A cosmological view of extreme mass-ratio inspirals in nuclear star clusters

TL;DR

This paper investigates the potential of space-based gravitational wave detectors to observe extreme mass-ratio inspirals of stellar-mass black holes into supermassive black holes within nuclear star clusters, highlighting detection prospects and rate sensitivities.

Contribution

It provides predictions for EMRI detection rates in nuclear star clusters for LISA, NGO, and DECIGO, considering different SMBH mass scaling models and their impact on event rate estimates.

Findings

LISA and DECIGO could detect up to thousands of EMRIs annually.

NGO may observe up to tens of EMRIs per year.

Detection rates are highly sensitive to SMBH mass scaling assumptions.

Abstract

There is increasing evidence that many galaxies host both a nuclear star cluster (NC) and a super-massive black hole (SMBH). Their coexistence is particularly prevalent in spheroids with stellar mass 10^8-10^10 solar masses. We study the possibility that a stellar-mass black hole (BH) hosted by a NC inspirals and merges with the central SMBH. Due to the high stellar density in NCs, extreme mass-ratio inspirals (EMRIs) of BHs onto SMBHs in NCs may be important sources of gravitational waves (GWs). We consider sensitivity curves for three different space-based GW laser interferometric mission concepts: the Laser Interferometer Space Antenna (LISA), the New Gravitational wave Observatory (NGO) and the DECi-hertz Interferometer Gravitational wave Observatory (DECIGO). We predict that, under the most optimistic assumptions, LISA and DECIGO will detect up to thousands of EMRIs in NCs per year, while NGO will observe up to tens of EMRIs per year. We explore how a number of factors may affect the predicted rates. In particular, if we assume that the mass of the SMBH scales with the square of the host spheroid mass in galaxies with NCs, rather than a linear scaling, then the event rates are more than a factor of 10 lower for both LISA and NGO, while they are almost unaffected in the case of DECIGO.