[mesa-users] EOS / Gamma_1 derivatives

[Frank Timmes]

just a note. most of eos sources that comprise mesa's
tables start from a free energy. first derivatives wrt
T and rho give the primary quantities of interest, P, E, and S. 
second derivatives give things like specific heats, gamma_1,
and others. third derivatives then can give things like 
d(gamma_1)/d)(rho) and others. very few (one?) of the eos's
that go into mesa's tables are capable of returning such 
third derivative information. plus, interpolating eos data
from a table adds its own wrinkles on providing accurate,
thermodynamically-consistent second derivatives of, say, P.
finally, most of the eos's encapsulate the composition in
terms of the average atomic weight abar and average charge zbar.
things like d(abar)/d(4he) are easy, but getting first, second,
and third derivatives wrt to the encapsulated composition is
a tall order. these are some of the reasons columns 26-28 are empty.

of course, for a simple ideal gas with simple compositions
it is possible to fill these columns.

fxt



> On Nov 28, 2016, at 7:47 AM, Earl Bellinger <bellinger at mps.mpg.de> wrote:
> 
> Dear Bill and Rich,
> 
> Thanks for your quick replies. Yes, I am trying to use these
> quantities for my calculations. Do you happen to know how to obtain
> them? If not, I'll try to work on it.
> 
> Best regards,
> Earl Bellinger
> 
> 
> 
> ---
> www.earlbellinger.com
> Department of Astronomy, Yale University
> Stellar Ages & Galactic Evolution Group, Max Planck Institute
> 
> 
> On Mon, Nov 28, 2016 at 8:35 AM, RICHARD H D TOWNSEND
> <townsend at astro.wisc.edu> wrote:
>> Hi Earl —
>> 
>> My understanding is that these fields are used to explore how asteroseismic kernels are sensitive to changes in the helium abundance. But, as you have noted, MESA doesn’t write meaningful data to them (and GYRE doesn’t use them).
>> 
>> Do you actually need these data, or were you concerned that they didn’t make sense?
>> 
>> cheers,
>> 
>> Rich
>> 
>>> On Nov 27, 2016, at 3:18 PM, Bill Paxton <paxton at kitp.ucsb.edu> wrote:
>>> 
>>> 
>>> On Nov 27, 2016, at 12:49 PM, Earl Bellinger wrote:
>>> 
>>>> In the specification of the FGONG file format [1, section 2.1.3],
>>>> model variables 26-28 are to contain derivatives of \Gamma_1 with
>>>> respect to density, pressure, and helium abundance, respectively;
>>>> with, in each case, the other two unused variables being held
>>>> constant.
>>> 
>>> Hi Earl,
>>> 
>>> Good to hear you are plugging away.  It seems you've turned up an error of omission in mesa's FGONG output.
>>> 
>>> You can see it in star/private/pulse_fgong.f90 in subroutine get_fgong_data.
>>> 
>>> The code carefully sets the variables as expected, but it jumps from 25 to 29 neatly skipping over the ones you want.
>>> 
>>> Then in subroutine write_fgong_data it writes out uninitialized values for those missing entries - hence the results you see.
>>> 
>>> Rich Townsend is the one for you to talk to about this to see if there is a simple fix.
>>> 
>>> Good luck,
>>> Bill
>>> 
>>> 
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