Detection Rate Estimates of Gravity Waves Emitted during Parabolic Encounters of Stellar Black Holes in Globular Clusters

Abstract

The rapid advance of gravitational wave (GW) detector facilities makes it very important to estimate the event rates of possible detection candidates. We consider an additional possibility of GW bursts produced during parabolic encounters (PEs) of stellar-mass compact objects in globular clusters (GCs). We estimate the rate of successful detections for specific detectors: the initial Laser Interferometric Gravitational-Wave Observatory (InLIGO), the French-Italian gravitational wave antenna VIRGO, the near-future Advanced-LIGO (AdLIGO), the space-based Laser Interferometric Space Antenna (LISA), and the Next Generation LISA (NGLISA). Simple GC models are constructed to account for the compact object mass function, mass segregation, number density distribution, and velocity distribution. We both calculate encounters classically and account for general relativistic corrections by extrapolating the results for infinite mass ratios. We also include the cosmological redshift of waveforms and event rates. We find that typical PEs with masses m1 = m2 = 40 M☉ are detectable with matched filtering over a signal-to-noise ratio S/N = 5 within a distance dL ~ 200 Mpc for InLIGO and VIRGO, z = 1 for AdLIGO, 0.4 Mpc for LISA, and 1 Gpc for NGLISA. We estimate single data stream detection rates of 5.5 × 10-5 yr-1 for InLIGO, 7.2 × 10-5 yr-1 for VIRGO, 0.063 yr-1 for AdLIGO, 2.9 × 10-6 yr-1 for LISA, and 1.0 yr-1 for NGLISA, for reasonably conservative assumptions. These estimates are subject to uncertainties in the GC parameters, most importantly the total number and mass distribution of BHs in the cluster core. In reasonably optimistic cases, we get ≳1 detection for AdLIGO per year. We expect that a coincident analysis using multiple detectors and accounting for GW recoil capture significantly increases the detection rates. The regular detection of GWs during PEs would provide a unique observational probe for constraining the stellar BH mass function of dense clusters.