[Mesa-users] EOS: unphysical low-temperature mu from OPAL/SCVH and HELM? (Farag, Ebraheem)
Francis Timmes
fxt44 at mac.com
Wed May 13 16:06:10 UTC 2026
> I'm not sure why the original extended table boundaries were chosen to be near logRho = -10,
the original helm table went to rho = 1e-6 g/cm^3. when mesa started i extended the table to 1e-10 g/cm³ as that was deemed low enough. this is the origin of the "original extended table boundaries". years later, that got lowered again for mesa to the current 1e-12 g/cm³ (and at much higher table densities, 100 points/decade). i've heard calls in recent times to lower the helm table boundary yet again to 1e-15 g/cm^3.
fxt
> On May 13, 2026, at 8:47 AM, Farag, Ebraheem via Mesa-users <mesa-users at lists.mesastar.org> wrote:
>
> Hello Emily,
>
> • "There's no SCVH-based reason that MESA's OPAL/SCVH table edge needs to be at log10rho ~= -10 rather than log10rho ~=-15"
>
> Yes this is a good point.
>
> From the original SCVH paper abstract "the range 2.10 < log T(K) < 7.06 and 4 < log P(dyn cm-2 ) < 19", so the SCVH tables only go down to:
> logP = 4 or logRho ~ 6.5 at T = 10^3 K as shown in the figure you shared.
>
> MESA's EOS preprocessor extends these tables via a smooth blending procedure and some ideal gas assumptions to extend these tables to: logP ~ -0.6 (logRho ~ 10) at T = 10^3 K. This procedure was done once a long time ago, and I don't know why logP = -0.6 was chosen as the new extended boundary. This extension of the tables was computed and tabulated alongside the original tables. Extending further would require redoing whatever procedure created these extended_SCVH tables.
>
> MESA-docs highlight this somewhat vaguely: To extend to lower temperatures and densities, we use the SCVH tables (Saumon, Chabrier, & van Horn 1995), and construct a smooth transition between these tables in the overlapping region. This blend occurs in a pre-processing step and cannot be modified at runtime.
>
> Going down to logRho = -15, would require extending the tables further beyond it's density/logP floor for scvh, which might be possible, but not physically identical to have a self-consistent eos computed in this territory.
>
> So the "reason" is the published SCVH EOS tables are tabulated in T and P, not directly in rho. In MESA, evaluating SCVH at fixed T and rho requires solving for the pressure. The SCVH tables in MESA extended this work to a lower pressure of logP = -0.60 corresponding to the logRho = -10 floor in MESA’s SCVH to avoid evaluating the already extended SCVH tables below their new edges.
>
> Without extending the calculations of SCVH, to extend the tables, we would need to redo the ideal gas extension calculations and to recover lower logP, extrapolate below the current SCVH table, or explicitly fill that region with some other EOS/ideal-gas fallback. At the moment, MESA tries to extrapolate but falls back to HELM before it can. If we didn't extrapolate, falling back to ideal gas might still be better than MESA's HELM fallback in this low Rho-T territory.
>
> I'm not sure why the original extended table boundaries were chosen to be near logRho = -10, however addressing this issue is an opportunity to rediscover and document why. I don't see the routines do this in the current MESA source that constructed these extended tables, so it might require some digging and work on the development sidehttps://github.com/MESAHub/mesa/issues/995.
>
> -EbFFrom: Mesa-users <mesa-users-bounces at lists.mesastar.org> on behalf of Emily Sandford via Mesa-users <mesa-users at lists.mesastar.org>
> Sent: Wednesday, May 13, 2026 6:32 AM
> To: mesa-users at lists.mesastar.org <mesa-users at lists.mesastar.org>
> Cc: mesa-users-request at lists.mesastar.org <mesa-users-request at lists.mesastar.org>
> Subject: [Mesa-users] EOS: unphysical low-temperature mu from OPAL/SCVH and HELM? (Farag, Ebraheem)
> Hi all,
>
> Just to quickly note--the low-density regime under discussion is well
> outside the boundaries of the SCVH H/He tables (see attached figure,
> just a quick overlay of SCVH 1995 fig. 1 on top of the mu plot Natasha
> sent; the long-dashed line is the limit of SCVH coverage). There's no
> SCVH-based reason that MESA's OPAL/SCVH table edge needs to be at
> log10rho ~= -10 rather than log10rho ~= -15 (but I can't speak to OPAL,
> perhaps there's some justification there).
