don't know how reliable the models are, but it seems like they should do pretty well so the luminosity growth seems reasonable.

As for the cause of it, note that you will very often see it said that increased core temperatures increase fusion rates and cause higher luminosities, owing to the extreme temperature sensitivity of fusion. This is not correct-- indeed the extreme temperature sensitivity is exactly why the fusion rate is not controlled by the temperature, the temperature is controlled by the fusion rate. I will bet you dollars to donuts that as the helium concentration increases, some other process causes the luminosity to increase, and the core temperature is forced to rise in response to this elevated need for luminosity. That's pretty much what a stellar core does-- it makes minute adjustments to itself to provide whatever luminosity the star needs to maintain the required structure. My guess is, more helium means fewer electrons and therefore the photons escape more rapidly, increasing luminosity simply by getting out at a faster rate as the Sun ages.

Ronald Brak
2006-Oct-10, 07:35 AM
The earth's atmosphere would be full of greenhouse gas until photosynthesis developed and had enough time to remove most of the CO2. If this resulted in average global temperatures dropping below 0 then you would have a snowball earth, which may have happened in the past. This would stop most photosynthesis and the removal of CO2. Volcanic activity, which presumably would have been more active back then, would gradually return carbon dioxide to the atmosphere until there was enough greenhouse gas to thaw the earth.

Ken G
2006-Oct-10, 07:42 AM
That might be a reasonable feedback mechanism, I don't know because H2O is also a greenhouse gas, and ice is very reflective, so a lot of issues come into play there. Also, I think most of the CO2 elimination is by inorganic chemical processes in the ocean, not related to life. I'm not sure the role of photosynthesis in eliminating CO2, that came up on another thread but seemed controversial. But you're basic point is right that there certainly could be mechanisms that tend to maintain a planet just above the melting point of ice, and that seems to be the case for Earth however it is happening.

Ronald Brak
2006-Oct-10, 08:25 AM
Most carbon removed from the atmosphere in the oceans is done by lifeforms using it to make their shells. Without life the oceans would be saturated with carbonic acid and would absorb no more, so chemical weathering of rock probably wouldn't absorb much CO2. Photosynthesis removes CO2 from the astmosphere by trapping it in plant remains which then become part of the crust. This is gradually recycled by tentonic activity. Photosynthesis also makes large amounts of free oxygen possible in the atmosphere. If photosynthesis mostly stopped volcanoes would increase the levels of CO2. It might take time to overcome the high albedo resulting from an icy planet, but it should eventually happen.

Nereid
2006-Oct-10, 01:53 PM
Maybe we can refine our discussion a bit - that there is, was, and has been since the magma oceans of the period of late heavy bombardment cooled (~3.5 bya?) lots of liquid water underground is not in question. That bacteria can live in such environments is also clear (though the fossil record is sufficiently imprecise for us to say just what sort of bacteria the earliest fossil are, and I don't know to what extent the rock matrix they are found in can tell the nature of the environment of the time).

Fast forward to ~600 Mya, in the late Precambrian, after the (second?) snowball Earth episode. Lots of surface water, plenty of oxygen in the atmosphere, and geological carbon cycles operating much as they do today (life is a key player in those cycles).

That the global thermostat worked, and still words, keeping much of the Earth's surface above freezing, irrespective of solar input, from ~600 Mya to today, seems a pretty sound conclusion. And this set of regulatory feedback loops barely sneezed in the face of the KT asteroid/comet impact, the Deccan and Siberian traps, ... so it's pretty robust.

So the question we're examining is, surely, what about the period from ~3 bya to the end of the (second) snowball Earth? What was the average temperature of the Earth's surface in that period?

Well, there were at least two episodes of global glaciation ('snowball Earth'), in which all but, perhaps, a few small seas were completely covered with ice. (the ice cover cannot have been both thick and complete; plants evolved well before these episodes, and didn't go extinct during them; during this time, and for a long time afterwards, plants were aquatic, and, except possibly towards the end of the last snowball, single celled).

So what kept the Earth (relatively) warm, from at least ~1.2 bya (when plants came onto the scene), or maybe ~2 bya (when photosynthesis appeared in bacteria)?

