The role of the supermassive black hole spin in the estimation of the EMRI event rate

TL;DR

This paper investigates how the spin of supermassive black holes influences the rate of extreme mass ratio inspirals (EMRIs), highlighting the significance of plunges and high-eccentricity orbits for future gravitational wave observations.

Contribution

It provides a detailed calculation of EMRI event rates considering black hole spin, orbital dynamics, and relativistic effects, emphasizing the dominance of high-eccentricity EMRIs.

Findings

Plunges can produce thousands of GW cycles in detector bandwidth.

Black hole spin and inclination significantly affect EMRI event rates.

High-eccentricity EMRIs are more prevalent due to relativistic precession effects.

Abstract

A common result to all EMRI investigations on rates is that the possibility that a compact object merges with the MBH after only one intense burst of GWs is much more likely than a slow adiabatic inspiral, an EMRI. The later is referred to as a "plunge" because the compact object dives into the MBH. The event rates for plunges are orders of magnitude larger than slow inspirals. On the other hand, nature MBH's are most likely Kerr and the magnitude of the spin has been sized up to be high. We calculate the number of periapsis passages that a compact object set on to an extremely radial orbit goes through before being actually swallowed by the Kerr MBH and we then translate it into an event rate for a LISA-like observatory, such as the proposed ESA mission eLISA/NGO. We prove that a "plunging" compact object is conceptually indistinguishable from an adiabatic, slow inspiral; plunges spend on average up to hundred of thousands of cycles in the bandwidth of the detector for a two years mission. This has an important impact on the event rate, enhancing in some cases significantly, depending on the spin of the MBH and the inclination. Moreover, it has been recently proved that the production of low-eccentricity EMRIs is severely blocked by the presence of a blockade in the rate at which orbital angular momenta change takes place. This is the result of relativistic precession on to the stellar potential torques and hence affects EMRIs originating via resonant relaxation at distances of about $\sim 10^{-2}$ pc from the MBH. Since high-eccentricity EMRIs are a result of two-body relaxation, they are not affected by this phenomenon. Therefore we predict that eLISA EMRI event rates will be dominated by high-eccentricity binaries, as we present here.