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 \sim 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 power-law form for the distribution of true masses , d \Gamma / dM _ { c } \propto M _ { c } ^ { \alpha } , for integer values -3 \leq \alpha \leq 3 .
We show that for low transit probabilities , these probabilities reduce to a constant multiplicative factor f _ { \alpha } of the corresponding prior transit probability , where f _ { \alpha } in general depends on \alpha and an assumed upper limit on the true mass .
The prior and posterior probabilities are equal for \alpha = -1 .
The posterior transit probability is \sim 1.5 times larger than the prior for \alpha = -3 and is \sim 4 / \pi times larger for \alpha = -2 , but is less than the prior for \alpha \geq 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 .
We find that for Jupiter-mass planets , the posterior transit probability is roughly equal to the prior probability , whereas the posterior is likely higher for Super-Earths and Neptunes ( 10 M _ { \oplus } -30 M _ { \oplus } ) and Super-Jupiters ( 3 \textrm { M } _ { Jup } -10 \textrm { 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 better-than-expected targets for transit follow-up , and we identify promising targets from RV-detected 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 .