Spaceman Spiff
2006-Oct-10, 05:05 PM
As for the cause of it, note that you will very often see it said that increased core temperatures increase fusion rates and cause higher luminosities, owing to the extreme temperature sensitivity of fusion. This is not correct-- indeed the extreme temperature sensitivity is exactly why the fusion rate is not controlled by the temperature, the temperature is controlled by the fusion rate. I will bet you dollars to donuts that as the helium concentration increases, some other process causes the luminosity to increase, and the core temperature is forced to rise in response to this elevated need for luminosity. That's pretty much what a stellar core does-- it makes minute adjustments to itself to provide whatever luminosity the star needs to maintain the required structure. My guess is, more helium means fewer electrons and therefore the photons escape more rapidly, increasing luminosity simply by getting out at a faster rate as the Sun ages.



Ken G.

We don't have to guess, and it's nothing to do with a change in the core's opacity (which isn't that important in setting a star's surface luminosity). The pressure P exerted by the gas (to offset the weight of the star above, loosely speaking) is in proportion to the number density of particles n (number per unit volume) and its temperature T. So:

P = n kT = rho kT/(mu*mh), where

k = Boltzmann's constant
rho = mass density of gas (mass per unit volume)
mu is the mean mass per particle (nucleons and free electrons)
mh is the mass of the hydrogen atom

Since the MS star is fusing 4H --> 1He (+ energy) zillions of times per second, then very gradually the number density of particles to provide pressure support is diminished within the core (or equivalently, the mean molecular weight mu increases there), within which the thermonuclear reactions occur. Hydrostatic equilibrium within the core thus moves to higher T and mass density.

The higher T especially drives up the luminosity released from fusion, some of which does work on the star's envelope, and some of which escapes as excess luminosity. This is why a star evolves, even while on the MS. Our Sun probably began life on the ZAMS with a central T of a bit over 13 million K, and will move off the MS with a central T of 17.5 million K (something like that). It's present value is 15.7 million K.

Yes, it is indeed true that the fusion rate is extremely temperature sensitive, and so any changes in T tend to be small. Temperature sensitive pressure support (e.g., normal gas pressure) acts as a thermostat (positive feedback mechanism) to keep the T-sensitive nuclear reactions from running away as a bomb (kaboom) or from turning off (pffft). That is, small deviations from equilibrium are rapidly driven back to the equilibrium point. But that can happen only as long as the core remains stationary in its properties in time. By definition: over a good fraction of the nuclear time scale, the core's composition changes significantly, in this case as H is fused into Helium. Thus, for reasons discussed above, the equilibrium position of the thermostat shifts to one of higher temperature (gravity does work on the core in compressing it). Changes on the inside ultimately result in changes on the outside (R, T_surf, L_surf).

You and I discussed much of this about a year ago...

Ken G
2006-Oct-10, 08:48 PM
The pressure P exerted by the gas (to offset the weight of the star above, loosely speaking) is in proportion to the number density of particles n (number per unit volume) and its temperature T. So:

P = n kT = rho kT/(mu*mh)
Or use number density instead of rho, and mh doesn't appear at all. What's the point?


Since the MS star is fusing 4H --> 1He (+ energy) zillions of times per second, then very gradually the number density of particles to provide pressure support is diminished within the core (or equivalently, the mean molecular weight mu increases there), within which the thermonuclear reactions occur. Hydrostatic equilibrium within the core thus moves to higher T and mass density.
No, this is not a structural argument, it is an adiabatic compression argument. But the core does not undergo adiabatic compression. It does compress, true, but there is absolutely no reason to expect this to increase the core temperature, unless the stellar structure requires a higher luminosity. If the new stellar structure requires a lower luminosity, then the core will compress but move to lower temperature, that's certainly possible as this is not an adiabatic situation. Indeed that is precisely what would happen to the Sun if we, for example, remove 0.1 solar masses and wait for the star to re-equilibrate. None of this explains why the luminosity must rise when H -> He, that is a completely separate argument that I suspect quite strongly depends on opacity issues.


