[mesa-users] recombination energy

[Bill Paxton]

Hi Falk,

On Jan 31, 2013, at 9:30 AM, Falk Herwig wrote:

> I had a question about the treatment of recombination in MESA. The EOS will take care of the effect of ionization and recombination on the mean molecular weight and then the pressure. But strictly speaking, ionization requires energy, and recombination will release energy. Is that taken into account explicitly? I imagine in a typical stellar evolution environment this is a small effect where recombination energy release and ionization energy consumption is almost balancing itself. But we are thinking about the rapidly mass loosing stars Jean-Claude has looked into, and in such non-equilibrium situations one may have to worry ….

for a phase transition like crystallization in a WD core, we need to use the difference in entropy directly in calculating T Ds/Dt
normally we use the form the uses differences in the basic variables (lnT and either lnRho or lnPgas).   this form is much better
numerically since we are solving the newton iterations for the changes (e.g., dlnT and dlnRho) so we have good accuracy for estimating
the time derivatives.  However when using entropy time derivates, we resort to (lnS_new - lnS_old) to get dlnS, so it is subject to nasty roundoff.

For the WD case, there are controls that let you stay with the more stable form for eps_grav in regions of outside of the core and only switch
to the dlnS form where it is needed.    here are the details from controls_defaults

         use_lnS_for_eps_grav = .false.
            ! if true, then we calculate eps_grav as -T*dS/dt
         ! otherwise, we rewrite T*dS/dt in terms of time derivatives of basic variables
            ! if using lnPgas in place of lnRho as a basic variable, then
               ! eps_grav = -T*cp*(dlnT/dt - grada*dlnP/dt)
            ! otherwise
               ! eps_grav = -T*cp*((1-grada*chiT)*dlnT/dt - grada*chiRho*dlnRho/dt)

         ! automatic switch to lnS form for regions with high Gamma
         ! set use_lnS_for_eps_grav false to use these controls
         Gamma_lnS_eps_grav_full_off = 130d0 
            ! as if use_lnS_for_eps_grav false for Gamma <= this
         Gamma_lnS_eps_grav_full_on = 160d0 
            ! as if use_lnS_for_eps_grav true for Gamma >= this
         ! intermediate values of Gamma use a blend of lnS form with non-lnS form.


So, back to your question about recombination energy,  if it needs to be treated as a 1st order phase transition,
then we need to do something like we have done for WD core crystallization.    Please let me know!

-B