[mesa-users] Creating a gamma Dor model

Sat Jul 16 17:40:49 EDT 2016

i had a interesting and fun journey looking back at vardya (1964)
and related works of this era. a few even made it into my personal
paper library.

vardya (1964) presents an analytical equation of state for ionizing hydrogen
in the non-degenerate, non-relativsitic, non-pressure-ionized limit. 
it is chiefly focused on expressions for the specific heats, which of course 
are derivatives of thermal energy, pressure and entropy. rather uniquely the 
paper also offers closed-form expressions for the derivatives of the specific heats 
and ionization fraction with respect to temperature and density. these second derivative
based quantities may not be so surprising given that vadya was working closely with henyey 
on his stellar evolution instrument.

in my opinion, like the wigner-seitz cell based coulomb correction presented 
in clayton (1968), the main downside of the approach is the lack of thermodynamic 
consistency (i.e., deriving everything from a thermodynamic potential and a root-find
for chemical potentials). for example, adding terms to the pressure without accounting 
for the accompanying changes in the thermal energy or entropy is a sure-fire way to 
effectively be including an entropy or temperature source term in the equation of state. 

an unspoken challenge with the warner et al (2003) is how they blend the iben eos
with the vardya eos without generating yet additional entropy or temperature 
source terms. 

i'm not in any mood to attempt a recreation of the warner et al eos and install
it in mesa, but i am left with the impression that ehsan & aaron may well be right:
the thicker convective zone in warner et al could be from the spurious generation of
entropy/temperature from an inconsistent eos.

fxt

> On Jul 14, 2016, at 9:51 AM, Francis Timmes <fxt44 at mac.com> wrote:
> 
> vardya (1964) is behind a paywall, but i got it. 
> i'll email it if anyone is interested. i'll send my thoughts 
> on it and the stated coulomb corrections later today.
> 
> fxt
> 
> 
> 
> 
>> On Jul 14, 2016, at 6:54 AM, Aaron Dotter <aaron.dotter at gmail.com> wrote:
>> 
>> Hi folks,
>> 
>> I think Ehsan is on the right track.  Quoting Warner et al., 
>> 
>> "The equation of state (EOS)is a variation of that presented by Iben (1975) using the Eggleton, Faulkner, & Flannery (1973) EOS for temperatures greater than 4.5 × 106 K and the Vardya (1964) EOS for lower temperatures, and it has been corrected for Coulomb shielding (see, e.g., Clayton 1968)."
>> 
>> Since the section of the model Rich is interested is in the partially-ionized regime, the quality of the Iben EOS is not directly relevant.  (As Bill says "stellar evolution is highly nonlinear" so it's not irrelevant.)  Vardya (1964) does not seem to be readily available to the interested reader but I'm willing to bet that it gives sufficiently different results to the OPAL EOS that is a plausible culprit, though it may be impossible to put this to the test in 2016.
>> 
>> Aaron
>> 
>> 
>> 
>> On Wednesday, July 13, 2016, Francis Timmes <fxt44 at mac.com> wrote:
>> generally, the pressure and thermal energy from the iben eos
>> is within 0.1% of other independent eos routines and the
>> derivatives of those quantities are within 1%. the largest
>> deficiency of the iben eos is that it does not include positrons,
>> a very reasonable approximation for the main topics that icko pioneered.
>> 
>> if one would like to basis for the statements above:
>> 
>> http://adsabs.harvard.edu/abs/1999ApJS..125..277T
>> 
>> and if one is so inclined, the iben eos can be downloaded here:
>> 
>> http://cococubed.asu.edu/code_pages/eos.shtml
>> 
>> fxt
>> 
>> 
>> 
>> 
>> 
>>> On Jul 13, 2016, at 5:12 PM, Ehsan Moravveji <e.moravveji at gmail.com> wrote:
>>> 
>>> Hi Rich,
>>> 
>>> Naively, I just took a very quick peek at the Sect. 2 in Warner et al. (2003)  and noticed that there is a significant version difference between the EOS they use (Iben 1976), compared to that of MESA (updated OPAL 2005). Since nabla_ad is among the return columns of the EOS, “perhaps”, the difference you see in your boundary locations stems from different EOS values for nabla_ad through the two EOS versions.
>>> If this is so, I do not have an immediate idea how to “downgrade” to the old EOS, and reproduce Warner's models; else, let’s hope that the more recent MESA EOS gives is more accurate in providing nabla_ad values.
>>> 
>>> B.t.w. the clocks have ticked since the 70s, and our understanding of stellar EOS has advanced. Thus, your model “might be” a more accurate representation of gamma Dor stars: Your instability strips will tell ;-)
>>> 
>>> The good thing is that your composition (Z=0.02, Y=0.28) and mixture (GN93) is identical to theirs.
>>> 
>>> Best regards,
>>> Ehsan.
>>> 
>>>> On 13 Jul 2016, at 20:03, RICHARD H D TOWNSEND <townsend at astro.wisc.edu> wrote:
>>>> 
>>>> Hi folks —
>>>> 
>>>> I’m interested in creating a models for gamma Dor stars, in which gravity modes are unstable due to convective flux blocking. I’ll be using GYRE to do the stability calculations; I appreciate that the convection-pulsation interaction probably needs a more-sophisticated approach than GYRE’s current method (convective freezing), but for now GYRE should suffice.
>>>> 
>>>> My first step is attempting to reproduce some of the gamma Dor models presented in Warner, Kaye & Guzik (2003, ApJ 593, 1049). However, try as I might, I seem to end up with models that don’t have the (relatively) thick outer convection zone reported by Warner et al.
>>>> 
>>>> As a specific example, I attach a MESA inlist which aims to reproduce the M=1.55 Msun model reported in Table 1 of Warner et al. Running this inlist with MESA 8118 results in a final model with the following properties:
>>>> 
>>>> Teff = 6927 K
>>>> L/Lsun = 6.82
>>>> Age = 1.049 Gyr
>>>> 
>>>> This model is somewhat cooler than the model reported in Warner et al (their Teff = 6965K), but the difference is small. The luminosity matches exactly, and the age is close (their age = 1.076 Gyr). So, it looks like I’m in the right ballpark.
>>>> 
>>>> However, when I look at the internal structure of the model, I’m struck by the fact that the inner edge of the envelope convection zone is at T ~ 63 kK (logT ~ 4.75), rather than the ~ 240 kK (logT ~ 5.4) reported by Warner et al. Here’s a plot of the radiative vs total flux, as a function of temperature, which demonstrates this:
>>>> 
>>>> <figure_1.png>
>>>> 
>>>> Indeed, I find that to get the convection zone(s) to extend to deeper layers, I have to allow the star to be significantly cooler and more evolved.
>>>> 
>>>> Since I’m not all too familiar with gamma Dor stars, I’m likely making a stupid mistake in my inlist file. Can anyone suggest what might be the problem?
>>>> 
>>>> Many thanks,
>>>> 
>>>> Rich
>>>> 
>>>> <inlist><profile_columns.list>
>>>> 
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