Bad astronomy in massive star luminosity

[Ken G]

I've often wondered why there is so much misinformation around the topic of the reasons that very massive main sequence stars are so luminous. It even shows up in books, but if we restrict to seemingly reliable internet sites, I'll bet that in 10 google hits of sites that offer an explanation, you'll find at least seven that claim massive stars are more luminous because their cores are hotter, and maybe as many as five that add it is because the pressure in the core is higher. Those are both wrong explanations, the first for subtle reasons, and the second for appallingly blatant reasons. The blatant reason that it's not because of the high pressure is that massive star cores have lower pressures than low-mass stars, for the simple reason that their high mass allows the core to reach fusion temperatures with much less compression and much lower pressure. At least higher core temperatures is actually true, but the subtler reason why that is not the explanation for the high luminosity is that it reverses the correct logic: the higher temperature core is because of the higher luminosity, not the other way around. So why is this wrong so many places?

 

[Chronos]

The energy produced by stars comes from fusion. Fusion only occurs in the cores of stars. The layers of gas surrounding the core merely merely convey heat to the surface and radiate it off into space. A massive stars must have a higher core temperatures to resist the efforts of gravity to collapse it upon itself. The only way a star can generate higher core temperature is by increasing core density. These explanations are consistent with our current understanding of physics.

 

[Ken G]

Thank you for your response, and for making my point about how widely spread are these misconceptions. Much of what you said is correct, but much is not. First of all, there is a difference between asserting something that is true about stars, versus giving an explanation for their luminosity. The fusion rate of a main sequence star is most definitely not what determines the star's luminosity, however, the luminosity of the star is what determines its fusion rate. That is consistent with your first two sentences. But your next three are false. You are certainly to be forgiven-- it is my whole point that these false statements get repeated so often they become accepted without further thought, this is why the phenomenon is so interesting. I will support these claims:

The statement "massive stars must have a higher core temperatures to resist the efforts of gravity to collapse it upon itself" is untrue because it is pressure that holds up the core, not temperature. The temperature is determined by the thermostatic effect of fusion, which needs to supply the necessary luminosity required by the stellar structure itself. Given the temperature, the density must adjust to give the appropriate pressure, and the appropriate pressure in a high-mass star is less than in a low-mass star (a fact that extends all the way to the surface, giving the connection between pressure broadening and luminosity class).

The statement "The only way a star can generate higher core temperature is by increasing core density" is patently untrue-- as I said above, massive main sequence stars do not have higher core densities than low-mass stars, they have lower core densities. This is the whole reason they do not encounter degeneracy pressure in their cores as readily as do low-mass stars. This then tells us why the last statement is not true.

These are actually rather basic truths about stars, verifiable with simple scaling analyses, so I ask again: why is it that they are so often muddled in otherwise perfectly reliable sources? My theory is that it is the "oft repeated error" phenomenon-- something that is wrong but sounds reasonable makes its way into an authoritative source, which is then used as a reference for a bunch of other sources, until it takes on a kind of life of its own. It is not my goal to hold up any scapegoats, merely so assert that as scientists, we must always beware this unfortunate effect!

 

[Ken G]

At this point I have the following questions:
1) Does anyone on this forum still think that more massive main-sequence stars have higher pressure and density in their cores than less massive main-sequence stars?
2) Does anyone on this forum still think that the luminosity of a main-sequence star is determined primarily by its fusion rate, instead of the other way around?
If you answered yes to either of those questions, there are things about stars that you may wish to understand better, and it might stimulate an interesting discussion getting there.

 

[Q-reeus]

2) Does anyone on this forum still think that the luminosity of a main-sequence star is determined primarily by its fusion rate, instead of the other way around?...

I'm only on this site 'by accident' owing to following up the progress of a thread that was moved from elsewhere. But as a dummy re astrophysics, this statement seems odd. Unless there is an implication of highly non-equilibrium rate, or that neutrino flux (non-luminous component) becomes significant, how is there any distinction as to which way matters?

