Detection Rate Estimates of Gravity-waves Emitted During Parabolic Encounters of Stellar Black Holes in Globular Clusters

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. 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 calculate encounters both 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 m_1=m_2=40 Msun are detectable with matched filtering over a signal to noise ratio of 5 within a distance d_L~200Mpc for InLIGO and VIRGO, z=1 for AdLIGO, 0.4Mpc for LISA, and 1Gpc for NGLISA. We estimate single datastream total detection rates of 5.5 x 10^{-5} for InLIGO, 7.2 x 10^{-5} for VIRGO, 0.063 for AdLIGO, 2.9 x 10^{-6} for LISA, and 1.0 for NGLISA per year, for reasonably conservative assumptions. These estimates are subject to uncertainties in the GC parameters, most importantly the total number and mass-distribution of black holes (BHs) in the cluster core. In reasonably optimistic cases, we get >~1 detections for AdLIGO per year. The regular detection of GWs during PEs would provide a unique observational probe for constraining the stellar BH mass function of dense clusters. (abridged)