Really cool stars and the star formation history at the Galactic center

We present lambda/Deltalambda = 550-1200 near-infrared H and K spectra for a magnitude-limited sample of 79 asymptotic giant branch and cool supergiant stars in the central approximate to5 pc (diameter) of the Galaxy. We use a set of similar spectra obtained for solar neighborhood stars with known T-eff and M-bol that is in the same range as the Galactic center (GC) sample to derive T-eff and M-bol for the GC sample. We then construct the H-R diagram for the GC sample. Using an automated maximum likelihood routine, we derive a coarse star formation history of the GC. We find that (1) roughly 75% of the stars formed in the central few parsecs are older than 5 Gyr; (2) the star formation rate (SFR) is variable over time, with a roughly 4 times higher SFR in the last 100 Myr compared to the average SFR; (3) our model can match dynamical limits on the total mass of stars formed only by limiting the initial mass function to masses above 0.7 M. (this could be a signature of mass segregation or of the bias toward massive star formation from the unique star formation conditions in the GC); (4) blue supergiants account for 12% of the total sample observed, and the ratio of red to blue super-giants is roughly 1.5; and (5) models with isochrones with [Fe/H] = 0.0 over all ages fit the stars in our H-R diagram better than models with lower [Fe/H] in the oldest age bins, consistent with the finding of Ramirez et al. that stars with ages between 10 Myr and 1 Gyr have solar [Fe/H].