 

[Ken G]

Unless there is an implication of highly non-equilibrium rate, or that neutrino flux (non-luminous component) becomes significant, how is there any distinction as to which way matters?

That is indeed the important question here, and certainly there can be some discussion over what constitutes a causal relationship, versus a simple consistency requirement. But I feel that causal relationships are determinable, and I'll give an everyday analogy. Let's say you have a salary of $50,000 a year, would we not say that the amount of money you spend each year is determined by this salary? Granted, all we can really say is that if the numbers don't match there will be trouble, but there seems to be a clear causal relationship that you pick a lifestyle that fits your salary, you do not pick a salary that fits your lifestyle. This would be analogous to the claim that the fusion rate determines the luminosity, if we associate the fusion rate to a salary, and the luminosity to a spending rate.

However, let's say you don't have a job, instead you have a diamond mine in your back yard. And let's further say that any time you desire something that costs money, you simply go into your back yard and dig up a suitable sized diamond. Could we not then claim that the rate you mine diamonds is caused by the lifestyle you wish to live? This is the better analogy for how main-sequence stars work-- they require a certain luminosity based on their basic structure, and they simply "mine" nuclear energy at whatever rate they require to maintain that structure. Thus we can say that the luminosity determines the burning rate, not the other way around, as is so often claimed.

 

[Q-reeus]

...However, let's say you don't have a job, instead you have a diamond mine in your back yard...

I wish. But hey if I wish upon the right star...

This is the better analogy for how main-sequence stars work-- they require a certain luminosity based on their basic structure, and they simply "mine" nuclear energy at whatever rate they require to maintain that structure. Thus we can say that the luminosity determines the burning rate, not the other way around, as is so often claimed.

I see your point here - luminosity is the driver in the feedback cycle. So if it drops a little, star contracts a little, driving up internal (especially core) pressure which in turn cranks up fusion rate, and vice versa if luminosity rises. That's about right? Does this imply all main sequence stars 'breathe' to a detectable degree, and if so is this more noticeable for more massive stars?

 

[Ken G]

That's exactly right, and it is a good way to bring in the thermal stability of nuclear fusion in a star (in contrast to, say, a runaway situation). I don't think the "breathing" of main-sequence stellar fusion would be perceptible (except around class F in the "instability strip", but that has to do with envelope physics not core fusion), because the fusion is so well stabilized that variations would be hard to detect, and the energy releases take a long time to reach the surface so what we see represents a wide average. It would be better to see it in the neutrino flux, but the statistics on that are already low because they are so hard to detect. However, there are periods that evolved stars go through called "thermal pulses" and "helium flashes", where fusion does go through unstable intervals. And of course, there are type Ia supernovae...

 

[Q-reeus]

I don't think the "breathing" of main-sequence stellar fusion would be perceptible (except around class F in the "instability strip", but that has to do with envelope physics not core fusion), because the fusion is so well stabilized that variations would be hard to detect, and the energy releases take a long time to reach the surface so what we see represents a wide average...

That 'breathing bit I just grabbed from memory, having come across material mentioning our sun goes through a cyclic variation in diameter of I think decades in period. Thanks for reminding me though that energy transport from the interior of our sun takes something of the order of tens or hundreds of thousands of years to get to the surface. So clearly no connection between those two. That envelope physics bit is more about feedback from convective (and/or radiative) processes near the surface layers I take it?

However, there are periods that evolved stars go through called "thermal pulses" and "helium flashes", where fusion does go through unstable intervals. And of course, there are type Ia supernovae...

Fingers crossed Old Sol aint one of those, at least for a long time!:zzz:

 

[Ken G]

That envelope physics bit is more about feedback from convective (and/or radiative) processes near the surface layers I take it?

Quite so, the small pulsations are often due to stirring up by the convection, and big pulsations are usually do to some kind of radiative driving of oscillations. No worries-- ol' Sol won't supernova!

