Simulations of star formation in a gaseous disc around Sgr A* - A failed active galactic nucleus

We numerically model fragmentation of a gravitationally unstable gaseous disc under conditions that may be appropriate for the formation of the young massive stars observed in the central parsec of our Galaxy. In this study, we adopt a simple prescription with a locally constant cooling time. We find that, for cooling times just short enough to induce disc fragmentation, stars form with a top-heavy Initial Mass Function (IMF), as observed in the Galactic Centre (GC). For shorter cooling times, the disc fragments much more vigorously, leading to lower average stellar masses. Thermal feedback associated with gas accretion onto protostars slows down disc fragmentation, as predicted by some analytical models. We also simulate the fragmentation of a gas stream on an eccentric orbit in a combined Sgr A* plus stellar cusp gravitational potential. The stream precesses, self-collides and forms stars with a top-heavy IMF. None of our models produces large enough co-moving groups of stars that could account for the observed ``mini star cluster'' IRS13E in the GC. In all of the gravitationally unstable disc models that we explored, star formation takes place too fast to allow any gas accretion onto the central super-massive black hole. While this can help to explain the quiescence of `failed AGN' such as Sgr A*, it poses a challenge for understanding the high gas accretion rates infered for many quasars.