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

¹ INAF – Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, 35122 Padova, Italy
e-mail: michela.mapelli@oapd.inaf.it
² Università Milano Bicocca, Dipartimento di Fisica G. Occhialini, Piazza delle Scienze 3, 20126 Milano, Italy
³ School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
⁴ Centre for Astrophysics and Supercomputing, Swinburne University of Technology, Hawthorn, 3122 Victoria, Australia
⁵ Max-Planck Institut für Astrophysik, Karl-Schwarzschild-Strasse 1, 85748 Garching, Germany

Received: 11 November 2011
Accepted: 9 May 2012

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 10⁸–10¹⁰ M_⊙. 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.