X-ray flares reveal mass and angular momentum of the Galactic Center black hole

We have analysed the light curve of the two brightest X-ray flares from the Galactic Center black hole, one flare observed by XMM-Newton on October 3, 2002 (Porquet et al. 2003), and the other flare observed by Chandra on October 26, 2000 (Baganoff et al. 2001). The power density spectra show five distinct peaks at periods of ~ 100 s, 219 s, 700 s, 1150 s, and 2250 s common to both observations within their estimated measurement uncertainties. The power density spectrum of the recently reported infrared flare of June 16, 2003 (Genzel et al. 2003) shows distinct peaks at two, if not three, periods (including the 1008 +/- 120 s infrared period), which are consistent with the X-ray periods. The remaining two periods could not be covered by the infrared measurements. Each period can be identified with one of the characteristic gravitational cyclic modes associated with accretion disks, i.e. either Lense-Thirring precession, Kepler orbital motion and the vertical and radial epicyclic oscillation modes, in such a way that a consistent value for the black hole mass of M_BH = 2.72^{+0.12}_{-0.19} x 10^6 M_odot and the angular momentum $a$ = 0.9939^{+0.0026}_{-0.0074} is obtained. The available data on M_BH derived from studies of the orbital motion of the S2 (S0-2) star (Schoedel et al. 2002, Ghez et al. 2003) agree with our findings. Finally we discuss some implications of the fairly high value for the angular momentum.