incorporating eccentricity-omega constraints from transit modeling.

[petigura]

I've been thinking about joint transit and RV modeling. In a full joint model, one would include the following parameters

{P, tc, e, w, K, Rp/Rstar, a/Rstar, b}

• some variables are informed by both datasets: {P, tc, e, w}
• some are just informed by RVs: {K}
• some are just informed by the transits {Rp/Rstar, a/Rstar}

However, in general P and tc are typically much better constrained from photometry that we fix-it and forget-it in RV modeling. I think we can do something similar with e and w.

One typically gets a joint constraint on e and w from transit modeling if mean stellar density is known. This could be implemented into radvel 1.4.1 using the existing functionality, but this requires a KDE evaluation.

I sketched out a solution that I think should be much more efficient and could be implemented in a straight forward manner using radvel.prior.UserDefinedPrior. See attached PDF. A project for @mason-macdougall perhaps?

e-w-constraints-into-radvel.pdf

[bjfultn]

Also see https://radvel.readthedocs.io/en/latest/tutorials/CustomModel-tutorial.html that goes through how one might set up a joint RV+transit fit.