Abstract
We present spatially resolved imaging and integral field spectroscopy data for 450 cool giant stars within 1\,pc from Sgr\,A*. We use the prominent CO bandheads to derive effective temperatures of individual giants. Additionally we present the deepest spectroscopic observation of the Galactic Center so far, probing the number of B9/A0 main sequence stars ($2.2-2.8\,M_\odot$) in two deep fields. From spectro-photometry we construct a Hertzsprung-Russell diagram of the red giant population and fit the observed diagram with model populations to derive the star formation history of the nuclear cluster. We find that (1) the average nuclear star-formation rate dropped from an initial maximum $\sim10$\,Gyrs ago to a deep minimum 1-2\,Gyrs ago and increased again during the last few hundred Myrs, and (2) that roughly 80% of the stellar mass formed more than 5\,Gyrs ago; (3) mass estimates within $\rm R\sim1\,pc$ from Sgr\,A* favor a dominant star formation mode with a 'normal' Chabrier/Kroupa initial mass function for the majority of the past star formation in the Galactic Center. The bulk stellar mass seems to have formed under conditions significantly different from the young stellar disks, perhaps because at the time of the formation of the nuclear cluster the massive black hole and its sphere of influence was much smaller than today.
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