On the Inference of a Star's Inclination Angle from its Rotation Velocity and Projected Rotation Velocity

It is possible to learn about the orientation of a star's rotation axis by combining measurements of the star's rotation velocity (v) and its projection onto our line of sight (v sin i). This idea has found many applications, including the investigation of the obliquities of stars with transiting planets. Here, we present a method for the probabilistic inference of the inclination of the star's rotation axis based on independent data sets that constrain v and v sin i. We also correct several errors and misconceptions that appear in the literature.