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Thread: Question about convection in stars

  1. #31
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    Quote Originally Posted by chornedsnorkack View Post
    When fusion rate cannot meet the luminosity, the star contracts.
    Correct.
    When fusion rate exceeds luminosity, the star expands, or accelerates to.
    This can only happen in the situations where fusion is unstable. In the normal stable situation, the fusion will not exceed the luminosity.
    Importance of the slowness of protium fusion is that it remains at timescales slower than free fall timescale even when accelerated, due to those weak steps.
    Not clear what you are saying here, free fall does not happen unless there is a strong cooling instability, nothing to do with fusion.
    No. Providing the luminosity IS a problem - thatīs what defines brown dwarfs. Young brown dwarfs produce significant amount of energy by protium fusion, but not enough to meet heat loss by conduction. Red dwarfs do provide enough energy.
    But that's just completely obvious, of course there are situations where the temperature never gets high enough for the onset of fusion. My comment was that when the temperature does get high enough, the slowness of protium fusion will not be a problem, because it is plenty fast enough. Speed is never the problem for fusion, the Coulomb barrier is. The reason protium fusion is slow is that it has to wait for a type of decay, but again, that's never going to be a long enough wait to matter-- if the temperature is right and the protons are fusing in the first place, they will happily self-regulate their temperature to provide whatever fusion rate is needed.

    Which means you could have two young stars of equal mass, internal temperature and fusion energy productions, of which one has low conductivity and luminosity and meets the luminosity by fusion, being a red dwarf, but the other with higher conductivity has higher luminosity, which it cannot meet by fusion and never will be able to, and is a brown dwarf.
    That is just what I am saying does not happen. That is not at all the difference between a red dwarf and a brown dwarf. The difference is not conduction rates, it is core temperature. If you take a brown dwarf with its low core temperature, you can increase its conduction rate as much as you like (more likely convection rate, but it matters not what process is setting the star's luminosity), and it will not become a red dwarf-- it will just be a more rapidly cooling off brown dwarf. The distinction between a red dwarf and a brown dwarf is not actually a distinction in luminosity, which would depend on the processes that set that luminosity. It is a distinction in core temperature, which relates to whether or not there is stably self-regulated fusion going on.

  2. #32
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    Quote Originally Posted by chornedsnorkack View Post
    Yes. The topic that concentrated attention here was the question of what determines red dwarf luminosity. So the point of concentration was around the red dwarf/brown dwarf boundary.
    Actually, that was not at all the topic, but it was a topic that you decided to raise. The topic was about typical red dwarfs, and what sets their luminosity. Of course the boundary of any type of object with some other type of object is going to introduce other issues not relevant to the object in question. But it is still an interesting physics question, albeit off topic. And the answer is, whatever is the physics that sets the luminosity of boundary objects between red dwarfs and brown dwarfs, the key dividing line is whether or not fusion is able to supply that luminosity, and that will depend on the temperature the core is able to reach before degeneracy sets in. If the core can get hot enough that stable fusion can supply the luminosity, then it will do just that, and degeneracy will have to wait out the end of the fusion fuel. If degeneracy gets there first, then it can prevent fusion from ever taking hold by preventing the core temperature from getting high enough for the onset of fusion.

    And if a situation is created where degeneracy is raised first but later mass is added that brings the star up to fusion onset, then the fusion will be unstable because of the high degeneracy, and there will be a flash of fusion that removes the degeneracy and returns the core to stable fusion conditions as if the degeneracy had never had been there in the first place.

    The important effect, however, is probably the effect of metallicity on conductivity.
    What is with this focus on conductivity? The place where opacity matters is only near the surface, elsewhere the star is convective. But again, what I'm saying does not depend on the details that set the luminosity, it is enough that the star has some structure that determines some luminosity, and the question then becomes, can fusion supply it. If it can, it will.
    Last edited by Ken G; 2020-Feb-13 at 05:49 AM.

