Understanding the Formation of Young Stars in the Central 0.5 Pc of the Galaxy: Methods for Extending the Imf to Dim Stellar Populations

We test and analyze an existing statistical typing method, and further apply that method to construct a luminosity functions which covers stars down to a luminosity of 16.0 mag. These methods are implemented on data sets collected using the near-infrared integral field spectrograph OSIRIS on Keck II. Previously, the data has allowed for separation of early-type stars (∼4-6 Myr) from late-type stars (>1 Gyr) down to K ′ = 15.5 mag. We further confirm the ability of the spectral typing method to accurately differentiate between earlyand late-types stars to K ′ = 15.5 mag, and also demonstrate the effectiveness of the method at magnitudes to K ′ = 16.0 mag. In confirming that the statistical spectral typing methods can be extended to dimmer populations, near 16.0 mag, we are able to further establish that the luminosity function of the early-type stars observed at fainter magnitudes indicates a mass function which is less top-heavy than previously derived, but which is still not in agreement with the Salpeter model. These conclusions call for further observational evidence for lower mass stars, beyond 16.0 mag. Subject headings: Galaxy: center – stars: early-type, late-type, luminosity function, mass function – methods: statistical, spectral typing