A Statistical Study of Threshold Rotation Rates for the Formation of Disks around Be Stars

This paper presents a detailed statistical determination of the equatorial rotation rates of classical Be stars. The rapid rotation of Be stars is likely to be linked to the ejection of gas that forms dense circumstellar disks. The physical origins of these disks are not understood, though it is generally believed that the ability to spin up matter into a Keplerian disk depends on how close the stellar rotation speed is to the critical speed at which the centrifugal force cancels gravity. There has been recent disagreement between the traditional idea that Be stars rotate between 50 and 80 percent of their critical speeds and new ideas (inspired by the tendency for gravity darkening to mask rapid rotation at the equator) that their rotation may be very nearly critical. This paper utilizes Monte Carlo forward modeling to simulate distributions of the projected rotation speed (v sin i), taking into account gravity darkening, limb darkening, and observational uncertainties. A chi-squared minimization procedure was used to find the distribution parameters that best reproduce observed v sin i distributions from R. Yudin's database. Early-type (O7e-B2e) Be stars were found to exhibit a roughly uniform spread of intrinsic rotation speed that extends from 40 to 60 percent up to 100 percent of critical. Late-type (B3e-A0e) Be stars exhibit progressively narrower ranges of rotation speed as the effective temperature decreases; the lower limit rises to reach critical rotation for the coolest Be stars. The derived lower limits on equatorial rotation speed represent conservative threshold rotation rates for the onset of the Be phenomenon. The significantly subcritical speeds found for early-type Be stars represent strong constraints on physical models of angular momentum deposition in Be star disks.