 

[Q-reeus]

Cleaning up on that solar surface breathing issue, found from http://en.wikipedia.org/wiki/Helioseismology that there are a huge number of both 'p' (acoustic) and 'g' (gravitational) modes going on, with perhaps only the former making an appreciable appearance at the surface. Interestingly the power spectrum continues to rise toward the low frequency end; at what point there is effective cutoff have no idea.
Getting back to the 'core' issue, again from Wikipedia: http://en.wikipedia.org/wiki/Sun, under "Core":
"The fusion rate in the core is in a self-correcting equilibrium: a slightly higher rate of fusion would cause the core to heat up more and expand slightly against the weight of the outer layers, reducing the fusion rate and correcting the perturbation; and a slightly lower rate would cause the core to cool and shrink slightly, increasing the fusion rate and again reverting it to its present level.[40][41]
The gamma rays (high-energy photons) released in fusion reactions are absorbed in only a few millimeters of solar plasma and then re-emitted again in random direction and at slightly lower energy. Therefore it takes a long time for radiation to reach the Sun's surface. Estimates of the photon travel time range between 10,000 and 170,000 years.[42]"

This suggests that feedback cycle is largely confined to the core itself, over for sake of argument a 10,000yr cycle time, and I assume this then propagates outwardly in waves at first, but in the convective zone mixing/damping may blur such core cycles until at the surface it's all essentially smoothed out? Or maybe not - but who's been around long enough to tell for sure! Would this be in conflict with your model of surface -> core feedback, over let's say a 100,000yr cycle time, or of a complimentary nature (two superposed cycles)? In short, is Wikipedia here propagating old and misleading info as per your opening salvo?
On further thought, the core feedback cycle above perhaps should be understood as implying stable equilibrium rather than any cyclic 'breathing' going on, in which case the same perhaps for luminosity driven feedback - heavily over-damped with no cycling to speak of?

 

[Ken G]

This suggests that feedback cycle is largely confined to the core itself, over for sake of argument a 10,000yr cycle time, and I assume this then propagates outwardly in waves at first, but in the convective zone mixing/damping may blur such core cycles until at the surface it's all essentially smoothed out?

The timescale is much faster, the sound crossing time of a few minutes. That's the timescale for dynamical stability, and is so short that we may assume the gas is virialized. That means stars have a somewhat opposite response to being heated than you might think-- they get cooler when you add heat to them! "They plump when you cook 'em", basically, and the work done against gravity ends up lowering the temperature-- so sometimes it is said they have a "negative heat capacity," in effect. This prevents the thermal runaway that fusion might otherwise be given to.

Would this be in conflict with your model of surface -> core feedback, over let's say a 100,000yr cycle time, or of a complimentary nature (two superposed cycles)? In short, is Wikipedia here propagating old and misleading info as per your opening salvo?

The Wiki is fine there, because it is not asserting what determines the luminosity, it is only talking about why the fusion rate and the luminosity will be kept in balance by stability considerations. So in the earn/spend picture of my analogy, one could have that kind of stability either way-- in the $50,000 salary model, we'd just imagine a mechanism that increases your tendency to spend whenever you have money in the bank, or reduces it if you start falling into debt, to make sure that in the long run your expenses balance that $50,000 a year. Or, in the diamond mine model, we just imagine a mechanism that means you are too lazy to mine diamonds if you have money in the bank, but you are not too lazy to mine diamonds to avoid going into debt. So either model can be stabilized, but again I argue the latter is the one that applies to fusion in main-sequence stars.

On further thought, the core feedback cycle above perhaps should be understood as implying stable equilibrium rather than any cyclic 'breathing' going on, in which case the same perhaps for luminosity driven feedback - heavily over-damped with no cycling to speak of?

