Stellar disk in the galactic center -- a remnant of a dense accretion disk?

Observations of the galactic center revealed a population of young massive stars within 0.4 pc from Sgr A* -- the presumed location of a supermassive black hole. The origin of these stars is a puzzle as their formation in citu should be suppressed by the black hole's tidal field. We find that out of 13 stars whose 3-dimensional velocities have been measured by Genzel et. al. (2000), 10 lie in a thin disk. The half-opening angle of the disk is consistent with zero within the measurement errors, and does not exceed 10 degrees. We propose that a recent burst of star formation has occurred in a dense gaseous disk around Sgr A*. Such a disk is no longer present because, most likely, it has been accreted by the central black hole. The three-dimensional orbit of S2, the young star closest to Sgr A*, has been recently mapped out with high precision. It is inclined to the stellar disk by 75 degrees. We find that the orbit should undergo Lense-Thirring precession with the period of (5/a) Myr, where a<1 is the dimensionless spin of the black hole. Therefore it is possible that originally S2 orbit lay in the disk plane. If so, we can constrain the black hole spin $a$ be greater than 0.2(t_{S2}/5 Myr), where t_{S2} is the age of S2.