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.