>
> Best,
> Emily
>
>
> On 2026-05-13 03:56, mesa-users-request at lists.mesastar.org wrote:
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> > Today's Topics:
> >
> > 1. Re: EOS: unphysical low-temperature ? from OPAL/SCVH and
> > HELM? (Farag, Ebraheem)
> > 2. Re: EOS: unphysical low-temperature ? from OPAL/SCVH and
> > HELM? (Natasha Ivanova)
> > 3. Re: EOS: unphysical low-temperature ? from OPAL/SCVH and
> > HELM? (Farag, Ebraheem)
> > 4. Re: EOS: unphysical low-temperature ? from OPAL/SCVH and
> > HELM? (Natasha Ivanova)
> >
> >
> > ----------------------------------------------------------------------
> >
> > Message: 1
> > Date: Wed, 13 May 2026 02:45:09 +0000
> > From: "Farag, Ebraheem" <ebraheem.farag at yale.edu>
> > To: Natasha Ivanova <nata.ivanova at ualberta.ca>
> > Cc: Ali Pourmand <pourmand at ualberta.ca>, mesa-users
> > <mesa-users at lists.mesastar.org>
> > Subject: Re: [Mesa-users] EOS: unphysical low-temperature ? from
> > OPAL/SCVH and HELM?
> > Message-ID:
> > <BYAPR08MB414970994CECA7B0F329BB3EFD062 at BYAPR08MB4149.namprd08.prod.outlook.com>
> >
> > Content-Type: text/plain; charset="utf-8"
> >
> > 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://nam12.safelinks.protection.outlook.com/?url=https%3A%2F%2Fdocs.mesastar.org%2Fen%2F26.4.1%2Feos%2Foverview.html&data=05%7C02%7CEbraheem.Farag%40yale.edu%7C48e55abdfc5a400ea0f108deb0db0801%7Cdd8cbebb21394df8b4114e3e87abeb5c%7C0%7C0%7C639142651985194093%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=LxF60mZ6%2FlXmoHfUbuGACXSKJAZqYKSauGEvES9RWWo%3D&reserved=0). The green
> > region represents the blending region with controls for the blending
> > region in the eos controls documentation
> > https://nam12.safelinks.protection.outlook.com/?url=https%3A%2F%2Fdocs.mesastar.org%2Fen%2F26.4.1%2Feos%2Fdefaults.html%23freeeos-controls&data=05%7C02%7CEbraheem.Farag%40yale.edu%7C48e55abdfc5a400ea0f108deb0db0801%7Cdd8cbebb21394df8b4114e3e87abeb5c%7C0%7C0%7C639142651985218065%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=NGFBi8RPj5epivHvAaPmsipnotFd7aysJ%2Ba3qdaLSTg%3D&reserved=0.
> >
> > 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 ? 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 ? 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 (?,T)
> > plane and record the values returned by eosDT_get. The attached plots
> > show the returned ? 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 ? is again physically implausible.
> >
> > My questions are:
> >
> > 1. If OPAL/SCVH or HELM return clearly unphysical ? 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<mailto:mesa-users at lists.mesastar.org>
> > https://nam12.safelinks.protection.outlook.com/?url=https%3A%2F%2Flists.mesastar.org%2Fmailman%2Flistinfo%2Fmesa-users&data=05%7C02%7CEbraheem.Farag%40yale.edu%7C48e55abdfc5a400ea0f108deb0db0801%7Cdd8cbebb21394df8b4114e3e87abeb5c%7C0%7C0%7C639142651985240717%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=3cc3bE3r9WJRcRHENN6uLo3NwaAH6lkRtEvkSfMGbpA%3D&reserved=0
> >
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> >
> > ------------------------------
> >
> > Message: 2
> > Date: Tue, 12 May 2026 20:54:09 -0600
> > From: Natasha Ivanova <nata.ivanova at ualberta.ca>
> > 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 ? from
> > OPAL/SCVH and HELM?
