A Posteriori Transit Probabilities
Abstract
Given the radial velocity (RV) detection of an unseen companion, it is often of interest to estimate the probability that the companion also transits the primary star. Typically, one assumes a uniform distribution for the cosine of the inclination angle i of the companion’s orbit. This yields the familiar estimate for the prior transit probability of ∼R_{∗}/a, given the primary radius R_{∗} and orbital semimajor axis a, and assuming small companions and a circular orbit. 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}, given a measurement of the product of the two (the minimum mass M_{c} sin i) from an RV signal. 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 powerlaw form for the distribution of true masses, , for integer values 3 ≤ α ≤ 3. We show that for low transit probabilities, these probabilities reduce to a constant multiplicative factor f_{α} of the corresponding prior transit probability, where f_{α} in general depends on α and an assumed upper limit on the true mass. The prior and posterior probabilities are equal for α = 1. The posterior transit probability is ∼1.5 times larger than the prior for α = 3 and is ∼4/π times larger for α = 2, but is less than the prior for α≥0, and can be arbitrarily small for α > 1. We also calculate the posterior transit probability in different mass regimes for two physicallymotivated mass distributions of companions around Sunlike stars. We find that for Jupitermass planets, the posterior transit probability is roughly equal to the prior probability, whereas the posterior is likely higher for SuperEarths and Neptunes (10 M_{⊕}  30 M_{⊕}) and SuperJupiters (3 M_{Jup}  10 M_{Jup}), owing to the predicted steep rise in the mass function toward smaller masses in these regimes. We therefore suggest that companions with minimum masses in these regimes might be betterthanexpected targets for transit followup, and we identify promising targets from RVdetected planets in the literature. Finally, we consider the uncertainty in the transit probability arising from uncertainties in the input parameters, and the effect of ignoring the dependence of the transit probability on the true semimajor axis on i.
 Publication:

Publications of the Astronomical Society of the Pacific
 Pub Date:
 August 2013
 DOI:
 10.1086/672572
 arXiv:
 arXiv:1305.1298
 Bibcode:
 2013PASP..125..933S
 Keywords:

 Astrophysics  Earth and Planetary Astrophysics
 EPrint:
 18 pages, 10 figures. For a brief video highlighting the key results of this paper, see http://youtu.be/q72xoLbCCVU