Temperature sensitive pressure support (e.g., normal gas pressure) acts as a thermostat (positive feedback mechanism) to keep the T-sensitive nuclear reactions from running away as a bomb (kaboom) or from turning off (pffft).
This is correct, but has nothing to do with the present discussion. This is an analysis of the stability of the equilibrium, not what must happen to achieve a secularly advancing equilibrium. The latter is what I am talking about, and is quite a different matter. Again, consider what happens if you extract 0.1 solar masses: higher core density, lower luminosity, and finally in the chain of logic, lower core temperature.


Thus, for reasons discussed above, the equilibrium position of the thermostat shifts to one of higher temperature (gravity does work on the core in compressing it).
Same point-- you are making a dynamical argument, but this is an equilibrium calculation, not a dynamical one.


Changes on the inside ultimately result in changes on the outside (R, T_surf, L_surf).

You and I discussed much of this about a year ago...

This is exactly what I am saying is not true-- the behavior is highly outside-in, not inside-out, and the express reason for this is the extreme temperature sensitivity of the nuclear burning rate. Ironically, this sensitivity is often quoted as a reason for inside-out control, and that's exactly the opposite of the truth. I recall we discussed this, but I apparently did not make my point earlier. I think we agreed that the change in molecular weight may be crucial, but I would say that this is primarily because of what it implies about the electrons per gram, and is an opacity issue. Opacity is always crucial for setting the luminosity of main sequence stars, a point that very few of the sources I've seen appear to recognize. It's quite interesting, actually.

Kaptain K
2006-Oct-10, 09:35 PM
...positive feedback mechanism...
Minor nitpick:

What you desribe is a negative feedback mechanism.

Spaceman Spiff
2006-Oct-10, 09:50 PM
Minor nitpick:

What you desribe is a negative feedback mechanism.

yep. thanks!

Spaceman Spiff
2006-Oct-10, 10:34 PM
Ken G.

Here (http://www.bautforum.com/showpost.php?p=590670&postcount=15) in which I said:

Or expanding Ken G.'s explanation a bit more generally:

a) take kappa to be the opacity in cm^2/g (a larger value means that light interacts more strongly with matter), which Ken G. took to be a fixed value - nothing wrong with that, but let's put it in explicitly. It generally decreases inward through the star.

b) set mu to be the mean mass per particle (depends on the star's composition), then from the virial theorem (or equivalently, hydrostatic equilibrium) the temperature inside the star scales as
T ~ (mu*beta) * M/R , where beta = the ratio of gas/total pressure. beta is smaller for higher temperatures, for which radiation pressure ~ T^4 becomes increasingly important.

c) and set eta = (L(r)/M(r)) / (L*/M*), where L(r) and M(r) are the run of luminosity (due to fusion or lacking that: graviational contraction) and enclosed mass as a function of radius r through the star, while L* and M* are the star's surface luminosity and its full mass. So eta = 1 at the surface and generally increases inward.

L ~ M^3 * (mu*beta)^4 / (kappa * eta)

Sir Arthur Eddington derived the "Standard Stellar Model" that had this form roughly a century ago, well before anyone understood the role of nuclear fusion. While kappa and eta are not constant within the star, their product roughly is.

and here (http://www.bautforum.com/showpost.php?p=595323&postcount=30), are two of the posts I made 1 year ago addressing your comments, when we were discussing in your thread of why more massive stars arrive on the ZAMS as more luminous stars. And we (mostly) agreed (http://www.bautforum.com/showpost.php?p=595397&postcount=31) there.

This present thread is a different, yet related issue. I understand that you're talking about secular evolution. And MS stars do evolve on the MS and that reason is grounded in the change in mean molecular weight (or mean mass per particle, since there is nothing molecular about the centers of stars). The whole danged star must satisify hydrostatic equilibrium - even during this evolution on the MS, which is very slow in comparison to any other time scales of importance (dynamical or thermal). The number density of particles in the core must drop due to 4H-->He IF NOTHING else happens (and of course, we're conserving charge), and thus so must T so that sufficient pressure gradient is maintained in the core. This is first and foremost since it is fundamental to the star's structure (or existence!). Fusion need not even be present for the star to set up hydrostatic equilibrium. In that case this "star", too, would evolve, effectively obeying the Virial theorem, becoming smaller and hotter on the (the much shorter) Kelvin-Helmholtz time scale.

