The impact of realistic models of mass segregation on the event rate of extreme-mass ratio inspirals and cusp re-growth

Abstract

One of the most interesting sources of gravitational waves (GWs) for LISA is the inspiral of compact objects on to a massive black hole (MBH), commonly referred to as an ‘extreme-mass ratio inspiral’ (EMRI). The small object, typically a stellar black hole, emits significant amounts of GW along each orbit in the detector bandwidth. The slowly, adiabatic inspiral of these sources will allow us to map spacetime around MBHs in detail, as well as to test our current conception of gravitation in the strong regime. The event rate of this kind of source has been addressed many times in the literature and the numbers reported fluctuate by orders of magnitude. On the other hand, recent observations of the Galactic centre revealed a dearth of giant stars inside the inner parsec relative to the numbers theoretically expected for a fully relaxed stellar cusp. The possibility of unrelaxed nuclei (or, equivalently, with no or only a very shallow cusp, or core) adds substantial uncertainty to the estimates. Having this timely question in mind, we run a significant number of direct-summation N-body simulations with up to half a million particles to calibrate a much faster orbit-averaged Fokker–Planck code. We show that, under quite generic initial conditions, the time required for the growth of a relaxed, mass segregated stellar cusp is shorter than a Hubble time for MBHs with M• ≲ 5 × 106 M⊙ (i.e. nuclei in the range of LISA). We then investigate the regime of strong mass segregation (SMS) for models with two different stellar mass components. Given the most recent stellar mass normalization for the inner parsec of the Galactic centre, SMS has the significant impact of boosting the EMRI rates by a factor of ∼10 in comparison to what would result from a 7/4-Bahcall and Wolf cusp resulting in ∼250 events per Gyr per Milky Way type galaxy. Such an intrinsic rate should translate roughly into ∼102–7 × 102 sbh's (EMRIs detected by LISA over a mission lifetime of 2 or 5 years, respectively), depending on the detailed assumptions regarding LISA detection capabilities.