Three-component Phase Separation for Ultramassive White Dwarf Models

MESA (version 24.08.1) Inlist files for reproducing the models used in "Three-component Phase Separation for Ultramassive White Dwarf Models" and phase_separation.f90 routine from MESA modified to include 3-component phase separation from ternary phase diagrams. To use this extended version, replace the current phase_separation.f90 file in $MESA_DIR/star/private with the one provided here, then recompile your MESA version by reinstalling it with ./clean and ./install. In the work directory (work_UMWDs), do ./clean and ./mk. The tables for our extended phase separation routine are in the work_UMWDs directory; each phase diagram is composed of two tables that contain 996004 rows and 3 columns. Each column contains the following information: column 1: concentration of element 1 in the liquidus line x_1. column 2: concentration of element 2 in the liquidus line x_2. column 3: concentration difference in the liquidus and solidus Δx=x_solidus-x_liquidus corresponding to the given x_1 and x_2; one of the tables gives Δx_1, while the other gives Δx_2. x_1 and x_2 are sorted as follows: x_1 x_2 Δx 0.000 0.000 Δx(0.000,0.000) 0.000 0.001 Δx(0.000,0.001) ... ... ... 0.000 0.997 Δx(0.000,0.997) 0.001 0.000 Δx(0.001,0.000) 0.001 0.001 Δx(0.001,0.001) ... ... ... 0.997 0.000 Δx(0.997,0.000) 0.997 0.001 Δx(0.997,0.001) ... ... 0.997 0.997 Δx(0.997,0.997) So each x encompasses values from 0 to 0.997 with a separation of 0.001. Note that when x_1+x_2>1 the evaluation of Δx is equal to 0 and such combinations of x_1 and x_2 are included to have an interpolation in a square domain. Note also that having a white dwarf model with a concentration of more than 0.997 for one of the elements is extremely unlikely, and the missing range 0.997 to 1.000 should not be a problem for studyng crystallization in these objects; any evaluation outside the table range must result in Δx=0 given our boundary conditions in the interpolation. If you want to include your own phase diagram consider this table construction.