No doubt the changing opacity of the core, mainly electron scattering, plays a role in changing the radiative temperature gradient within the core. The electron scattering opacity (in cm^2/g) scales like a 0.2 * (1 + X) where X is the hydrogen abundance by mass. So the electron scattering opacity diminishes a tad, where X has dropped within the core.

But the changes in the core's composition, originating with hydrogen fusion are what initiate the structural evolution of the star while on the MS. And that's the the main point I am making.

I can see that to some degree we are speaking about effectively the same things, but there is something else that at the moment I cannot put my finger on that bugs me.

Ken G
2006-Oct-10, 11:12 PM
The number density of particles in the core changes, and thus so must T so that sufficient pressure gradient is maintained in the core.
All that must happen is hydrostatic equilibrium must be maintained. Density and temperature are independent variables, there's no obvious connection between them because you don't know what the pressure has to be. The real key is the size of the star, from that comes the density, then the luminosity, and finally, last in line, the minute corrections to the core temperature do whatever they need to (given that we know it'll have to be in the ball park of 10 million K).


Fusion need not even be present for the star to set up hydrostatic equilibrium.
Agreed, this is a key constraint, and one of the ones I have in mind that sets the stellar radius.


In that case this "star", too, would evolve, effectively obeying the Virial theorem, becoming smaller and hotter on the (the much shorter) Kelvin-Helmholtz time scale.
But this is just it-- how do you know the star must become smaller? Let's posit, for fun, that helium has a spectacularly high opacity for some bizarre and impossible reason. Then as H -> He, the particle number would drop, the mean molecular weight would rise, but the photons would have a heck of a time getting out. What would happen? I suspect the stellar radius would be little affected (might even expand a tad), but the luminosity would plummet, and the core temperature would drop slightly. All of this because it would be required for equilibrium, not because of any particular dynamical argument. The star would find a way, they are so darn robust. The point is you could never argue that the luminosity should end up higher because it seems like at first the core temperature would want to rise. If we take 0.1 solar masses away from the Sun, you might think the weaker gravity would cause it to expand, but it won't-- the core will contract, and that will make its temperature want to rise-- but again it won't, it'll end up dropping. I think the argument must always be in terms of the final equilibrium state, or else you end up with all kinds of expectations that don't pan out.


No doubt the changing opacity of the core, mainly electron scattering, plays a role in changing the radiative temperature gradient within the core. The electron scattering opacity (in cm^2/g) scales like a 0.2 * (1 + X) where X is the hydrogen abundance by mass. So the electron scattering opacity diminishes a tad, where X has dropped within the core.
Yes, I feel this is actually the dog that is wagging the tail.



But the changes in the core's composition, originating with hydrogen fusion are what initiate the structural evolution of the star while on the MS. And that's the the main point I am making.
No question, H -> He is the driving issue. My point is just this business about the sensitivity of nuclear burning to T, and how often it's used as an argument of why the core temperature causes the luminosity, when in fact that same sensitivity is exactly why the luminosity causes the core temperature.

Spaceman Spiff
2006-Oct-11, 03:39 AM
All that must happen is hydrostatic equilibrium must be maintained. Density and temperature are independent variables, there's no obvious connection between them because you don't know what the pressure has to be. The real key is the size of the star, from that comes the density, then the luminosity, and finally, last in line, the minute corrections to the core temperature do whatever they need to (given that we know it'll have to be in the ball park of 10 million K).

Unless I am misunderstanding you, its seems that you are minimizing the roles of gravity and the virial theorem (which holds on the time scales we are talking about, because dynamical times are ~minutes) that must be at work. If the darned core doesn't have sufficient particle number density (because 4 hydrogen nuclei are becoming 1 helium nucleus), then it cannot generate sufficient pressure to support itself against gravity (in loose language to allow everyone here to follow along). So rapid (instantaneous compared to the nuclear time scale) adjustments in structure must occur to preserve hydrostatic equlibrium within the core, as the composition is gradually changed. Gravitational potential energy is released in going from a zero age main sequence (ZAMS) core to a 4.57 billion year old core - and the result is a denser, hotter core, just as sophisticated models predict. By the time core helium fusion occurs the Helium core is over 100 million K and the density is at least 10,000 g/cm^3 (for stars the mass of our sun). How do you think it will get that way?

