# [Mesa-users] Question about calculating electron densities for high mass stars

Jeremy Sakstein sakstein at hawaii.edu
Wed May 6 18:32:25 EDT 2020

Thanks Frank,

When I checked for a solar mass object I found that exp(s% lnfree_e)/me
could end up giving values that were two orders of magnitude different.

For a 72 solar mass helium core I am finding that exp(s% lnfree_e)/me
exceeds the value calculated assuming no ep pairs by 1-2 orders of
magnitude and has a value around 10^26. Does this seem reasonable to you?

Should I only be using this quantity when HELM is the only EOS being
called? For the solar model this number was falling below [image: \langle
Z\rangle][image: \rho/(\langle A\rangle m_u)], which doesn't make any sense

Cheers,

Jeremy

On Wed, May 6, 2020 at 6:21 PM Francis Timmes <fxt44 at mac.com> wrote:

> helm's native table provides the number densities in 1/cm^3, as stated.
> its possible the mesa eos manipulates these number densities to meet
> other requirements when forming lnfree_e - i'd have to check.
> its also possible you have a stray electron mass floating around.
>
> yes, n_{electrons,matter} = n_{electrons,fermi_integral} ~1e26 1/cm^3
> and n_{positrons,fermi_integral} = 0 for solar-ish conditions, which i
> just checked in the standalone version of helm and the eos that
> generates the helm table.
>
> fxt
>
>
>
>
> > On May 6, 2020, at 2:55 PM, Jeremy Sakstein <sakstein at hawaii.edu> wrote:
> >
> > Yes, thank you!
> >
> > Does the definition of lnfee_e depend on which EOS table is being called?
> >
> > I ran some tests for a 1 solar mass model and found that exp(lnfree_e)
> is around unity at the center of the model. I was expecting 10^(25-27),
> which I get by calculating .
> >
> > Strangely, if I divide exp(lnfree_e) by the electron mass I get a number
> I expect. Could this be the electron density rather than the mass?
> >
> > Cheers,
> >
> > Jeremy
> >
> > On Wed, May 6, 2020 at 4:50 PM Francis Timmes <fxt44 at mac.com> wrote:
> > the charge neutrality equation
> >
> > n_{electrons,matter} = n_{electrons,fermi_integral} -
> n_{positrons,fermi_integral}
> >
> > determines the electron and positron chemical potentials in their fermi
> integrals,
> > hence all other thermodynamic quantities. here, each number density n is
> in 1/cm^3.
> >
> > the helm table tabulates n_{electrons,fermi_integral} +
> n_{positrons,fermi_integral}
> > and its first and second derivatives with respect to temperature and
> density.
> >
> > clearer?
> >
> > fxt
> >
> >
> >
> >
> > > On May 6, 2020, at 1:36 PM, Jeremy Sakstein <sakstein at hawaii.edu>
> wrote:
> > >
> > > Thanks Frank.
> > >
> > > Just to clarify, exp(lnfree_e) is the number density of all electrons
> and positrons in ?
> > >
> > > On Wed, May 6, 2020 at 4:34 PM Francis Timmes <fxt44 at mac.com> wrote:
> > > the straight sum of the electron and positron number densities, not
> per nucleon.
> > >
> > > fxt
> > >
> > >
> > >
> > > > On May 6, 2020, at 1:24 PM, Josiah Schwab via Mesa-users <
> mesa-users at lists.mesastar.org> wrote:
> > > >
> > > > Final question: does lnfree_e include positrons too?
> > > >
> > > > My memory was that when on HELM this is the combined number of e^- &
> e^+ per nucleon, but you should probably check that before relying on it.
> > > >
> > > > Josiah
> > > > _______________________________________________
> > > > mesa-users at lists.mesastar.org
> > > > https://lists.mesastar.org/mailman/listinfo/mesa-users
> > > >
> > >
> >
>
>
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