Combining Transit and Radial Velocity: A Synthesized Population Model

We present a framework for estimating exoplanet occurrence rates by synthesizing constraints from radial velocity and transit surveys simultaneously. We employ approximate Bayesian computation and various mass-radius (M-R) relations to explore the population models describing these surveys, both separately and in a joint fit. Using this approach, we fit a planet distribution function of the form d(2)N/d log Pd logM proportional to (PM alpha)-M-beta, with a break in the power law in mass at M-b, to planets orbiting FGK stars with periods P = [25, 200] days and masses M = [2, 50] M-circle plus. We find that the M-R relation from Otegi et al. (2020), which lets rocky and volatile-rich populations overlap in mass, allows us to find a model that is consistent with both types of surveys. Our joint fit gives M-b = 21.6(-3.2)(+2.5)M(circle plus) (errors reflect 68.3% credible interval). This is nearly a factor of three higher than the break from transit-only considerations and an M- R relation without such an overlap. The corresponding planet-star mass ratio break q(b) similar to 7 x 10(-5) may be consistent with microlensing studies (q(b) similar to 6 x 10(-5) - 2 x 10(-4)). The joint fit also requires that a fraction of F-rocky = 0.63(-0.04)(+0.04) planets in the overlap region belong to the rocky population. Our results strongly suggest that future M-R relations should account for a mixture of distinct types of planets in order to describe the observed planet population.