The energy released per gram from the pp chain in our sun goes something like:

E ~ X^2 * density * T^4, where X is the mass fraction of H in the core (which varies through the core, as do T and density). But the increase in total luminosity coming from the core, due to increases in density and T, more than compensates for the decrease in X as time ticks by (at least until the approach of core H exhaustion). That extra energy has gotta get dumped somehow (enter the temperature gradient and the equations of radiative and convective transport).

I have no qualms with you that ALL the differential equations of structure must hold true at every layer in the star. We have hydrostatic equilibrium, mass conservation, energy conservation, and energy transport to cover the biggies. And so yes, it all must hang together from core to surface.


But this is just it-- how do you know the star must become smaller?

I did not say the star must become smaller. The star itself (its radius) becomes larger. It is the core that becomes denser (more centrally concentrated) and hotter. The central conditions of our Sun are predicted to go from density and T of roughly 80 g/cm^3 and 13 million K 4.5 billion years ago, to well over 400 g/cm^3 and nearly 18 million K at the end of the main sequence phase (according to modern models). Note that the central density increases by a larger factor than the central T. I suspect that this is largely due to energy conservation and the temperature sensitivity of the energy released from fusion, and the star adjusting its structure so that it can balance energy in with energy out (taking into account the temperature gradient and available energy transport mechanisms).



Let's posit, for fun, that helium has a spectacularly high opacity for some bizarre and impossible reason. Then as H -> He, the particle number would drop, the mean molecular weight would rise, but the photons would have a heck of a time getting out. What would happen?

Well posit all you like, but this is not relevant. Helium and hydrogen provide opacity only if to the extent they possess their electrons. This happens in the outer envelopes of stars only, not their deep interiors or cores. The major source of opacity in the cores of most stars is electron scattering, and as I mentioned above, this opacity scales like 0.2 * (1 + X) cm^2/g . So as the hydrogen mass fraction X in the core goes down, so does this major opacity source.

Only the star's core is undergoing a change of composition - the rest of the star does not (at least not during the main sequence; we're ignoring major convective dredge up episodes that occur in later red giant stages in which the outer convective envelope overshoots into the outer core and convects various products of stellar nucleosynthesis into the envelope). So the darned envelope and surface don't care all that much if the opacity of the core is changing (dropping). The envelope does care about the rate of energy dumped into it due to changes in nuclear reaction rates.

If stellar evolution is driven entirely from the outside in, how and why does the star's surface luminosity (and radius, etc) change?

Spaceman Spiff
2006-Oct-11, 03:49 AM
Sorry folks, for the technical bout between Ken G. and myself. I suppose Ken G. and I ought to bring it to a close (he can give me another shot to the shoulder, if he'd like), shake hands and let the question pertaining to how an evolving Sun might affect Earth's paleo climate be pursued.

Romanus
2006-Oct-11, 05:11 AM
^
I'm pretty sure Spiff is right; the explanations I've seen for the Sun's increase in luminosity have all been related to a steadily-shrinking (and thus, heating) core related to the progressive depletion of hydrogen.

Ken G
2006-Oct-11, 11:18 AM
^
I'm pretty sure Spiff is right; the explanations I've seen for the Sun's increase in luminosity have all been related to a steadily-shrinking (and thus, heating) core related to the progressive depletion of hydrogen.

This is my entire point-- the oft-seen explanation is completely wrong, and for very simple reasons that I've explained. If you doubt this, then will one of you please simply tell me what you would expect to happen if I were to remove 10% of the Sun's mass. What will be the attributes of the resulting star, and why? When you answer this, you will understand the oft-repeated misconceptions. My points are too over-simplified to apply in detail to the structure as stars evolve, but they correct the misconceptions at least.

