[Mesa-users] The plasma interaction parameter

[Evan Bauer]

Hi Ana,

I think that remaining small disagreement is ok. You can see how "gam" is calculated in $MESA_DIR/star/private/micro.f90 line 498 for MESA version 12115. One thing you'll notice there is that the proper way of averaging over the ion charges is to average <Z^(5/3)> rather than averaging Z first and taking <Z>^(5/3). That can cause a ~10% discrepancy for a H/He mixture, which I think would explain your plot.

Cheers,
Evan

> On Nov 23, 2020, at 5:58 PM, Ana Brito <anaolimpiabrito at gmail.com> wrote:
> 
> Hi Evan,
> 
> So, gam it's the ionic parameter! Thank you!
> I attached a new figure where I took into account the factor zbar^(5/3). The two lines are much closer now but there is still a difference.
> 
> Best regards,
> 
> Ana
> 
> On Mon, Nov 23, 2020 at 9:46 PM Evan Bauer <evan.bauer.astro at gmail.com <mailto:evan.bauer.astro at gmail.com>> wrote:
> Hi Ana,
> 
> The quantity "gam" in the profile output is the plasma interaction parameter for ions rather than electrons, so it differs from \Gamma_e by a factor of approximately zbar^(5/3). Does that explain the difference that you're seeing?
> 
> Cheers,
> Evan
> 
> > On Nov 23, 2020, at 3:23 PM, Ana Brito via Mesa-users <mesa-users at lists.mesastar.org <mailto:mesa-users at lists.mesastar.org>> wrote:
> > 
> > Dear MESA users,
> > 
> > I have a question about the plasma interaction parameter.
> > 
> > This parameter can be computed using using the expression:
> > 
> > \Gamma_e = \frac{e^2}{d k_B T}
> > where
> > d = ( \frac{3}{4 \pi n_e} )^{1/3}.
> > (e is the electron charge, k_B the Boltzmann constant, T the temperature)
> > The electron density, n_e, can be obtained from ye (the electron to baryon ratio), one of the profile columns options:
> > n_e = ye*rho*AV.
> > Here, rho is the density, and AV the Avogadro number.
> > 
> > In the figure attached I represented this \Gamma_e with a black line for a 1 solar mass main-sequence stellar model. Later I noticed that the plasma interaction parameter is itself a profile output option. The \Gamma_e obtained directly from the profile output is represented in the same figure with a blue line. These two lines do not match. There is a difference between them that I don't know how to explain. Maybe I'm doing something wrong with the electron density. 
> > My question is: what could be the cause of this difference between black and blue lines? 
> > 
> > I am also sending attached the inlist used under MESA v12115. 
> > 
> > Thank you very much!
> > 
> > Best regards,
> > 
> > Ana
> > <inlist_solarmass1><starting1.mod><Gamma_e.png>_______________________________________________
> > mesa-users at lists.mesastar.org <mailto:mesa-users at lists.mesastar.org>
> > https://lists.mesastar.org/mailman/listinfo/mesa-users <https://lists.mesastar.org/mailman/listinfo/mesa-users>
> > 
> 
> <Gamma.png>

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