Incorporate effects of irradiation deviating from inverse-square law

[nichollsh]

Feature description

For cases of eccentric orbits, giant stars, small planets, and ultra-short periods, the irradiation environment of a planet deviates from the inverse square law. The IS law assumes that the system is spherically symmetric and the star is a point source. Furthermore, it does not readily incorporate spatial variations across the planet (e.g. near the terminator zone). These effects are especially relevant to USP lava planets.

This recently arose in a separate issue with @maraattia @EmmaPostolec @timlichtenberg: #594.

Going forward, we need a self consistent method for calculating the planetary instellation flux (across the spectrum) based on the orbital, planetary, and stellar parameters.

Preferred solution

There is a package for handling these here: https://github.com/Mradumay137/InstellCa
We could incorporate this Python package within PROTEUS.

Additional information

Lots of binary-star literature on this. See also: https://iopscience.iop.org/article/10.3847/1538-4357/ae29ea

Related to #241 and #187 and #484 and #63

[nichollsh]

Alternatively, given that the InstellCa code is quite small, we could incorporate this directly into AGNI to provide a direct calculation of zenith angle given longitude/latitude. Would be applicable for nichollsh/AGNI#26

[maraattia]

This is a nice feature to implement, thanks for the investigation @nichollsh ! I agree, if a package already exists, is small/fast, and implementation is painless, then why reinvent the wheel. This could elevate PROTEUS to a "1.5D" kind of code.

Nevertheless, InstellCa wouldn't solve the issue I flagged in #594 as it only provides the planetary (longitude/latitude) dependence, not the orbital (distance to star essentially) one. I still believe we should be cautious with this in case we're simulating eccentric orbits.