Comparing Be Star Inclination Angles Determined from H$\alpha$ Fitting and Gravitational Darkening

Using a sample of 92 Galactic Be stars, we compare inclination angles (the angle between a star's rotation axis and the line-of-sight) determined from H$\alpha$ emission line profile fitting to those determined by the spectroscopic signature of gravitational darkening. We find good agreement: 70% of the sample (64 out of 92 stars) is consistent with zero difference between the two methods using $1\sigma$ errors, and there is a strong linear correlation coefficient between the two methods of $r=+0.63\pm0.05$. There is some evidence that the H$\alpha$ profile fitting method overestimates the inclination angle for $i\lesssim 25^\circ$, perhaps due to the neglect of incoherent electron scattering on the H$\alpha$ line widths, while the gravitational darkening method underestimates the inclination angle for $i\gtrsim70^\circ$, perhaps due to the neglect of disk radiative transfer effects on the optical spectrum. Overall, it is demonstrated that a single H$\alpha$ spectrum of modest resolution and SNR can be used to extract a useful estimate for the inclination angle of an individual Be star. This allows equatorial rotation velocities for individual Be stars to be derived from $v \sin i$ measurements and will allow Be stars to be used to search for correlated spin axes in young, open clusters if unbiased (with respect to inclination) samples of Be stars are used.