Stable dynamical equilibria do overshoot and generate oscillation because of inertia, requiring damping. So "breathing" is an effect you normally find in the force equation, where the energy issues enter via the work being done. Core pulsations (like g or p waves) are apparently stabilized by some kind of damping in most cases, even though the energy transport times are indeed very long-- perhaps there is effectively marginal stability, but at least there is not instability (except in special cases like stars that are barely hanging together in the first place).

 

[Q-reeus]

The timescale is much faster, the sound crossing time of a few minutes. That's the timescale for dynamical stability, and is so short that we may assume the gas is virialized...

Wow, surprised at first. But a little thought and clearly convective flow rate vs speed of sound in a fluid are vastly different. A bit like conduction charge speed in a metal vs signal speed in the same. And these sound waves can cross the convective zone with little dissipation?

...That means stars have a somewhat opposite response to being heated than you might think-- they get cooler when you add heat to them! "They plump when you cook 'em", basically, and the work done against gravity ends up lowering the temperature-- so sometimes it is said they have a "negative heat capacity," in effect. This prevents the thermal runaway that fusion might otherwise be given to.

Ah yes - core pushing out experiences a damping back-reaction, meanwhile the outflow towards the exterior enlarges the star somewhat, which requires conversion of thermal into increased gravitational potential energy. Cool (pun intended)!

Rather than an issue of damping, I think it would be an issue of an absence of an "inertia" term. Stable dynamical equilibria overshoot and generate oscillation because of inertia, which then has to damp out, but stable thermal equilibria (or bank accounts) have no such inertia-- there is no term that drives the cycle to overshoot once the balance between fusion rate and luminosity is recovered.

Well in a sense, sans some interesting learning and relearning on the way, have come full cycle re original comment - it's all in equilibrium, so what the heck. But you will probably argue it's only quasi-equilibrium - there's a usually imperceptible dynamical balance driven from without, yes?

 

[Drakkith]

Maybe I'm missing something, but since fusion is the source of power in a star, how is Luminosity not a direct result of the amount of fusion? It looks to me like the rate of fusion is dependant on the mass of the star which then determines the luminosity of the star.

 

[Ken G]

Wow, surprised at first. But a little thought and clearly convective flow rate vs speed of sound in a fluid are vastly different. A bit like conduction charge speed in a metal vs signal speed in the same. And these sound waves can cross the convective zone with little dissipation?

Yes, for example p modes in the Sun bounce around willy nilly in the envelope.

Well in a sense, sans some interesting learning and relearning on the way, have come full cycle re original comment - it's all in equilibrium, so what the heck. But you will probably argue it's only quasi-equilibrium - there's a usually imperceptible dynamical balance driven from without, yes?

The presence of an equilibrium, and the need for the fusion rate to match the luminosity, does not preclude the possibility that one is the cause of the other and not the other way around. A star, when it forms, contracts until its core begins to fuse. So the fusion temperature is very important, but not the fusion rate. Imagine a fusion process that is so T sensitive that at 10 million K you get plenty of fusion, and at 10 million and 1 K you get a thousand times more fusion. Will the core T not simply stay at 10 million K? It will stay there because the required fusion rate is set by something else-- it is set by the luminosity of the star. Indeed, Eddington was able to use the Sun's luminosity to determine its internal structure, right down to its core temperature, without ever even knowing that fusion existed. What's more, if you double the coefficient of hydrogen fusion such fusion at the same T and P occurs at double the rate it actually does, do you think the luminosity of the Sun would double? It would not-- it would not change much at all in fact. This is the proof that the luminosity set by the stellar structure sets the fusion rate, not the other way around.

 

[Ken G]

Maybe I'm missing something, but since fusion is the source of power in a star, how is Luminosity not a direct result of the amount of fusion? It looks to me like the rate of fusion is dependant on the mass of the star which then determines the luminosity of the star.

