The supermassive black hole at the center of the Milky Way plays host to a massive , young cluster that may have formed in one of the most inhospitable environments in the Galaxy .
We present new measurements of the global properties of this cluster , including the initial mass function ( IMF ) , age , and cluster mass .
These results are based on Keck laser-guide-star adaptive optics observations used to identify the young stars and measure their Kp-band luminosity function as presented in .
A Bayesian inference methodology is developed to simultaneously fit the global properties of the cluster utilizing the observations and extensive simulations of synthetic star clusters .
We find that the slope of the mass function for this cluster is \alpha = 1.7 \pm 0.2 , which is steeper than previously reported , but still flatter than the traditional Salpeter slope of 2.35 .
The age of the cluster is between 2.5-5.8 Myr with 95 % confidence , which is a younger age than typically adopted but consistent within the uncertainties of past measurements .
The exact age of the cluster is difficult to determine since our results show two distinct age solutions ( 3.9 Myr and 2.8 Myr ) due to model degeneracies in the relative number of Wolf-Rayet and OB stars .
The total cluster mass is between 14,000 - 37,000 M _ { \odot } above 1 M _ { \odot } and it is necessary to include multiple star systems in order to fit the observed luminosity function and the number of observed Wolf-Rayet stars .
The new IMF slope measurement is now consistent with X-ray observations indicating a factor of 10 fewer X-ray emitting pre-main-sequence stars than expected when compared with a Salpeter IMF .
The young cluster at the Galactic center is one of the few definitive examples of an IMF that deviates significantly from the near-universal IMFs found in the solar neighborhood .