MG1962A
2006-Oct-11, 12:14 PM
Okay - I have pinned down where this supposed information came from.

Bahcall, J.N., Pinsonneault, M.H., Basu, S., 2001, “Solar Models: Current Epoch and Time Dependences, Neutrinos, and Helioseismological Properties”, Astrophys. J., 555, 990-1012, URL:

Now it appears the article is really talking about nutrino production in the early sun's core, and does not mention a specific time frames.

So sorry for wasting people's time

Ken G
2006-Oct-11, 12:35 PM
You're right that this is getting a bit technical, but it's still central to the thread, and note there are a number of oft-seen misconceptions that are being ironed out here. Ultimately though, I fear the answer is going to be that there really is no simple way to understand the evolution, the star is not behaving in a self-similar way with just a single secularly evolving driving variable the way we'd like.


Unless I am misunderstanding you, its seems that you are minimizing the roles of gravity and the virial theorem (which holds on the time scales we are talking about, because dynamical times are ~minutes) that must be at work. If the darned core doesn't have sufficient particle number density (because 4 hydrogen nuclei are becoming 1 helium nucleus), then it cannot generate sufficient pressure to support itself against gravity (in loose language to allow everyone here to follow along).
Ah, but what you are forgetting is that if you are assuming the virial theorem (as we both are, and this is a great simplification but it limits our accuracy in detail), if you don't change the gravitational potential (so no contraction/expansion), then there's no effect on pressure if you replace hydrogen with helium! The drop in particle number is completely offset by the increase in mass, and higher mean molecular weight means higher temperature in the virial theorem. That's not allowed here-- the fusion temperature must not change much. So if nothing else were going on, the core should expand as H --> He, to be able to maintain the right fusion temperature! Another way to look at this is, stars have a strange relationship between gravity and pressure-- contraction in equilibrium favors gravity over pressure, not the other way around! Dynamically, contraction favors pressure, but we are not talking about adiabatic compression here, equilibrium compression is much closer to isothermal compression and that is exactly not what you want if you want to give pressure the leg up. It's very counterintuitive I know, and this is why it is explained wrong almost every place you see it.



So rapid (instantaneous compared to the nuclear time scale) adjustments in structure must occur to preserve hydrostatic equlibrium within the core, as the composition is gradually changed.
But that's just it-- the adjustment is not rapid, it is on the nuclear time scale. This is the evolutionary time scale. Your argument applies on dynamical timescales, which are much shorter and are not relevant here.



By the time core helium fusion occurs the Helium core is over 100 million K and the density is at least 10,000 g/cm^3 (for stars the mass of our sun). How do you think it will get that way?
But this is an entirely different issue-- this is controlled not by hydrostatic considerations, but by helium nuclear physics. Our present discussion has nothing to do with helium fusion, helium isn't fusing during the main sequence evolution.


I did not say the star must become smaller. The star itself (its radius) becomes larger.
This is my point about expansion favoring pressure. I think we're seeing a problem that the details of the structure don't follow the simple one-point pressure vs. gravity argument, there are additional radially dependent issues. Neither of us wanted to get into that-- the real issue is, when H-->He, is there basically a tendency to expand or a tendency to contract? I've argued the former, so we can see why the radius increases. But the fact that the core actually contracts tells us that we can't succeed with the simplest argument.


It is the core that becomes denser (more centrally concentrated) and hotter. The central conditions of our Sun are predicted to go from density and T of roughly 80 g/cm^3 and 13 million K 4.5 billion years ago, to well over 400 g/cm^3 and nearly 18 million K at the end of the main sequence phase (according to modern models).
Then we see that all simple arguments about what happens to the core density will fail. The overall tendency is for expansion, but some interesting details must cause the core to part company and go the opposite way. Probably the temperature sensitivity is not enough (my argument always starts with the assumption of very strong sensitivity)-- we'd do better looking at CNO-cycle stars to see these arguments play out more simply. But still, the driving issue is not the fact that helium makes less pressure per gram per Kelvin than hydrogen, however-- that fact has very little effect when the virial theorem is at play.


