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

Abstract

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

14 pages, 10 figures, submitted to MNRAS

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• The Lunar Gravitational-wave Antenna: Mission Studies and Science Case
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• Rapid formation of a very massive star >50000 $M_{\odot }$ and subsequently an IMBH from runaway collisions. Direct N-body and Monte Carlo simulations of dense star clusters
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• Segregation and Collisions in Galactic Nuclei: Rates of Destructive Events Near a Supermassive Black Hole
• Secondary spins of extreme mass ratio inspirals: A probe to the formation channels
• Eccentricity distribution of extreme mass ratio inspirals
• Energy Flux and Particle Flux in Steady-State Solutions of Nuclear Star Clusters
• Gravitational waves from an eccentric population of primordial black holes orbiting Sgr A${}^{\star }$
• Co-evolution of Nuclear Star Clusters and Massive Black Holes: Extreme Mass-Ratio Inspirals
• Revealing massive black hole astrophysics: The potential of hierarchical inference with extreme mass-ratio inspiral observations
• Disks of Stars in the Galactic center triggered by Tidal Disruption Events
• Extreme Mass Ratio Inspirals in Light of Quasi-periodic Eruptions: Milli-Hertz Gravitational Wave Background