Extreme mass ratio inspiral rates: dependence on the massive black hole mass

TL;DR

This paper analyzes how the rate of stars spiraling into massive black holes due to gravitational waves depends on black hole mass, confirming an analytical M^{-1/4} relation and estimating detection rates for LISA.

Contribution

It provides an analytical and numerical study of EMRI rates as a function of black hole mass, including the dependence on stellar compact object type and model limitations.

Findings

Rate scales approximately as M^{-1/4}

LISA could detect hundreds of EMRIs annually

Event rate highest for stellar black holes

Abstract

We study the rate at which stars spiral into a massive black hole (MBH) due to the emission of gravitational waves (GWs), as a function of the mass M of the MBH. In the context of our model, it is shown analytically that the rate approximately depends on the MBH mass as M^{-1/4}. Numerical simulations confirm this result, and show that for all MBH masses, the event rate is highest for stellar black holes, followed by white dwarfs, and lowest for neutron stars. The Laser Interferometer Space Antenna (LISA) is expected to see hundreds of these extreme mass ratio inspirals per year. Since the event rate derived here formally diverges as M->0, the model presented here cannot hold for MBHs of masses that are too low, and we discuss what the limitations of the model are.