Tidal disruption events in post-starburst galaxies: the importance of a complete stellar mass function

A tidal disruption event (TDE) occurs when a star is destroyed by the strong tidal shear of a massive black hole (MBH). The accumulation of TDE observations over the last years has revealed that post-starburst galaxies are significantly overrepresented in the sample of TDE hosts. Here we address the post-starburst preference by investigating the decline of TDE rates in a Milky-Way like nuclear stellar cluster featuring either a monochromatic (1 M$\odot$) or a complete, evolved stellar mass function. In the former case, the decline of TDE rates with time is very mild, and generally up to a factor of a few in 10 Gyr. Conversely, if a complete mass function is considered, a strong TDE burst over the first 0.1-1 Gyr is followed by a considerable rate drop, by at least an order of magnitude over 10 Gyr. The decline starts after a mass segregation time-scale, and it is more pronounced assuming a more top-heavy initial mass function and/or an initially denser nucleus. Our results thus suggest that the post-starburst preference can be accounted for in realistic systems featuring a complete stellar mass function, even in moderately dense galactic nuclei. Overall, our findings support the idea that starbursting galactic nuclei are characterized by a top-heavy initial mass function; we speculate that accounting for this can reconcile the discrepancy between observed and theoretically predicted TDE rates even in quiescent galaxies.