[mesa-users] The MLT Jacobian

[Ehsan Moravveji]

Dear mesa users,

I’ve been taking a peek at the ml.f90 module, and came across two naive questions. So, I thought of sharing them with you, and ask for your kind feedbacks.

1. The MLT module returns the Jacobian of the output quantities w.r.t. the input, e.g. partial_gradT_div_partial_grada and so on.
On the other hand, the cgrav, mixing_length_alpha, and gradr_factor are three additional inputs, which are allowed to have spatial dependence too, e.g. s% cgrav(:). 
Furthermore, gradr in the convective region depends on alpha_MLT; e.g. see Eqs. (14.98), (14.94), and (14.107) in Cox and Giuli.

Consequently, I was speculating that derivatives of cgrav, mixing_length_alpha and grad_factor may also need be incorporated in the Jacobian matrix.
Is anyone willing to enlighten me on this?

2. Currently, the derivative of gradL_composition_term w.r.t. to all quantities is ignored when evaluating the derivative of Ledoux temperature gradient; see line 485 in mlt.f90. From Eq. (8) in MESA_II paper, the B-term depends explicitly on chi_T. So, I was wondering, as a rough, first-order estimate, it would be possible to include the derivative of B-term w.r.t. to chi_T, e.g.

         gradL = grada + gradL_composition_term
         d_gradL_composition_term_dvb(mlt_dchiT) = - gradL_composition_term / chiT
         d_gradL_dvb = d_grada_dvb + d_gradL_composition_term_dvb

I am aware that working out the composition dependence of gradL_composition_term could be involved; so, that might be ignored for now.
It is possible that a modified gradL derivative would influence, even slightly, the behaviour of growing convective cores. This "might be" important for seismic modelling Kepler F stars. I have to admit this is my naive speculation, and shall be exploited and tested first.

I appreciate and welcome your feedbacks.

Best regards,
Ehsan.