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

We present new high angular resolution near-infrared spectroscopic observations of the nuclear star cluster surrounding the Milky Way's central supermassive black hole. Using the integral-field spectrograph OSIRIS on Keck II behind the laser-guide-star adaptive optics system, this spectroscopic survey 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, which corresponds to ~10 \msun for the early-type stars. This work increases the radial extent of reported OSIRIS/Keck measurements by more than a factor of 3 from 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 a combination of star-planting simulations and Bayesian inference. We assign probabilities for the spectral type of every source detected in deep imaging down to K' = 15.5 mag using information from spectra, simulations, number counts, and the distribution of stars. The inferred radial surface-density profiles, $Σ(R) \propto R^{-Γ}$, for the young stars and late-type giants are consistent with earlier results ($Γ_{early} = 0.93 \pm 0.09$, $Γ_{late} = 0.16 \pm 0.07$). The late-type surface-density profile is approximately flat out to the edge of the survey. While the late-type stellar luminosity function is consistent with the Galactic bulge, the completeness-corrected luminosity function of the early-type stars has significantly more young stars at faint magnitudes compared to previous surveys with similar depth. This luminosity function indicates that the corresponding mass function of the young stars is likely less top-heavy than that inferred from previous surveys.