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

Wed May 13 02:54:09 UTC 2026

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>
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>
> *Sent:* Tuesday, May 12, 2026 10:10 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,
>
> 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>
> 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> on behalf of
> Ali Pourmand via Mesa-users <mesa-users at lists.mesastar.org>
> *Sent:* Tuesday, May 12, 2026 8:58 PM
> *To:* Natasha Ivanova <nata.ivanova at ualberta.ca>
> *Cc:* mesa-users <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
>
>
> [image: 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> 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
>
>
>
>
> _______________________________________________
> mesa-users at lists.mesastar.org
> https://lists.mesastar.org/mailman/listinfo/mesa-users
>
>
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