[Mesa-users] EOS: unphysical low-temperature mu from OPAL/SCVH and HELM? (Farag, Ebraheem)
Emily Sandford
sandford at strw.leidenuniv.nl
Wed May 13 10:32:30 UTC 2026
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:
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> 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://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 ? 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://lists.mesastar.org/mailman/listinfo/mesa-users
>
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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://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 ? 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://lists.mesastar.org/mailman/listinfo/mesa-users
>>
>>
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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://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 ? 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://lists.mesastar.org/mailman/listinfo/mesa-users
>
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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://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 ? 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://lists.mesastar.org/mailman/listinfo/mesa-users
>>
>>
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> ******************************************
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