Gravitational Waves and Intermediate-mass Black Hole Retention in Globular Clusters

<jats:title>Abstract</jats:title> <jats:p>The recent discovery of gravitational waves (GWs) has opened new horizons for physics. Current and upcoming missions, such as LIGO, VIRGO, KAGRA, and <jats:italic>LISA</jats:italic>, promise to shed light on black holes of every size from stellar mass (SBH) sizes up to supermassive black holes. The intermediate-mass black hole (IMBH) family has not been detected beyond any reasonable doubt. Recent analyses suggest observational evidence for the presence of IMBHs in the centers of two Galactic globular clusters (GCs). In this paper, we investigate the possibility that GCs were born with a central IMBH, which undergoes repeated merger events with SBHs in the cluster core. By means of a semi-analytical method, we follow the evolution of the primordial cluster population in the galactic potential and the mergers of the binary IMBH-SBH systems. Our models predict ≈1000 IMBHs within 1 kpc from the galactic center and show that the IMBH-SBH merger rate density changes from <jats:inline-formula> <jats:tex-math> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjaab368ieqn1.gif" xlink:type="simple"/> </jats:inline-formula> Gpc<jats:sup>−3</jats:sup> yr<jats:sup>−1</jats:sup> beyond <jats:italic>z</jats:italic> ≈ 2 to <jats:inline-formula> <jats:tex-math> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjaab368ieqn2.gif" xlink:type="simple"/> </jats:inline-formula> Gpc<jats:sup>−3</jats:sup> yr<jats:sup>−1</jats:sup> at <jats:italic>z</jats:italic> ≈ 0. The rates at low redshifts may be significantly higher if young massive star clusters host IMBHs. The merger rates are dominated by IMBHs with masses between 10<jats:sup>3</jats:sup> and 10<jats:sup>4</jats:sup> <jats:italic>M</jats:italic> <jats:sub>⊙</jats:sub>. Currently, there are no LIGO/VIRGO upper limits for GW sources in this mass range, but our results show that at design sensitivity, these instruments will detect IMBH-SBH mergers in the coming years. <jats:italic>LISA</jats:italic> and the Einstein Telescope will be best suited to detect these events. The inspirals of IMBH-SBH systems may also generate an unresolved GW background.</jats:p>