[Mesa-users] EOS: unphysical low-temperature μ from OPAL/SCVH and HELM?

Wed May 13 03:37:51 UTC 2026

Yes,  I can reproduce your initial issue (in the attached image) mu.

I can say at least that the sliver region on the right in the rho-T EOS diagram is using Helm and therefore will return fully ionized mu. I do agree that this is potentially physically problematic, but connects well with SKYE's full ionization assumption. However at lowT, low density regime you've highlighted, OPAL/SCVH and FREE_EOS both appear to give an unphysical result. This indeed seems physically problematic.

-EbF
________________________________
From: Natasha Ivanova <nata.ivanova at ualberta.ca>
Sent: Tuesday, May 12, 2026 10:54 PM
To: Farag, Ebraheem <ebraheem.farag at yale.edu>
Cc: Ali Pourmand <pourmand at ualberta.ca>; mesa-users <mesa-users at lists.mesastar.org>
Subject: Re: [Mesa-users] EOS: unphysical low-temperature μ from OPAL/SCVH and HELM?

Hello Ebraheem,

I am aware that FreeEOS is not supported by default in this region. That was exactly the reason for my first email in this thread: the full default MESA EOS returns values that appear unphysical there.

My attempt to call FreeEOS directly was only a fallback test, to see whether any MESA EOS component can provide physically meaningful values in this regime. It was not my original concern.

This is also why I asked whether other returned quantities, such as pressure and internal energy, should be considered physically reliable if the returned mu is clearly not physical.

So far, the discussion has mostly focused on fitting, boundaries, and blending. But my concern is about the physical outcome. The plotted mu is the returned EOS result, and in the highlighted low-temperature regions it does not make physical sense.

Could someone please test the two regions circled in red in my first email, using a solar-like composition, for example X=0.70, Y=0.28? If you also obtain a mu close to the fully ionized value, around mu = 0.61-0.62, then the returned EOS quantities in this regime look physically problematic. If you instead obtain values appropriate for neutral or molecular gas, then I will be happy to send my wrapper so that we can identify what I am doing wrong.

Thank you,

Natasha

On Tue, May 12, 2026 at 8:45 PM Farag, Ebraheem <ebraheem.farag at yale.edu<mailto:ebraheem.farag at yale.edu>> wrote:
Hello Natasha,

Thanks for clarifying.

One potential suggestion when running the plotter. Perhaps in your plots test lower the following eos control defaults for Free_EOS to temperatures below the logT = 3 eos boundary:
logT_min_FreeEOS_hi = 3.1d0
logT_min_FreeEOS_lo = 3.0d0

In those regions you highlight MESA does not adopt Free_EOS by default, hence the controls above. Instead, MESA defaults nack to OPAL/SCVH and HELM in the two regions you highlight (See attached image from the MESA EOS documentation https://docs.mesastar.org/en/26.4.1/eos/overview.html). The green region represents the blending region with controls for the blending region in the eos controls documentation https://docs.mesastar.org/en/26.4.1/eos/defaults.html#freeeos-controls.

Perhaps you can test with HELM and OPAL/SCVH on as well which might better represent the default behavior encountered when using MESA. In a normal stellar model, MESA would not be using Free_EOS in this region.

In your original test, Perhaps the opal/scvh tables were unsupported with your given parameters so MESA fell back to a fully ionized mu? But the problem seems to be more an issue of eos coverage in this region. If we had an eos in this region (other than OPAL/SCVH), it would ideally supply the correct relevant ionization states and electron fraction, and corresponding molecular weight needed.

All this aside, It could be worthwhile to figure out why a fully ionized mu is returned at the lower boundary, and if it's coming directly out of Free_EOS when asked for quantities at or beyond the boundary, maybe that's something that could be improved.

-EbF

________________________________
From: Natasha Ivanova <nata.ivanova at ualberta.ca<mailto:nata.ivanova at ualberta.ca>>
Sent: Tuesday, May 12, 2026 10:10 PM
To: Farag, Ebraheem <ebraheem.farag at yale.edu<mailto:ebraheem.farag at yale.edu>>
Cc: Ali Pourmand <pourmand at ualberta.ca<mailto:pourmand at ualberta.ca>>; mesa-users <mesa-users at lists.mesastar.org<mailto:mesa-users at lists.mesastar.org>>
Subject: Re: [Mesa-users] EOS: unphysical low-temperature μ from OPAL/SCVH and HELM?

Hello Ebraheem,

It is not only a blending-boundary issue.

In the zoom-in that I attached, I show the large region where FreeEOS itself returns successful values, with frac_FreeEOS = 1 and ierr = 0. Therefore, at least for those points, the result is not due to blending with HELM, OPAL/SCVH, or ideal EOS.

