Constraining the initial mass function of stars in the Galactic Centre

For half a century, evidence has been growing that the formation of stars follows a universal distribution of stellar masses. In fact, no stellar population has been found showing a systematic deviation from the canonical initial mass function (IMF) found for example for the stars in the solar neighbourhood. The only exception may be the young stellar discs in the Galactic Centre, which have been argued to exhibit a top-heavy IMF. Here we discuss the question whether the extreme circumstances in the centre of the Milky Way may be the reason for a significant variation of the IMF. By means of stellar evolution models using different codes, we show that the observed luminosity in the central parsec is too high to be explained by a long-standing top-heavy IMF as suggested by other authors, considering the limited amount of mass inferred from stellar kinematics in this region. In contrast, continuous star formation over the Galaxy's lifetime following a canonical IMF results in a mass-to-light ratio and a total mass of stellar black holes (SBHs) consistent with the observations. Furthermore, these SBHs migrate towards the centre due to dynamical friction, turning the cusp of visible stars into a core as observed in the Galactic Centre. For the first time here we explain the luminosity and dynamical mass of the central cluster and both the presence and extent of the observed core, since the number of SBHs expected from a canonical IMF is just enough to make up for the missing luminous mass. We conclude that observations of the Galactic Centre are well consistent with continuous star formation following the canonical IMF and do not suggest a systematic variation as a result of the region's properties such as high density, metallicity, strong tidal field etc. If the young stellar discs prove to follow a top-heavy IMF, the circumstances that led to their formation must be very rare, since these have not affected most of the central cluster.