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We present new high angular resolution near-infrared spectroscopicobservations of the nuclear star cluster surrounding the Milky Way's centralsupermassive black hole. Using the integral-field spectrograph OSIRIS on KeckII behind the laser-guide-star adaptive optics system, this spectroscopicsurvey enables us to separate early-type (young, 4-6 Myr) and late-type (old,>1 Gyr) stars with a completeness of 50% down to K' = 15.5 mag, whichcorresponds to ~10 \msun for the early-type stars. This work increases theradial extent of reported OSIRIS/Keck measurements by more than a factor of 3from 4" to 14" (0.16 pc to 0.56 pc), along the projected disk of young stars.For our analysis, we implement a new method of completeness correction using acombination of star-planting simulations and Bayesian inference. We assignprobabilities for the spectral type of every source detected in deep imagingdown to K' = 15.5 mag using information from spectra, simulations, numbercounts, and the distribution of stars. The inferred radial surface-densityprofiles, $\Sigma(R) \propto R^{-\Gamma}$, for the young stars and late-typegiants are consistent with earlier results ($\Gamma_{early} = 0.93 \pm 0.09$,$\Gamma_{late} = 0.16 \pm 0.07$). The late-type surface-density profile isapproximately flat out to the edge of the survey. While the late-type stellarluminosity function is consistent with the Galactic bulge, thecompleteness-corrected luminosity function of the early-type stars hassignificantly more young stars at faint magnitudes compared to previous surveyswith similar depth. This luminosity function indicates that the correspondingmass function of the young stars is likely less top-heavy than that inferredfrom previous surveys.

Stellar Populations in the Central 0.5 pc of the Galaxy I: A New Method for Constructing Luminosity Functions and Surface-Density Profiles