[mesa-users] Dependence of EOS on mixture

[Ehsan Moravveji]

Thanks Rich,

> On 27 Oct 2015, at 11:24, Richard Townsend <rhtownsend at icloud.com> wrote:
> 
> Hi Ehsan —
> 
>> On Oct 27, 2015, at 8:32 AM, Ehsan Moravveji <e.moravveji at gmail.com <mailto:e.moravveji at gmail.com>> wrote:
>> 
>> Hi Rich,
>> Based on the 1st instrument paper, the MESA EOS tables use the OPAL tables from Rogers & Nayfonov (2002) <http://iopscience.iop.org/article/10.1086/341894/pdf;jsessionid=FAE385221B5B75D90355602FFF1A9004.c3.iopscience.cld.iop.org>.
>> Figure 13 in this paper shows clearly how Gamma_1 varies just below the surface if you use a 6-element mixture vs. 14-element mixture. The difference is eye-catching. Interestingly, in the OPAL tables, Fe is not accounted for, while its abundance is quite comparable to C, N, O and Ne. Thus, it is obvious that changing to a different mixture with tiny little differences in individual metal abundances “could potentially” influence the structure (and seismic frequencies) to a considerable level. However, I am not sure if the effect of such assumptions on the structure are well quantified in the literature. Do you know?
>> 
>> Let me also ask a question from the users, a long the same line: The adiabatic temperature gradient, \nabla_ad, returned from MESA EOS module is computed at: 
>> (a) constant entropy and composition (i.e. X, Y, Z)? 
>> or
>> (b) constant entropy and mixture (i.e. X_i)?
> 
> These are the same thing! In fact, I think you mean “constant entropy and mu” as the second option, right?
Yes. My option (b) is equivalent to “constant S and mu” once the partial ionisation are accurately accounted for in mu.

Another way of asking my question is: 
In the computation of the buoyancy frequency, where is the partial ionisation considered? In the s% grada coming from the EoS, or in the s% brunt_N2_composition_term?

Reading through get_brunt_B() subroutine in star/private/brunt.f90, there are two calls to the EoS to get lnP at two neighbouring points. I only “guess” that the ionisation is handled internally by the EoS to get lnP (because the call to eos_get() needs s% abar(k) and s% zbar(k) as an input). Thus, I only “guess” that partial ionisation is present in s% brunt_N2_composition_term. But, I could be totally wrong. 

I would be glad if someone enlightens me.

Best regards
Ehsan.

> 
> cheers,
> 
> Rich
> 
>> This is critically important when computing the composition gradient, \nabla_\mu, because of the effect of partial ionisation. Looking at Eq. (5) in the 2nd instrument paper, let’s bet on (b), but it is always very informative to hear from the experts in the user list.
>> 
>> Best regards
>> Ehsan. 
>> 
>>> On 20 Oct 2015, at 15:49, Richard Townsend <rhtownsend at icloud.com <mailto:rhtownsend at icloud.com>> wrote:
>>> 
>>> Hi folks —
>>> 
>>> I believe the MESA EOS tables are calculated for one specific metal mixture. Has anyone ever examined the effect this might have on stellar structure, especially on the presence (or absence) of convection in partial ionization zones?
>>> 
>>> cheers,
>>> 
>>> Rich
>>> 
>>> 
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