[mesa-users] White dwarf crystallization

[Bill Paxton]

Hi,

As you know the crystallization phase transition gives discontinuities in various eos parameters.  These are driving the code crazy since it depends on nice smooth changes, ideally with smooth 1st derivatives.

You might not know that there is a similar case in the lowT range, the "plasma phase transition".  I believe there is still debate about whether or not such a thing really exists, but it was a horrible problem for evolution of cold lower mass stars and planets.  In MESA we use the SCVH eos in that (T,Rho) range, and because of the known problems for evolution codes, the authors provide smoothed tables in addition to the "true" ones.  The smoothed tables remove the phase transition discontinuities enough that the evolution codes have a hope of working.

We do not have the equivalent smoothed results for the crystallization phase transition, and until we do, I don't except things to work very well.  As Dean mentioned, I've added magic here and there to allow the current implementation to do the (pathetic) things it does to get around the problem.   But for nicer results, we need to hide the abrupt transition behind a cloak of smoothness that doesn't yet exist.

-Bill


On Mar 29, 2015, at 7:54 PM, Reggie Caginalp wrote:

> Dear MESA-users,
> 
> I am studying white dwarf cooling using MESA-r7184, MESASDK version 4.10.0 20140710 on OS 10.9.4 Mavericks.
> 
> Using the wd_cool_0.6M test suite case, with the default model, gives oscillations in the value of the Coulomb parameter Gamma at the center as in gamma_def.pdf.  Furthermore, the gravitational energy oscillates rapidly around the onset of crystallization, as in def_Lgrav.pdf (the y-axis is Lgrav/Lsun). Attached are profiles of eps_grav (epsgrav_prof_spike.pdf) and gamma (Gamma_prof_at_spike.pdf) from one of the spikes. The part of the star that is just beginning to crystallize experiences a huge spike in gravitational energy from resettling, as compared with an eps_grav profile from well before the onset of crystallization (epsgrav_prof_flat.pdf). (These last three figures are from running the test suite case with a different model, but using the default model gives similar results.) 
> 
> Is this normal behavior? If anyone knows a better implementation of crystallization, I would appreciate it greatly!
> 
> Thanks for your time!
> 
> Sincerely,
> Reggie Caginalp
> <def_Lgrav.pdf><gamma_def.pdf><epsgrav_prof_flat.pdf><epsgrav_prof_spike.pdf><Gamma_prof_at_spike.pdf>------------------------------------------------------------------------------
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