  3. #33
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    Quote Originally Posted by Ken G View Post
    Not clear what you are saying here, free fall does not happen unless there is a strong cooling instability, nothing to do with fusion.
    I said free fall timescale. If there is a strong heating instability at timescales faster than free fall, it cannot be resolved by expansion.
    Quote Originally Posted by Ken G View Post
    But that's just completely obvious, of course there are situations where the temperature never gets high enough for the onset of fusion. My comment was that when the temperature does get high enough, the slowness of protium fusion will not be a problem, because it is plenty fast enough. Speed is never the problem for fusion,
    No, the speed is the problem. Because it is the speed of fusion that participates in setting which temperatures are "high enough" and which are "not quite high enough".
    Quote Originally Posted by Ken G View Post
    if the temperature is right and the protons are fusing in the first place, they will happily self-regulate their temperature to provide whatever fusion rate is needed.
    Degeneracy sets the maximum temperature and maximum fusion rate to which the core can be regulated.
    Quote Originally Posted by Ken G View Post
    That is not at all the difference between a red dwarf and a brown dwarf. The difference is not conduction rates, it is core temperature. If you take a brown dwarf with its low core temperature, you can increase its conduction rate as much as you like (more likely convection rate, but it matters not what process is setting the star's luminosity), and it will not become a red dwarf-- it will just be a more rapidly cooling off brown dwarf.
    Because you then are displacing the brown dwarf away from the limit.
    If you took a red dwarf with its low core temperature and increased its conduction rate, it would try to increase its fusion rate by contracting and heating, fail - because of degeneracy, it would pass the maximum temperature and start cooling, and shut down fusion instead.
    If you took a brown dwarf with its low core temperature and decreased its conduction rate, the heat insulation would cause the modest amount of fusion heat to accumulate and lead to runaway heating into a red dwarf.
    Quote Originally Posted by Ken G View Post
    The distinction between a red dwarf and a brown dwarf is not actually a distinction in luminosity, which would depend on the processes that set that luminosity. It is a distinction in core temperature, which relates to whether or not there is stably self-regulated fusion going on.
    My point is that the processes that set the luminosity define whether a given core fusion output and a given core temperature are or are not stable.

  4. #34
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    Quote Originally Posted by chornedsnorkack View Post
    I said free fall timescale. If there is a strong heating instability at timescales faster than free fall, it cannot be resolved by expansion.
    Yes, it leads to things like supernovae. But these are rare situations.
    Degeneracy sets the maximum temperature and maximum fusion rate to which the core can be regulated.
    Yes, that's what the "onset of fusion" is all about. If the maximum fusion rate is sufficient to supply the luminosity, then it will, and we say we have fusion onset.
    If you took a red dwarf with its low core temperature and increased its conduction rate, it would try to increase its fusion rate by contracting and heating, fail - because of degeneracy, it would pass the maximum temperature and start cooling, and shut down fusion instead.
    But that's where the temperature sensitivity of fusion comes into play. The temperature required to supply the luminosity is only weakly affected by changes in luminosity, it precipitates only a small adjustment. Yes that could mean a tiny fraction of brown dwarfs are unable to become red dwarfs, but it's only a tiny fraction. The point is, there is a map from stellar mass to maximum core temperature allowed by degeneracy, and that is a scaling like mass to the 4/3 power. The fusion rate is then a steep function of that temperature, perhaps temperature to the 4th power though it depends on just what the T is. So we have an expression like maximum fusion rate scales like mass to the 16/3 power. Hence, if one increases the luminosity at the current boundary of brown dwarfs and red dwarfs by a factor of 2, that would move the mass boundary by the factor 2^(3/16), merely 14%. This is why the boundary is regarded as a fairly sharp "onset" boundary.

    My point is that the processes that set the luminosity define whether a given core fusion output and a given core temperature are or are not stable.
    That's not what stability means. It is about what happens if the fusion rate is a little higher than the luminosity, it doesn't matter what the luminosity actually is. The question to ask is, does such an excess turn itself back down, or continue to ramp up? Whenever the degeneracy is high, this is the situation you get into, but the fusion rate has to be faster than the time it takes to remove the heat, so it only applies above the "onset" dividing line. Normally, a red dwarf is not particularly degenerate when it begins fusion, so it's not unstable, but if it went degenerate first, then gained mass, it would be unstable. The real point is, degeneracy can only prevent the temperature from reaching the fusion threshold-- once there, degeneracy is powerless to prevent the onset of fusion, and indeed, degeneracy would only make that onset all the more unstable, and that would lift the degeneracy until the fusion fuel is expended.

  5. #35
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    Quote Originally Posted by Ken G View Post
    Yes, it leads to things like supernovae. But these are rare situations.
    Yes. And my point is that protium cannot explode as supernova because protium fusion is too slow.
    Quote Originally Posted by Ken G View Post
    That's not what stability means. It is about what happens if the fusion rate is a little higher than the luminosity, it doesn't matter what the luminosity actually is. The question to ask is, does such an excess turn itself back down, or continue to ramp up? Whenever the degeneracy is high, this is the situation you get into, but the fusion rate has to be faster than the time it takes to remove the heat, so it only applies above the "onset" dividing line. Normally, a red dwarf is not particularly degenerate when it begins fusion, so it's not unstable,
    The point is, what happens if the luminosity is a little higher than fusion rate? Does the core shrink slightly, heat up and increase fusion rate till it matches the luminosity? Or does the core shrink slightly, pass the maximum temperature and fusion rate without meeting the luminosity, and continue to cool down and shrink at increasing degeneracy?
    Now, to the issue of convection vs. conduction.
    Note that convection can carry an arbitrarily large luminosity at a constant (adiabatic) heat gradient. But the minimum luminosity at that heat gradient is fixed by the conductivity - the convection can slow down but at a certain minimum luminosity, conduction forces the heat gradient below the adiabatic one.
    Since in a convective star, it is the convection rate/fraction that can self-regulate, how is the actual luminosity set?

