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

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.

11 pages, 5 figures, accepted for publication in Astronomy and Astrophysics

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• Science with the TianQin observatory: Preliminary result on extreme-mass-ratio inspirals
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• Expected intermediate mass black holes in the Virgo cluster. II. Late-type galaxies
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• Dynamics around supermassive black holes: Extreme mass-ratio inspirals as gravitational-wave sources
• Invoking the virial theorem to understand the impact of (dry) mergers on the $M_{\mathrm{bh}}$-$\sigma$ relation
• The (Black Hole Mass)-(Spheroid Stellar Density) Relations: $M_{\mathrm{BH}}$--$\mu$ (and $M_{\mathrm{BH}}$--$\Sigma$) and $M_{\mathrm{BH}}$--$\rho$
• Splitting the lentils: Clues to galaxy/black hole coevolution from the discovery of offset relations for non-dusty versus dusty (wet-merger-built) lenticular galaxies in the $M_{\mathrm{bh}}$-$M_{\ast ,\mathrm{spheroid}}$ diagram
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• Refining the mass estimate for the intermediate-mass black hole candidate in NGC 3319
• Astrophysics with the Laser Interferometer Space Antenna