[Mesa-users] Internal energy profile

[Luke Chamandy]

Hi Josiah,

Also, I just want to confirm something: the MESA tabular EoS (or maybe just
the OPAL part of the tables?) includes the radiation energy density, and
assumes this to be given by Erad=aT^4 with a the radiation constant, but
the radiation pressure is not included at all in the EoS tables. Rather
Prad is added separately by MESA and the P in the tables is the gas
pressure only. Is this correct? If I wanted to remove the radiation energy
from the tables, would I just subtract aT^4/rho from the specific internal
energy?

Thanks for your help,
Luke

On Fri, Aug 7, 2020 at 3:59 PM Luke Chamandy <lchamandy at gmail.com> wrote:

> Hi Josiah,
>
> Thanks!! Yes, your first two points had been taken into account but your
> third point is correct. The right hand side is not equal to the thermal
> energy when ionization and recombination are taking place. So I was just
> confused about the physics, and everything seems to make sense now
> that I've cleared that up. (I also managed to run MESA r12778 and confirm
> the results are very similar to r8845 for this case.)
>
> Best wishes,
> Luke
>
> On Thu, Aug 6, 2020 at 11:48 AM Josiah Schwab <jwschwab at ucsc.edu> wrote:
>
>> Hi Luke,
>>
>> I am trying to understand the internal energy density profile of my ZAMS
>>> 2 Msun RGB star. When I plot the expected thermal energy density of the gas
>>> P_gas/(gamma3-1), I find that in the outer part of the profile it exceeds
>>> the internal energy density (specific energy times mass density). I don't
>>> see how the thermal energy could exceed the internal energy, particularly
>>> considering that the latter includes the latent recombination energy
>>> (please see attached--I don't understand why the magenta line is sometimes
>>> above the black line). When I add the recombination energy from hydrogen
>>> and helium the problem naturally gets worse. I am using version 8845. Is
>>> there something in the code (or physics) that I am not understanding?
>>>
>>
>> A few thoughts:
>>
>>   * be careful about what MESA EOS quantities include radiation.  lnPgas
>> excludes radiation, but other EOS qualities (i.e. lnE) include it
>>   * you don't need to add recombination energy.  It is already there in
>> the EOS. See some discussion in Paxton et al. (2018), Sec 8.4.
>>   * I don't think I understand why E > Pgas / (gamma3 - 1) would always
>> be true.  Seems like this can (and does) flip when gamma3 softens in
>> regions where the ionization state is changing.
>>
>> Josiah
>>
>>
>
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