Note that the central density increases by a larger factor than the central T. I suspect that this is largely due to energy conservation and the temperature sensitivity of the energy released from fusion, and the star adjusting its structure so that it can balance energy in with energy out (taking into account the temperature gradient and available energy transport mechanisms).
What it tells you is that the virial theorem is not satisfied for the core by itself, so this is what I mean by life getting complicated and no simple argument sufficing any more. Bother.




The major source of opacity in the cores of most stars is electron scattering, and as I mentioned above, this opacity scales like 0.2 * (1 + X) cm^2/g . So as the hydrogen mass fraction X in the core goes down, so does this major opacity source.
I've said that all along-- the opacity goes down. That's what I'm talking about, the free electron opacity per gram. My money says this is the fundamental reason that luminosity increases during main sequence evolution, despite the other details we don't know about. Your point that the envelope's opacity is not changing is well taken-- but still, the escape time will also depend on the core opacity, so it is relevant. You may have put your finger on part of the reason that the core and envelope are parting ways-- they have different compositions, and that's confusing things a lot.


If stellar evolution is driven entirely from the outside in, how and why does the star's surface luminosity (and radius, etc) change?

Because the outside-in elements include everything that impedes photon escape, including core opacity. Remember the density is much higher in the core, so that's where the photons spend a lot of their time.

Spaceman Spiff
2006-Oct-11, 02:42 PM
Apologies, Ken G. I am afraid we will have to agree to disagree on this.

-Spaceman Spiff

StupendousMan
2006-Oct-11, 04:06 PM
Chapters 7, 8 and 9 of "Astrophysics I: Stars", by Bowers and Deeming, provides a good introduction to stellar structure and the inter-dependence of size, luminosity, temperature and other variables. These chapters walk through the stages of stellar evolution on the main sequence, and then off the main sequence.

I suggest that people read this material -- or similar material elsewhere -- before continuing this discussion. I have just done this, and it appears to me that one of the points of view expressed in this thread is supported by the detailed theory, and the other point of view is not.

Ken G
2006-Oct-12, 03:12 AM
Please describe the material that causes you to reach this conclusion, we don't have access to that text. In fact I'm quite curious what those authors have to say. (And a word of caution-- there is much incorrect information about stellar structure in introductory texts. I'd recommend Kippenhahn for the straight skinny, he actually does the research.)

StupendousMan
2006-Oct-12, 02:19 PM
Please describe the material that causes you to reach this conclusion, we don't have access to that text. In fact I'm quite curious what those authors have to say. (And a word of caution-- there is much incorrect information about stellar structure in introductory texts. I'd recommend Kippenhahn for the straight skinny, he actually does the research.)

First, I will address your advice to stick to material written by someone who "actually does the research":

Richard L. Bowers' list of publications, from ADS:

http://adsabs.harvard.edu/cgi-bin/nph-abs_connect?db_key=AST&qform=AST&sim_query=YES&ned_query=YES&aut_logic=OR&obj_logic=OR&author=bowers%2C+r+l%0D%0A&object=&start_mon=&start_year=&end_mon=&end_year=&ttl_logic=OR&title=&txt_logic=OR&text=&nr_to_return=100&start_nr=1&jou_pick=ALL&ref_stems=&data_and=ALL&group_and=ALL&start_entry_day=&start_entry_mon=&start_entry_year=&end_entry_day=&end_entry_mon=&end_entry_year=&min_score=&sort=SCORE&data_type=SHORT&aut_syn=YES&ttl_syn=YES&txt_syn=YES&aut_wt=1.0&obj_wt=1.0&ttl_wt=0.3&txt_wt=3.0&aut_wgt=YES&obj_wgt=YES&ttl_wgt=YES&txt_wgt=YES&ttl_sco=YES&txt_sco=YES&version=1

