2015MNRAS.446.2887S

We analytically discuss probability distribution functions (PDFs) for inclinations of merging compact binaries whose gravitational waves are coherently detected by a network of ground-based interferometers. These PDFs would be useful for studying the possibility of (1) simultaneously detecting electromagnetic signals (such as gamma-ray bursts) associated with binary mergers and (2) statistically constraining the related theoretical models using actual observational data from multi-messenger astronomy. Our approach is similar to Schutz , but we explicitly include the dependence of the polarization angles of the binaries, based on the concise formulation given in Cutler & Flanagan . We find that the overall profiles of the PDFs are similar for any network of second-generation detectors (Advanced-LIGO, Advanced-Virgo, KAGRA and LIGO-India). For example, 5.1 percent of detected binaries would have inclination angle less than 10° with at most 0.1 percent differences between the potential networks. A perturbative expression is also provided for generating the PDFs with a small number of parameters given by directional averages of the quantity ε that characterizes the asymmetry of network sensitivities to two incoming orthogonal polarization modes.