Extreme mass ratio inspirals and tidal disruption events in nuclear clusters – I. Time-dependent rates

In this paper we develop a computationally efficient, two-population, time-dependent Fokker-Plank approach in the two dimensions of energy and angular momentum to study rates tidal disruption events (TDEs), extreme mass ratio inspirals (EMRIs) direct plunges occurring around massive black holes (MBHs) galactic nuclei. We test our code by exploring wide range astrophysically relevant parameter space, including MBH masses, galaxy central densities inner density slopes. find that segregation and, more general, time dependency distribution function regulate event rate: TDEs always decline with time, whereas EMRIs reach maximum undergo subsequent nearly exponential decay. Once suitably normalized, associated different choices overlap perfectly. Based on this, provide simple scaling allows reproduce for any underlying nucleus. Although peak are general agreement literature relying steady-state (non-time dependent) assumption, those can be sustained timescale strongly depends properties system. particular much shorter than Gyr relatively light MBHs residing dense systems. This warns against using steady state models compute global TDE, EMRI plunge calls sophisticated, dependent treatment problem.