The "missing" YSOs in the central parsec of the Galaxy: evidence for   star formation in a massive accretion disk and a top-heavy IMF
  Few dozens of young high mass stars orbit Sgr A* at distances as short as 0.1 parsec, where star formation should be quenched by the strong tidal shear from Sgr A*. The puzzling young stellar population is believed to come into existence in one of the two ways:   (i) "normal" star formation at several tens of parsec in a very massive star cluster that then spiraled in, or (ii) star formation in situ in a massive self-gravitating disk. We propose to constrain these two scenarios via the expected X-ray emission from young low mass stars that should have formed alongside the massive stars. To this end we compare the recent Chandra observations of X-ray emission from young stars in the Orion Nebula, and the Chandra observations of Sgr A* field. We show that the cluster inspiral model is ruled out irrespectively of the initial mass function (IMF) of the young stars. In addition, for the in situ model, we find that no more than few thousand low-mass stars could have formed alongside the massive stars. This is more than a factor of ten fewer than expected if these stars were formed with the standard IMF as elsewhere in the Galaxy. The young stars in the GC are thus the first solid observational evidence for star formation in AGN disks and also require the IMF of these stars to be top-heavy. We briefly consider implication of these results for AGN in general. 
Sergei Nayakshin and Rashid Sunyaev