Terry Deeming's list of publications, from ADS:

http://adsabs.harvard.edu/cgi-bin/nph-abs_connect?db_key=AST&qform=AST&sim_query=YES&ned_query=YES&aut_logic=OR&obj_logic=OR&author=deeming%2C+t&object=&start_mon=&start_year=&end_mon=&end_year=&ttl_logic=OR&title=&txt_logic=OR&text=&nr_to_return=100&start_nr=1&jou_pick=ALL&ref_stems=&data_and=ALL&group_and=ALL&start_entry_day=&start_entry_mon=&start_entry_year=&end_entry_day=&end_entry_mon=&end_entry_year=&min_score=&sort=SCORE&data_type=SHORT&aut_syn=YES&ttl_syn=YES&txt_syn=YES&aut_wt=1.0&obj_wt=1.0&ttl_wt=0.3&txt_wt=3.0&aut_wgt=YES&obj_wgt=YES&ttl_wgt=YES&txt_wgt=YES&ttl_sco=YES&txt_sco=YES&version=1

It takes less than one minute to make such a search.

Second, you wrote:


Please describe the material that causes you to reach this conclusion, we don't have access to that text.

Sorry, I don't have time to summarize three chapters of a book for you today. I guess the discussion will have to wait until either you read the chapters, or I find a free afternoon to go through the mathematics and boil it all down to a paragraph or two.

Ken G
2006-Oct-12, 03:36 PM
First, I will address your advice to stick to material written by someone who "actually does the research":
All right, those authors certainly seem to be quite authoritative on the subject. Still, as I don't know what specific argument you are talking about, I can't comment on what you are saying. I'm certain I already know the majority of what are in those three chapters, so that's why I would need to know what specifically you are referring to-- it would by no means be necessary for you to "summarize the chapters". You may assume I am well acquainted with all the equations, what we are talking about here is understanding the logic of what those equations are saying.

In terms of the discussions in this thread, there have been a lot of arguments given, and whether or not they are correct depends on what they are trying to explain. My fundamental point is that if you want to understand why the luminosity goes up, you cannot do it by looking at arguments for why the temperature goes up-- the temperature goes up for essentially the sole reason that the luminosity must go up, so any attempt to argue the other way is circular. This is a direct result of the extreme sensitivity of luminosity to core temperature, and the fact that the argument is often made (incorrectly) the opposite way is one of the more interesting elements of this discussion. If Bowers and company are making that particular argument, they are just plain wrong.

On the other hand, there is the separate issue of why the core contracts. Those are separate discussions. My point there is that if you look at molecular weight by itself, you actually expect the star to expand to seek its new equilibrium, surprisingly, that's how stars work. The reason that contraction instead occurs is that the core is relatively full of helium ash, as compared to regions farther from the core, so you have a gradient in the hydrogen fuel and that complicates life a lot. When you solve for the final pressure balance, of course molecular weight appears, and that's the part of the issue that SpacemanSpiff was talking about. But that's not why the luminosity goes up, and it's not even all that directly related to the contraction, it appears only in concert with the gradient in fusion fuel. Those issues get complicated, and I'm not saying that everything SpacemanSpiff said is wrong (he's quite knowledgeable), nor that everything you claim those authors are saying is wrong (they are also quite knowledgeable, as you have showed). However, I am saying that if they claim the luminosity goes up because the core has to reach a higher temperature due to the force balance, then they are indeed completely wrong, regardless of their qualifications. I would be happy to clarify this argument beyond what I have said already, if there are specific points of contention. It all comes down to the way the opacity is actually what sets the luminosity of the star. Note above all, this is not a matter of who can claim they are right, it's really a very fascinating issue about what are the physics that really govern main sequence stars, and the large number of places where you will find incorrect or misleading information on this topic.

Ken G
2006-Oct-19, 06:06 PM
StupendousMan and SpacemanSpiff, and anyone else interested in this thread, might care to check out the recent Q&A thread "How stars handle pressure", to resolve any lingering questions they may have had about the claims I've made in this thread. There are several aspects of stellar structure and evolution that I find over and over again that quite knowledgeable people and sources don't have right, so the real question is, do they care.

Nereid
2006-Oct-19, 06:59 PM
And maybe, if anyone's interested, we could also get back to discussing how good the Earth's 'thermostat' was, way back then ....

Ken G
2006-Oct-19, 07:24 PM
Yeah, that was an interesting discussion, I'd recommend using the "How stars handle pressure" thread to talk about the stellar evolution part.