> > Message-ID:
> > <CACK6fdnAMhPUv7PTio3uz0T+AbrmcYqNPy4pZZPYcYJ6cRETzg at mail.gmail.com>
> > Content-Type: text/plain; charset="utf-8"
> >
> > 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://nam12.safelinks.protection.outlook.com/?url=https%3A%2F%2Fdocs.mesastar.org%2Fen%2F26.4.1%2Feos%2Foverview.html&data=05%7C02%7CEbraheem.Farag%40yale.edu%7C48e55abdfc5a400ea0f108deb0db0801%7Cdd8cbebb21394df8b4114e3e87abeb5c%7C0%7C0%7C639142651985329705%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=rON7NkNazMsPdjIlnmqI%2F2dTzb95rbuL66Tw%2FFOHWJY%3D&reserved=0).
> >> The
> >> green region represents the blending region with controls for the
> >> blending
> >> region in the eos controls documentation
> >> https://nam12.safelinks.protection.outlook.com/?url=https%3A%2F%2Fdocs.mesastar.org%2Fen%2F26.4.1%2Feos%2Fdefaults.html%23freeeos-controls&data=05%7C02%7CEbraheem.Farag%40yale.edu%7C48e55abdfc5a400ea0f108deb0db0801%7Cdd8cbebb21394df8b4114e3e87abeb5c%7C0%7C0%7C639142651985354826%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=9y2t1heDOX6vIOeFZioLV77K5QiQxsT41Pdk5HsI8K4%3D&reserved=0.
> >>
> >> 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 ? 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 ? 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 (?,T)
> >> plane
> >> and record the values returned by eosDT_get. The attached plots show
> >> the
> >> returned ? 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
> >> ? is again physically implausible.
> >>
> >> My questions are:
> >>
> >> 1. If OPAL/SCVH or HELM return clearly unphysical ? 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://nam12.safelinks.protection.outlook.com/?url=https%3A%2F%2Flists.mesastar.org%2Fmailman%2Flistinfo%2Fmesa-users&data=05%7C02%7CEbraheem.Farag%40yale.edu%7C48e55abdfc5a400ea0f108deb0db0801%7Cdd8cbebb21394df8b4114e3e87abeb5c%7C0%7C0%7C639142651985379862%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=f2s8%2BgBUUphTOjnV9UuaMKlU6NpW%2BStWhZPlCWM62Cw%3D&reserved=0
> >>
> >>
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> >
> > ------------------------------
> >
> > Message: 3
> > Date: Wed, 13 May 2026 03:37:51 +0000
> > From: "Farag, Ebraheem" <ebraheem.farag at yale.edu>
> > To: Natasha Ivanova <nata.ivanova at ualberta.ca>
> > Cc: Ali Pourmand <pourmand at ualberta.ca>, mesa-users
> > <mesa-users at lists.mesastar.org>
> > Subject: Re: [Mesa-users] EOS: unphysical low-temperature ? from
> > OPAL/SCVH and HELM?
> > Message-ID:
> > <BYAPR08MB4149267735C4A6279899217CFD062 at BYAPR08MB4149.namprd08.prod.outlook.com>
> >
> > Content-Type: text/plain; charset="utf-8"
> >
> > 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 ? 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://nam12.safelinks.protection.outlook.com/?url=https%3A%2F%2Fdocs.mesastar.org%2Fen%2F26.4.1%2Feos%2Foverview.html&data=05%7C02%7CEbraheem.Farag%40yale.edu%7C48e55abdfc5a400ea0f108deb0db0801%7Cdd8cbebb21394df8b4114e3e87abeb5c%7C0%7C0%7C639142651985460678%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=P3njN9UE2RNJYdSwIHeUb0FbaYCpq4azUoH73T1akDY%3D&reserved=0). The green
> > region represents the blending region with controls for the blending
> > region in the eos controls documentation
> > https://nam12.safelinks.protection.outlook.com/?url=https%3A%2F%2Fdocs.mesastar.org%2Fen%2F26.4.1%2Feos%2Fdefaults.html%23freeeos-controls&data=05%7C02%7CEbraheem.Farag%40yale.edu%7C48e55abdfc5a400ea0f108deb0db0801%7Cdd8cbebb21394df8b4114e3e87abeb5c%7C0%7C0%7C639142651985486502%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=fFQNmMobH9mqP6AumZAFN8oYUh1EDMfETnmA5iYnP1E%3D&reserved=0.
