  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.
