If there's a simple explanation, I don't know it. The reason for the
general trend of shallower convective layers in hotter stars is the
one I gave in the previous post: hotter temperatures. Location of
convective zones is, of course, an output of any detailed model.

On Apr 21, 4:06 pm, will...@cfa.harvard.edu (Steve Willner) wrote:

If there's a simple explanation, I don't know it. The reason for the
general trend of shallower convective layers in hotter stars is the
one I gave in the previous post: hotter temperatures. Location of
convective zones is, of course, an output of any detailed model.

Degeneracy pressure, right? For a star to be convective all the way
down,
I believe it must have a source of support other than ideal gas
pressure or
it would be unstable. This is degeneracy in red dwarfs, and radiation
pressure in massive stars.

I think that a star must have a source of support other than radiation

Degeneracy pressure, right?

For a star to be convective all the way down, I believe it must
have a source of support other than ideal gas pressure or it would
be unstable.

In article <b80f3645-6a91-493f-87ae-bf685885f...@24g2000hsh.googlegroups.com>,
Andrew Usher <k_over_hb...@yahoo.com> writes:

Degeneracy pressure, right?

Perhaps you are thinking of the stability of the entire star.
Degenerate cores are stable if their mass is below the "Chandrasekhar
limit" (about 1.4 solar masses) and unstable if more massive than
that. Stars supported entirely by radiation pressure (as very hot,
massive stars are) are also unstable.

Convective stability is a question of how energy is transferred in
each layer.

For a star to be convective all the way down, I believe it must
have a source of support other than ideal gas pressure or it would
be unstable.

Nope. Red dwarfs are non-degenerate all the way down as long as
nuclear burning continues. So are massive stars burning hydrogen via
the carbon cycle.

Precisely how does "degenerate" matter differ from non-"degenerate"

Precisely how does "degenerate" matter differ from non-"degenerate"
liquid or solid?

In article <04281fea-a9ec-4e0c-85ba-fe0e976f0...@c58g2000hsc.googlegroups.com>,
Crown-Horned Snorkack <chornedsnork...@hush.ai> writes:

Precisely how does "degenerate" matter differ from non-"degenerate"
liquid or solid?

It's a matter of the "equation of state," which relates pressure to
temperature and density. In degenerate matter, the pressure comes
from the Fermi exclusion principle, either from electrons (in white
dwarfs and the cores of massive stars) or neutrons (in neutron
stars).

Pressure depends on density but not at all on temperature.

In non-degenerate stars, pressure is given to a good approximation
by the ideal gas law and depends on both temperature and density.

And the pressure of light is independent of density.

And in liquids and solids, pressure comes from Fermi exclusion of
electrons.

Compressing a solid or liquid changes its pressure a lot. Changing
temperature at constant pressure causes a small change of volume,

changing temperature at constant volume causes small changes of
pressure, but small compared to the density dependence.

And the pressure of light is independent of density.

In article <b80f3645-6a91-493f-87ae-bf685885f...@24g2000hsh.googlegroups.com>,
Andrew Usher <k_over_hb...@yahoo.com> writes:

Degeneracy pressure, right?

Perhaps you are thinking of the stability of the entire star.

Convective stability is a question of how energy is transferred in
each layer.

For a star to be convective all the way down, I believe it must
have a source of support other than ideal gas pressure or it would
be unstable.

Nope. Red dwarfs are non-degenerate all the way down as long as
nuclear burning continues.

On Apr 24, 3:53 pm, will...@cfa.harvard.edu (Steve Willner) wrote:

In article <b80f3645-6a91-493f-87ae-bf685885f...@24g2000hsh.googlegroups.com>,
Andrew Usher <k_over_hb...@yahoo.com> writes:

Degeneracy pressure, right?

Perhaps you are thinking of the stability of the entire star.

No, I have worked it out.

Convective stability is a question of how energy is transferred in
each layer.

Yes, convection occurs if the temperature gradient exceeds a critical
value; and because convection is so efficient, the gradient
practically does not exceed that value.

Agreed.

For a star to be convective all the way down, I believe it must
have a source of support other than ideal gas pressure or it would
be unstable.

Nope. Red dwarfs are non-degenerate all the way down as long as
nuclear burning continues.

Wrong. A fully convective star must be described by a polytrope whose
index is equal to Cv - 3/2 for an ideal monoatomic gas. Therefore, it
is unstable against small changes in energy production (as long as Cv
is constant)

In article <66aca9e2-db9c-4b06-9268-89a3387d6...@34g2000hsf.googlegroups.com>,
Crown-Horned Snorkack <chornedsnork...@hush.ai> writes:

And in liquids and solids, pressure comes from Fermi exclusion of
electrons.

No, the pressure is from ordinary electromagnetic forces.

White
dwarfs are a lot denser than ordinary liquids and solids.

Compressing a solid or liquid changes its pressure a lot. Changing
temperature at constant pressure causes a small change of volume,

Yes.

changing temperature at constant volume causes small changes of
pressure, but small compared to the density dependence.

No; it causes huge changes in pressure. Imagine heating the material
first at constant pressure, then trying to get the volume back to
where it was. That takes enormous pressure.

If you heat water at 1 atm from 4 celsius to 100 celsius, its density

This is quite different behavior than degenerate matter.

And the pressure of light is independent of density.

Light pressure depends on energy density, but I don't see what that
has to do with degenerate matter. In a star, the relevant pressure
is the sum of all forms of pressure. That includes magnetic
pressure, for example, but that would be trivally small in normal
stars.

Sure. My point is that at low temperatures and high densities, it is

For a star to be convective all the way down, I believe it must
have a source of support other than ideal gas pressure or it would
be unstable.

Nope. Red dwarfs are non-degenerate all the way down as long as
nuclear burning continues.

Wrong. A fully convective star must be described by a polytrope whose
index is equal to Cv - 3/2 for an ideal monoatomic gas. Therefore, it
is unstable against small changes in energy production (as long as Cv
is constant)

Explain why.

The temperature gradient in a convective star cannot be changed by
changes in energy production.