inconsistency between photo and mod file restarts

Inspired by testing the following merged branch: https://github.com/MESAHub/mesa/pull/597.

This branch implemented some mathematical identities into the thermal neutrino module which should in theory be identical to the math it replaced. In practice, this yielded bit for bit differences in the neutrino module output at the 10^-12 to 10^-15 level.

In measuring the impact this would have on the MESA test_suite, Warrick found that the final Fe core masses from the '20Msun_pre_ms_to_cc’ test_suite were different between runs with and without these minor bit for bit changes. (a change from 1.5 to 1.58 Msun)

Initially I thought the '20Msun_pre_ms_to_cc’ test_suite might just be extremely sensative to numerics, which was a little disconcerting. However, I think I managed to deduce that most of this difference in Fe core mass convergence was a result of opting for .mod file over photo restarts in the '20Msun_pre_ms_to_cc’ test_suite.

[20M_pre_ms_to_core_collapse_restarts_example.zip](https://github.com/MESAHub/mesa/files/13696719/20M_pre_ms_to_core_collapse_restarts_example.zip)
[mod_restart_output.txt](https://github.com/MESAHub/mesa/files/13696721/mod_restart_output.txt)
[photo_restart_output.txt](https://github.com/MESAHub/mesa/files/13696722/photo_restart_output.txt)

Attached is an example where I’ve also provided the output from both runs running with a .mod file restart (using the rn executable) and .photo restart (using the run_all_photo_restarts executable). The .mod file restart leads to a final Fe core mass of ~ 1.55 Msun and the photo restart yields ~ 1.61 Msun.

Besides prompting some tweaks to the '20Msun_pre_ms_to_cc’ test_suite, this experiment begs the question of what information is being lost on a .mod file restart that could result in these differences. I’ve always been a proponent of restarting from photos as a opposed to .mod files, although I thought the .mod files were a little more robust in recalculating the structure. Since we use .mod file restarts for testing the test_suite, this could make it hard to properly test or achieve the desired convergence we’d like to see out of test_suites like '20Msun_pre_ms_to_cc' and '12Msun_pre_ms_to_cc' without moving to photo restarts.

All in all, some important model information is missing when restarting from a .mod file in a massive star run.

I’m documenting this behavior in this thread so we can have some discussion on this topic and hopefully a better long term solution. Perhaps there is something missing or not being recalculated correctly in a .mod restart which can be identified and fixed.