> >
> > 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 ? 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 ? 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 (?,T)
> > plane and record the values returned by eosDT_get. The attached plots
> > show the returned ? 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 ? is again physically implausible.
> >
> > My questions are:
> >
> > 1. If OPAL/SCVH or HELM return clearly unphysical ? 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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> >
> > ------------------------------
> >
> > Message: 4
> > Date: Tue, 12 May 2026 21:56:36 -0600
> > From: Natasha Ivanova <nata.ivanova at ualberta.ca>
> > To: "Farag, Ebraheem" <ebraheem.farag at yale.edu>
> > Cc: mesa-users <mesa-users at lists.mesastar.org>
> > Subject: Re: [Mesa-users] EOS: unphysical low-temperature ? from
> > OPAL/SCVH and HELM?
> > Message-ID:
> > <CACK6fdkWcBf3JPf1MGO06mJ42MRq3y49srH=V4Ap_fH5kQFzHw at mail.gmail.com>
> > Content-Type: text/plain; charset="utf-8"
> >
> > Hi Ebraheem,
> >
> > Thank you for confirming my findings.
> >
> > Given that the original SCVH paper explicitly treats hydrogen
> > dissociation
> > and molecular hydrogen in this temperature regime, it is difficult to
> > understand why the MESA OPAL/SCVH path would return a fully ionized
> > value
> > of mu there. This makes it look less like a physical limitation of SCVH
> > itself and more like a possible issue in how this EOS quantity is being
> > returned or interpreted in MESA.
> >
> > It would be very helpful if this could be checked. Ideally, the issue
> > would
> > be fixed, but at minimum I would like to know whether it affects only
> > mu,
> > or whether pressure, internal energy, entropy, and related quantities
> > are
> > also unreliable in the same region.
> >
> > Best,
> > Natasha
> >
> > On Tue, May 12, 2026 at 9:38?PM Farag, Ebraheem
> > <ebraheem.farag at yale.edu>
> > wrote:
> >
> >> 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 ? 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>
> >> 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://nam12.safelinks.protection.outlook.com/?url=https%3A%2F%2Fdocs.mesastar.org%2Fen%2F26.4.1%2Feos%2Foverview.html&data=05%7C02%7CEbraheem.Farag%40yale.edu%7C48e55abdfc5a400ea0f108deb0db0801%7Cdd8cbebb21394df8b4114e3e87abeb5c%7C0%7C0%7C639142651985619877%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=%2BDGOs%2BVzxYzSYeYAxCyz4lmysE%2BgXBpTuEDgtov1TjM%3D&reserved=0).
> >> The
> >> green region represents the blending region with controls for the
> >> blending
> >> region in the eos controls documentation
> >> https://nam12.safelinks.protection.outlook.com/?url=https%3A%2F%2Fdocs.mesastar.org%2Fen%2F26.4.1%2Feos%2Fdefaults.html%23freeeos-controls&data=05%7C02%7CEbraheem.Farag%40yale.edu%7C48e55abdfc5a400ea0f108deb0db0801%7Cdd8cbebb21394df8b4114e3e87abeb5c%7C0%7C0%7C639142651985644003%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=A%2Btd%2Fm83tcp80zVLN93ctlSyegtZ0JATW4ukGscwlK0%3D&reserved=0.
> >>
> >> 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 ? 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 ? 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 (?,T)
> >> plane
> >> and record the values returned by eosDT_get. The attached plots show
> >> the
> >> returned ? 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
> >> ? is again physically implausible.
> >>
> >> My questions are:
> >>
> >> 1. If OPAL/SCVH or HELM return clearly unphysical ? 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://nam12.safelinks.protection.outlook.com/?url=https%3A%2F%2Flists.mesastar.org%2Fmailman%2Flistinfo%2Fmesa-users&data=05%7C02%7CEbraheem.Farag%40yale.edu%7C48e55abdfc5a400ea0f108deb0db0801%7Cdd8cbebb21394df8b4114e3e87abeb5c%7C0%7C0%7C639142651985674187%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=NDFrRxZsEGDHHPngAgLGK5yGSfNFsmxQ5V4H9feQPMk%3D&reserved=0
> >>
> >>
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> >
> > End of Mesa-users Digest, Vol 106, Issue 7
> > ******************************************
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