Constraining the Stellar Mass Function in the Galactic Center via Mass Loss from Stellar Collisions

The dense concentration of stars and high velocity dispersions in the Galactic centre imply that stellar collisions frequently occur. Stellar collisions could therefore result in significant mass loss rates. We calculate the amount of stellar mass lost due to indirect and direct stellar collisions and find its dependence on the present-day mass function of stars. We find that the total mass loss rate in the Galactic centre due to stellar collisions is sensitive to the present-day mass function adopted. We use the observed x-ray luminosity in the Galactic centre to preclude any present-day mass functions that result in mass loss rates $> 10^{-5} \mathrm{M_{\odot} yr^{-1}}$ in the vicinity of $\sim 1"$. For present-day mass functions of the form, $dN/dM \propto M^{-\alpha}$, we constrain the present-day mass function to have a minimum stellar mass $\lesssim 7\mathrm{M_{\odot}}$ and a power law slope $\gtrsim 1.25$. We also use this result to constrain the initial mass function in the Galactic centre by considering different star formation scenarios.