The distribution of stars near the supermassive black hole in the Galactic center

We analyze three sets of infrared star counts in the inner similar to 0.5 pc of the Galactic center. We perform statistical tests on the star counts and model in detail the extinction field and the effects of dwarf-giant collisions on the luminosity function. We find that both the star counts and the depletion of the brightest stars in the inner similar to 0.05 pc can be explained by an n proportional to r(-alpha) stellar cusp with alpha in the range 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 solution 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 are 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).