Fusion is indeed the source of the luminosity, but that does not tell you that fusion determines the luminosity-- the luminosity could still determine the fusion (and it does). Consider my analogy again-- if you had a diamond mine in your back yard, are the diamonds not the source of your spending power? Yet the rate you mine diamonds would not determine the rate you spend money, if you are the lazy type who only mines diamonds when you want to buy something. In that case, you would find that diamonds are the source of your wealth, but the rate you mine them is set by the rate you spend money, not the other way around.

That analogy only proves that the causal arrow could go either way, so to see how it goes in stars, we have to look more closely. A star is basically a leaky bucket of light. Given that the core temperature has to be about 10 million K to get fusion, and given the virial theorem, we can immediately estimate the radius of the star given its mass-- for a given mass, the star just contracts until the radius gives you a characteristic escape speed that is appropriate for the speed to get H to fuse. That's the virial theorem of a main sequence star. So now we know the basic T and basic R, for a given M, so we know how much light (thermal radiation) our star holds in its volume, and we know how long it takes to leak out of the bucket (opacity physics gives us that), so we know the luminosity-- even though we have not said squat about the fusion rate, or the coefficient involved in determining that rate given the T and P. So that coefficient does not determine the luminosity, and changing it hypothetically would have only a small effect on the luminosity. Instead, the core just adjusts a little, for whatever coefficient you take, to provide the necessary luminosity to balance the losses from the leaky bucket. That's just the process that determines the fusion rate-- there is no possible way to know the fusion rate until you know what the luminosity needs to be, but you can certainly know what the luminosity needs to be without even specifying what the coefficient of fusion is (or any details about the fusion process other than the fusion temperature).

This means that ironically, it is the extreme temperature sensitivity of fusion that makes the fusion rate the slave to luminosity, despite the fact that that same sensitivity is often (erroneously) cited as the reason that the fusion process is the cause of the high luminosity of massive stars. Indeed, all fusion ever does in stars is cause their luminosity to reach a long-lived steady state-- if you magically turn off fusion, the luminosity of the star will increase, not decrease, as the leaking bucket causes the star to contract and release gravitational energy. Fusion merely serves as a stabilizer that controls the evolutionary timescale-- the physics of the fusion rate never controls the luminosity, once we assert that fusion is very temperature sensitive and turns on at a given known temperature. The luminosity that the star has when its core reaches that fusion temperature is what will set the fusion rate, regardless of any other detail of the fusion process (thiis is also why there is a single prevailing relation between the mass and luminosity of a main sequence star, despite the fact that at some mass, p-p chain fusion is taken over by CNO cycle fusion, a comipletely different process with totally different rate coefficients).

 

[Drakkith]

Hrmm. Answer me this please. Does the light from a star come from the energy released during fusion, or is it from something else, like gravitational compression and heating? I thought it was a direct result of the fusion.

 

[Ken G]

Hrmm. Answer me this please. Does the light from a star come from the energy released during fusion, or is it from something else, like gravitational compression and heating? I thought it was a direct result of the fusion.

It is a direct result of fusion, during the main sequence phase. That question and answer does not tell us if a main sequence star's luminosity sets its fusion rate or if the fusion rate sets the luminosity, it only tells us the two will be equal once we work out the causal connections. If we plot a star's luminosity as a function of time, with and without the existence of nuclear fusion, the only difference is that with fusion, there is a long plateau in the luminosity over the main sequence lifetime. If we are not interested in how long-lived is each luminosity stage, then we don't much care that there is any such thing as fusion.

 

[Chronos]

I am admittedly confused. Fusion is triggered by the gravitational collapse of a sufficiently massive gas cloud. The newly formed star ceases to collapse when the fusion energy in the core [radiation pressure] is sufficient to offset the energy of gravity trying to further collapse the star. Are we in agreement thus far?

 

[D H]

Fusion is indeed the source of the luminosity, but that does not tell you that fusion determines the luminosity-- the luminosity could still determine the fusion (and it does).

