The distribution of stars near the supermassive black hole in the Galacticcenter

We analyze three sets of infrared star counts in the inner similar to 0.5 p c of the Galactic center. We perform statistical tests on the star counts a nd model in detail the extinction field and the effects of dwarf-giant coll isions on the luminosity function. We find that both the star counts and th e depletion of the brightest stars in the inner similar to 0.05 pc can be e xplained by an n proportional to r(-alpha) stellar cusp with alpha in the r ange 3/2-7/4, in which the envelopes of the brightest giants are destroyed by stellar collisions. Such a cusp is consistent with the Bahcall-Wolf solu tion for the distribution of stars that have undergone two-body relaxation around a black hole. We show that systematic uncertainties due to variable extinction and unrelaxed stars are probably small, but deeper star counts a re required to confirm these results. We estimate that the tidal disruption rate of cusp stars by the black hole is a few x 10(-5) yr(-1).