Physical Processes in the Vicinity of a Supermassive Black Hole

The Galactic center offers us an opportunity to study the environment around a supermassive black hole at a level of detail not possible in other galactic nuclei. This potential has been greatly expanded by the implementation of laser guide star adaptive optics and integral field spectroscopy on large ground-based telescopes. This thesis takes advantage of these technologies to address the nature of the variable near-infrared emission from the black hole as well as test theories of the equilibrium configuration of a star cluster with a supermassive black hole at its center.;First, we present the results of near-infrared (2 and 3 mum) monitoring of Sgr A*-IR with 1 min time sampling. Sgr A*-IR was observed continuously for up to three hours on each of seven nights, between 2005 July and 2007 August. Sgr-AIR is detectable at all times and is continuously variable, with a median observed 2 mum flux density of 0.192 mJy, corresponding to 16.3 magnitude at K'. These observations allow us to investigate Nyquist sampled periods ranging from about 2 minutes to an hour. Using Monte Carlo simulations, we find that the variability of Sgr At in this data set is consistent with models based on correlated noise with power spectra having frequency dependent power law slopes between 2.0 to 3.0, consistent with those reported for AGN light curves. Of particular interest are periods of ∼ 20 min, corresponding to a quasi-periodic signal claimed based upon previous near-infrared observations and interpreted as the orbit of a `hot spot' at or near the last stable orbit of a spinning black hole. We find no significant periodicity at any time scale probed in these new observations for periodic signals. This study is sensitive to periodic signals with amplitudes greater than 20% of the maximum amplitude of the underlying red noise component for light curves with duration greater than ∼2 hours at a 98% confidence limit.;Second, we report on the structure of the nuclear star cluster in the innermost 0.16 pc of the Galaxy as measured by the number density profile of late-type giants. Using laser guide star adaptive optics in conjunction with the integral field spectrograph, OSIRIS, at the Keck II telescope, we are able to differentiate between the older, late-type (∼ 1 Gyr) stars, which are presumed to be dynamically relaxed, and the unrelaxed young (∼ 6 Myr) population. This distinction is crucial for testing models of stellar cusp formation in the vicinity of a black hole, as the models assume that the cusp stars are in dynamical equilibrium in the black hole potential. In the survey region, we classified 77 stars as early-type 79 stars as late-type. We find that contamination from young stars is significant, with more than twice as many young stars as old stars in our sensitivity range (K' < 15.5) within the central arcsecond. Based on the late-type stars alone, the surface stellar number density profile, Sigma(R) ∝ R-Gamma, is flat, with Gamma = --0.26 +/- 0.24. Monte Carlo simulations of the possible de-projected volume density profile, n(r) ∝ r-gamma, show that gamma is less than 1.0 at the 99.7 % confidence level. These results are consistent with the nuclear star cluster having no cusp, with a core profile that is significantly flatter than predicted by most cusp formation theories, and even allows for the presence of a central hole in the stellar distribution. Of the possible dynamical interactions that can lead to the depletion of the red giants observable in this survey -- stellar collisions, mass segregation from stellar remnants, or a recent merger event mass segregation is the only one that can be ruled out as the dominant depletion mechanism. The degeneracy in the true distribution of stars cannot be broken with number counts alone, but we show how the addition of kinematic measurements can remove the degeneracy. Resolving the physical origin of the lack of a stellar cusp will have important implications for black hole growth models and inferences on the presence of a black hole based upon stellar distributions.