[mesa-users] entropy of accreting materials

Bill Paxton paxton at kitp.ucsb.edu
Thu Jun 6 14:13:30 EDT 2013


Hi,

On Jun 6, 2013, at 10:30 AM, Masanobu Kunitomo wrote:
> In MESA, the entropy of the accreting materials is determined by the compressional heating.
> Is it possible to just set that the entropy of the accreting material is the same as the stellar surface?

Good question.   As you mention, currently compressional heating determines the entropy.
In general, entropy is determined indirectly in the code -- the eos tells us the local entropy as a function
of the local temperature, density, and composition.  The energy equation has a term corresponding to
T*Ds/Dt that couples changes in entropy to the rest of the system.  So the entropy isn't
set directly, it "emerges" from the coupled changes in other values.  This means we
can't just set the entropy to a value we'd like it to have.  We need to go at it indirectly
and find ways to change the state of the cells in a manner that makes the entropy change
to what we want. 

In your case, you might try changing the entropy at or near the surface by using one of the
"hooks" for extending mesa/star -- either "other_energy" or "other_energy_implicit".
The 1st of these lets you set the vector "extra_heat" at the start of each timestep,
so you can selectively add heat in the outer layers to change the entropy.   
The 2nd hook, other_energy_implicit, is for cases in which you need to revise
the extra_heat value at each iteration of the newton solver as it searches for
a new model.  In that case, your routine is called at each iteration and must
return partials of extra_heat with respect to temperature and density.

You'll find that you will need to spread the extra_heat over multiple cells -- if you
try to put too much in any one cell, the code will probably fail to converge.
Try experimenting with it to see how much you need to smooth out the injected heat.

Also notice that if you are trying to change the entropy in a cell that is in a convective
region, then the system will adjust to distribute the extra heat to the rest of the
convective region in order to keep gradT nearly equal to grad_ad.  So you can't
make an isolated region in a convective zone have an entropy that is unrelated to
the rest of the zone -- convection won't let you do that.   

And then there's the whole issue of inefficient convection near the surface leading
to a drop in entropy in the outermost layers just below the photosphere.   

So, you can see that it isn't just a matter of "setting the entropy" to be what you want!
You have to find a way to convince the star that it wants to have that entropy, or
else it won't go along with you.

Good luck!

-Bill




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