You're playing semantics here, Ken. Luminosity and fusion form a feedback system in large stars. Which is cause and which is effect becomes a bit murky in any feedback system. Arguing that one or the other is the primal cause is a semantic game and it misses the big picture that this is a feedback system.

 

[Q-reeus]

Accepting the basic premise here that re feedback it's a question of sensitivity - once luminosity is set by the basic parameters of stellar mass and radius, it is insensitive to fusion rate because changes in the latter auto-adjust to maintain essentially constant luminosity (which I find is inclusive of 'non-luminous' neutrino emission), the matter of opacity in this equation is interesting. Some study has found that transport mechanisms vary radically depending on stellar mass range. In lower mass stars, it's convection essentially 'all the way' (high relative opacity throughout). In approximately solar mass stars, there's radiation dominated transport in the inner regions (low opacity), and convective flow in the outer regions (high opacity), whist for larger stars the converse applies (owing to high temperature gradients in the inner regions vs outer regions). Surprising to me that luminosity completely determines fusion rate in all cases (main sequence).

 

[Ken G]

I am admittedly confused. Fusion is triggered by the gravitational collapse of a sufficiently massive gas cloud. The newly formed star ceases to collapse when the fusion energy in the core [radiation pressure] is sufficient to offset the energy of gravity trying to further collapse the star. Are we in agreement thus far?

Not quite, one cannot distinguish "fusion energy" from any other type-- it's just thermal energy, and it was already in the core before fusion started. I would put it that the collapse ceases when the fusion rate balances the luminosity, but since the luminosity was already there, this shows that the fusion rate is determined by the pre-existing luminosity. After all, the star's luminosity does not change dramatically when fusion begins.

 

[Ken G]

You're playing semantics here, Ken. Luminosity and fusion form a feedback system in large stars. Which is cause and which is effect becomes a bit murky in any feedback system. Arguing that one or the other is the primal cause is a semantic game and it misses the big picture that this is a feedback system.

Not so, indeed the entire point of the two money spending analogies I gave was to demonstrate conclusively that causation can still be attributed in feedback systems. Granted, it will never be 100% vs. 0% when one attributes causation to closely coupled processes, but all the same, it is possible to recognize the difference between the dog and its tail. To keep anyone from having to look back, I'll repeat the analogies:
#1) You make $50,000 a year, and you hate to go into debt but you prefer to spend than to save. That is a feedback situation-- if money builds up in your bank account, your tendency to spend rises, and if you start to go into debt, you curtail your spending. It is also a situation where your salary is clearly causative to your lifestyle.
#2) You have a diamond mine in your back yard, and you hate to go out there and mine it but you do like to acquire neat stuff. That is also a feedback situation-- if you start to go into debt, you mine some more diamonds, but if you have money on hand, you don't. Here we have a situation where your preferred lifestyle is clearly causative of your diamond mining rate.

Saying that the causative differences in those two situations is a semantic game clearly misses the important differences there.

 

[Ken G]

Accepting the basic premise here that re feedback it's a question of sensitivity - once luminosity is set by the basic parameters of stellar mass and radius, it is insensitive to fusion rate because changes in the latter auto-adjust to maintain essentially constant luminosity (which I find is inclusive of 'non-luminous' neutrino emission), the matter of opacity in this equation is interesting. Some study has found that transport mechanisms vary radically depending on stellar mass range. In lower mass stars, it's convection essentially 'all the way' (high relative opacity throughout). In approximately solar mass stars, there's radiation dominated transport in the inner regions (low opacity), and convective flow in the outer regions (high opacity), whist for larger stars the converse applies (owing to high temperature gradients in the inner regions vs outer regions). Surprising to me that luminosity completely determines fusion rate in all cases (main sequence).

That's very much the point-- the luminosity is set by some other physics, and whatever it is, the fusion rate will be forced to provide just that luminosity, or else it will self-correct. Note that in all cases when fusion begins in a main-sequence star, there is very little change in the stellar luminosity.

 

[D H]

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