A Posteriori Transit Probabilities

TL;DR

This paper derives analytic expressions for the posterior transit probability of companions, considering the distribution of their true masses, and finds it can be significantly higher than the prior estimate in certain regimes.

Contribution

It introduces a novel analytic framework for calculating the posterior transit probability accounting for mass distribution assumptions.

Findings

Posterior probability can be larger or smaller than prior depending on mass distribution.

For alpha = -1, prior and posterior probabilities are equal.

Posterior probability is higher for Super-Earths, Neptunes, and Super-Jupiters.

Abstract

Typically, when estimating the prior transit probability, one assumes a uniform distribution for the cosine of the inclination angle i of the companion's orbit, which yields the familiar estimate of ~R_*/a. However, the posterior transit probability depends not only on the prior probability distribution of i but also on the prior probability distribution of the companion mass M_c. In general, the posterior can be larger or smaller than the prior transit probability. We derive analytic expressions for the posterior transit probability assuming a power-law form for the distribution of true masses with exponent alpha. For low transit probabilities, these probabilities reduce to a constant multiplicative factor of the corresponding prior transit probability. The prior and posterior probabilities are equal for alpha = -1, whereas the posterior transit probability is ~1.5 times larger and ~4/pi larger for for alpha = -3 and alpha = -2, but is less than the prior for alpha >= 0, and can be arbitrarily small for alpha > 1. We also calculate the posterior transit probability in different mass regimes for two physically-motivated mass distributions of companions around Sun-like stars, finding that the posterior is likely higher for Super-Earths, Neptunes and Super-Jupiters. We therefore suggest that companions with minimum masses in these regimes might be better-than-expected targets for transit follow-up, and we identify promising targets from RV-detected planets in the literature.