[mesa-users] mesa-users Digest, Vol 74, Issue 9

[Mike Montgomery]

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?

Partial ionization should be automatically taken into account in the EoS call. From equation 8 in the second Mesa paper (Paxton et al. 2013), the composition term is computed using pressures calculated at (rho, T) values at neighboring shells (which can have different compositions) as well as pressures calculated at (rho, T) values in the same shell, but again with potentially different compositions. For the requested rho, T, and composition the value of the pressure returned by the EoS calls will self-consistently include the effects of partial ionization. 

Whether there is an alternate formulation that is formally equivalent to this one is another question, but this seems to be the simplest and most robust prescription that we’ve come up with so far. 

Cheers,

Mike

> 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.
>