[Mesa-users] MESA's Molecular Hydrogen EOS in low-Temperature & low-Pressure Regime

[Evan Bauer]

Hi Charlie,

This is a great diagnosis and question! Sorry it took so long to get back to you.

MESA ideal EOS is a fallback for regions where we just don't have coverage from anything else. It is designed to do the simplest thing possible, mostly to provide approximate thermodynamics for the solver when it is iterating toward solutions and strays away from the regions where we have more realistic EOS coverage. We don't want the models to just error out and return NaN, so ideal EOS is mostly a way to hopefully point the solver in the right direction so that it can converge back to where we have good EOS coverage. If you are making models that actually live in the regime where they need to use the ideal EOS, MESA probably is not up to the task of giving you accurate physics for that regime.

So the MESA ideal EOS fallback assumes all neutral atoms, no molecules. We could perhaps patch it up to at least include neutral hydrogen, but it might be misguided to start putting in that sort of physics without going much further. Of course, if there's a counterargument here that we haven't thought of, we're always open to suggestions and/or pull requests!

Does that help answer the question?

Cheers,
Evan

> On Nov 6, 2022, at 11:01 AM, Charlie Willard via Mesa-users <mesa-users at lists.mesastar.org> wrote:
> 
> Hello all,
> 
> I have a question regarding the representation of molecular/atomic/ionized (etc.) hydrogen in the Mesa EOS tables.
> 
> I have extracted the Mesa EOS information for mean molecular weight per gas particle (mu) and density (rho) for a pure hydrogen atmosphere.
> I am roughly working in the regime of 2<log(T)<4.5 Kelvin and 6<log(P)<13 dyne/cm^2 (for SubNeptune Exoplanet Atmospheres), which is primarily governed by the SVCH/OPAL EOS in Mesa.
> 
> The mu output by MESA appears to be different from the mu calculated directly from SCVH EOS. I've attached a plot where the blue dots show mu for SCVH while the red-orange surface shows mu output by MESA for pure hydrogen. Notably in the regime (lowT/lowP) where I had expected mu = 2 amu (Molecular Hydrogen), MESA output mu = 1 amu (atomic hydrogen).
> 
> In the ideal gas regime, the density rho of the gas output by MESA appears consistent with that of an ideal gas with mu=1amu, instead of mu=2 amu as expected for molecular hydrogen. In the P-T range spanned by the SCVH EOS in MESA, the density rho output by MESA appears to agree with the density I interpolated directly from SCVH (even if the mu's disagree).
> 
> Am I misinterpreting something, or is this the expected behavior of hydrogen in MESA?
> 
> I have attached the project folder containing the inlist/run_stars_extras files used to generate the data in the plot. Also in the folder are the data-lists extracted as well as the python notebook used to generate the plot.
> My specific use case was to compute the compressibility factor, Z = PV_m/RT (where V_m = mu/rho), for the gas in a planet's atmosphere.
> 
> Thank you for your help,
> Charlie Willard
> University of Chicago Undergraduate
> Mesa version: 22.05.1
> 
> <Screen Shot 2022-11-06 at 12.40.44 PM.png>
> 
>  Z_Test_Heos 2.zip <https://drive.google.com/file/d/13IxTQUjETxfq-MXb19CoQXxa6mTv3o1H/view?usp=drive_web>
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