The larger issue is that, over a broad low-temperature region, the returned value of mu is close to the fully ionized value. For example, at logT = 3 and logRho = -10.2, FreeEOS returns mu = 0.6157. At this temperature and density, matter should not be fully ionized in LTE. Hydrogen should be neutral or molecular, helium should certainly not be ionized, and pressure ionization is irrelevant at this density.

So the question is not only whether the blending boundary is smooth. The question is why an EOS component that is supposed to handle partial ionization returns a fully-ionized-like mu in a cold, low-density regime where such ionization is not physically plausible.

Best

Natasha

On Tue, May 12, 2026 at 8:07 PM Farag, Ebraheem <ebraheem.farag at yale.edu<mailto:ebraheem.farag at yale.edu>> wrote:
Hello Ali, Natasha (this reply is in reference to Ali's message)

Your figure appears to show the blending boundary region between the ideal gas (left) and helm (right) eos regions. I attach a reference image of the eos at Z=1 to illustrate where we are. In your image, the blending boundary does indeed look particularly unsmooth.

Both your region and Natash's problematic region (logT =3, logRho = -13) straddle the ideal gas boundary.

OPAL/SCVH and Free_EOS handle partial ionization
Helm EOS assumes full ionization
Ideal EOS assume no ionization

In reference to the jump in mu in your figure:
abar = 1/sum_i (X_i / A_i)
zbar = abar * sum_i (X_i Z_i / A_i)

For Helm with Z = 1, equal proportions C and O we get:
abar = 1 / ( 0.5/12 + 0.5/16 = 0.0729167) = 13.714
zbar = abar * (0.5*6/12 + 0.5*8/16) = 6.857

mu_ideal = abar = 13.714
mu_HELM = abar / (1 + zbar) = 13.714 / (1 + 6.857) = 1.745

The EOS does not blended in this regionat all, (hence there is no green in the figure I attached), but those narrow jagged features mightt deserve a closer look as it seems MESA is switching back and forth between HELM and ideal in your image. This could be related to some sort of interpolation in Z, although I'm not sure.

-EbF
________________________________
From: Mesa-users <mesa-users-bounces at lists.mesastar.org<mailto:mesa-users-bounces at lists.mesastar.org>> on behalf of Ali Pourmand via Mesa-users <mesa-users at lists.mesastar.org<mailto:mesa-users at lists.mesastar.org>>
Sent: Tuesday, May 12, 2026 8:58 PM
To: Natasha Ivanova <nata.ivanova at ualberta.ca<mailto:nata.ivanova at ualberta.ca>>
Cc: mesa-users <mesa-users at lists.mesastar.org<mailto:mesa-users at lists.mesastar.org>>
Subject: Re: [Mesa-users] EOS: unphysical low-temperature μ from OPAL/SCVH and HELM?

Hello all and Natasha,

I am writing just to confirm that we are facing similar problems, in a different regime and for different compositions however. Our mean molecular weight suddenly jumps from partially ionized to fully non-ionized in the wedge-like region you can see (where mu is roughly mu=14 for a Carbon-Oxygen mixture), which also corresponds to jumps in everything else. The reason is obvious if you look at the fractions of contribution from different underlying EOS tables. There do seem to be some regions that aren't covered smoothly but on the other hand fall out of conventional "stellar" regimes for (rho,u).

best regards
Ali

[EOS_rhoE_z0.9988_x0.0000.png]

On Wed, May 13, 2026 at 9:37 AM Natasha Ivanova via Mesa-users <mesa-users at lists.mesastar.org<mailto:mesa-users at lists.mesastar.org>> wrote:
Hello all,

I wrote earlier about this, but have not received a response yet. After digging further, the issue looks more serious.

I am testing MESA EOS through an external wrapper. I scan the (ρ,T) plane and record the values returned by eosDT_get. The attached plots show the returned μ and logP.

At low temperatures, some returned values look clearly unphysical. For example, at

log rho = -13, log T = 3

MESA returns

mu = 0.6157

which corresponds to fully ionized solar-composition gas. At this density and temperature, neither thermal ionization nor pressure ionization should apply. The EOS fractions show that this point comes fully from OPAL/SCVH:

frac_HELM      = 0
frac_OPAL_SCVH = 1
frac_FreeEOS   = 0
frac_PC        = 0
frac_Skye      = 0
frac_CMS       = 0

There is also another low-temperature region, also circled in the attached plot, where the fractions show that HELM is responsible, and the returned μ is again physically implausible.

My questions are:

  1.  If OPAL/SCVH or HELM return clearly unphysical μ in these regions, should pressure and internal energy returned there be considered reliable?
  2.  Is res(i_mu) intended to represent the physical mean molecular weight corresponding to the ionization state, or can it be only an effective/composition-based value?
  3.  Is there a supported way, from an external wrapper, to call FreeEOS only, without fallback to OPAL/SCVH or HELM, so that I can test whether FreeEOS behaves correctly in these regions?

thank you,
Natasha

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