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.

Disks of Stars in the Galactic Center Triggered by Tidal Disruption Events

“…The inferred TDE rates are of the order of ∼10 −5 -10 −4 yr −1 per galaxy (e.g., Donley et al 2002;Gezari et al 2008;van Velzen & Farrar 2014), which matches theoretical modeling of nuclear clusters dynamics (Magorrian & Tremaine 1999;Wang & Merritt 2004;Bar-Or & Alexander 2016). The rates further display a dependence on the SMBH mass, being more prominent around lower-mass SMBHs Broggi et al 2022).…”

On the Impact of Relativistic Gravity on the Rate of Tidal Disruption Events

“…8 A notable exception is Merritt (2013), who stated that tidally disrupted stars must have a Newtonian r t > 8 (gravitational radii), and hence concluded that SMBHs capable of producing observable TDEs must have a mass that satisfies M/M å  1.2 × 10 7 -a factor of ∼2.5 smaller than the one in Equation (30). Merritt (2013) let r t = 8 based on the work of , who defined the Newtonian pericenter by the expression (for a parabolic orbit) J 2 = 2r p with J 2 = 16 (see their Equation (17); this same condition has also been employed in, e.g., Broggi et al 2022). However, the true pericenter distance reached by the star is r p = 4 when J 2 = 16, and hence the correct limit is given by Equation (30) (or Equation (19) when r p = 4).…”

An Explanation for the Overrepresentation of Tidal Disruption Events in Post-starburst Galaxies

“…In this section, we introduce the orbit-averaged F-P equations and the numerical setup, which is mainly based on the works of Cohn & Kulsrud (1978), Stone & Metzger (2016), Pan & Yang (2021), Broggi et al (2022), andWang et al (2023a), where the numerical method for the F-P equations can be found in Pan & Yang (2021), Broggi et al (2022), andWang et al (2023a). We consider a central SMBH with mass M BH surrounded by a spherically stellar cluster with total mass M s and a star-forming disk.…”

“…In the transitional stage, the inner thin disk will gradually evaporate within the truncation radius (r tr ), and we neglect stardisk interactions for the region within r r tr < . When the standard accretion disk disappears completely, the galaxy will enter into the quiescent stage, where the advection terms D E g and D R g are substituted by D E and D R in Equation (12) (see Cohn & Kulsrud 1978;Pan & Yang 2021;Broggi et al 2022;Wang et al 2023a). Here, we do not include the process of scattering of the disk-component stars into the cluster after the disk disappears.…”