Stellar Inclination Angles from Be Star H$\alpha$ Emission-Line Profiles

We demonstrate that the angle between star's rotation axis and the observer's line-of-sight, usually called the inclination angle, can be reliably determined for Be stars via H$\alpha$ emission-line profile fitting. We test our method on a sample of 11 Be stars with available long-baseline interferometric data from the Navy Precision Optical Interferometer~(NPOI). We fit the H$\alpha$ emission line profile of each star to obtain a spectroscopic inclination angle $i_{\rm H\alpha}$. We then obtain an independent inclination angle estimate, $i_{\rm V^2}$, by fitting the observed interferometric visibilities with model visibilities based on a purely geometric representation of the light distribution on the sky. The sample differences, $\Delta i \equiv i_{\rm H\alpha} - i_{\rm V^2}$, are normally distributed with a mean of zero and a standard deviation of $6.7$ degrees, and the linear correlation coefficient between $i_{\rm H\alpha}$ and $i_{\rm V^2}$ is $r=0.93$. As Be stars comprise upwards of one fifth of all main-sequence B-type stars, this H$\alpha$ line profile fitting technique has the potential to provide an efficient method for detecting correlated stellar spin axes in young open clusters. Furthermore, if the orientation of the Be star circumstellar disk on the plane of the sky can be constrained by polarization measurements, it is possible to determine the full 3D stellar rotation vector of each Be star.