  6. #36
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    Quote Originally Posted by chornedsnorkack View Post
    Yes. And my point is that protium cannot explode as supernova because protium fusion is too slow.
    We covered that above, it was never in dispute. The issue is when does degeneracy prevent fusion, and when does fusion remove or pause the degeneracy. The answer is, the latter happens whenever the evolution of the core temperature brings it up to a level high enough for fusion to supply the stellar luminosity. How that luminosity is set is not important, and one barely even needs to know what it is because fusion is temperature sensitive enough that the core temperature need only be known in general terms, for a conceptual understanding.
    The point is, what happens if the luminosity is a little higher than fusion rate?
    This seems to be the fundamental mistake you are making, you are imagining that the ultimate outcome depends on whether some initial perturbation happens to be upward or downward in luminosity. But given my statement just above, we must imagine that there is some kind of evolutionary pressure that has brought the core temperature up to the relevant level (otherwise we have no need to even consider fusion). That evolutionary pressure is not going to go away based on some stability analysis. The answer to your question here is, assuming we have stable fusion (that seems to be the situation you are considering, so we have a red dwarf of fixed mass that is first encountering high core temperatures), if the luminosity is above the fusion rate, then we are in the same situation the star has been its entire life so far. It will contract, as per the virial theorem. That will raise its core temperature and we are no different from the entire evolutionary history of that star. Soon enough, it's core T will either rise high enough and fusion will balance luminosity, or degeneracy will prevent that. This is what I've said all along-- if degeneracy would stop fusion, it must get there before fusion is able to supply the luminosity. If the latter happens first, degeneracy must await the fusion fuel to be exhausted.

    If, on the other hand, degeneracy is already high by the time evolutionary pressure has brought the core to fusion temperature (which generally only happens if mass is being added to the star), then the fusion is unstable. If an initial perturbation reduces the fusion rate, it will now cause the core temperature to drop and shut fusion off altogether. BUt that is of no consequence at all, because it merely returns the core to its previous state of no fusion, which means it returns it to the evolutionary pressures that brought it to the brink of fusion in the first place, and we simply try again. That continues until a perturbation happens to raise the fusion, and this time it will run away until it lifts the degeneracy and stabilizes fusion. Either way, degeneracy must await the removal of the fusion fuel. That's all a red dwarf is.
    Now, to the issue of convection vs. conduction.
    Note that convection can carry an arbitrarily large luminosity at a constant (adiabatic) heat gradient. But the minimum luminosity at that heat gradient is fixed by the conductivity - the convection can slow down but at a certain minimum luminosity, conduction forces the heat gradient below the adiabatic one.
    If you recall, this entire thread is from a question about fully convective stars. So we already know we are talking about a convective star, and thus we already know the convection can, and is, carrying more luminosity than conduction could handle, and the convective heat flux will be controlled by the needs of the star based on considerations other than conduction. If we have a red dwarf well away from the boundary with brown dwarfs,we have little degeneracy to worry about, so we have a Hayashi track object whose luminosity is mostly controlled by its radius, and its radius is mostly controlled by the need to be hot enough in the core to have H fusion match the luminosity. That's what sets the luminosity of a red dwarf, considered as an archetype-- a point of reference if you will, perhaps early M dwarfs with the same surface temperature as a red giant it is being compared to. Individual red dwarfs will find their luminosity falls well below that archetypical answer if they are too near to the boundary with brown dwarfs (the later M dwarfs), as the physics is quite different down there (largely due to the importance of degeneracy, which is also responsible for there being a boundary in first place).
    Since in a convective star, it is the convection rate/fraction that can self-regulate, how is the actual luminosity set?
    That was the question I answered from the start. You pointed out that my answer could not explain the extreme drop in luminosity for stellar masses appoaching that of brown dwarfs. That is true, but my answer was never intended to apply for brown dwarfs, and that's why it begins to break down as that boundary is approached. It is the role of degeneracy that is not included in the Hayashi track argument, but the OP was not asking about how degeneracy reduces luminosity, the question contrasted red giants and red dwarfs, which to me focuses on the luminosity difference between two sizes of ideal-gas convective objects, and the answer in general terms is, the convection supplies the luminosity required by the radius of the star. I accept that degeneracy in low-mass red dwarfs / brown dwarfs reduces luminosity drastically, right down until you have Jupiter, so one could also take that perspective in answering the OP, but then the OP may as well have asked why fully convective red giants are so much more luminous than fully convective brown dwarfs.
    Last edited by Ken G; 2020-Feb-16 at 08:51 PM.

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