Probability distribution function for inclinations of merging compact binaries detected by gravitational wave interferometers

TL;DR

This paper derives an analytical probability distribution function for the inclinations of merging compact binaries detected by ground-based gravitational wave interferometers, aiding multi-messenger astronomy and model constraints.

Contribution

It explicitly includes polarization angle dependence in the inclination PDF, extending previous models and providing a perturbative expression for practical calculations.

Findings

Similar PDF profiles across second-generation detector networks

Approximately 5.1% of detected binaries have inclination less than 10 degrees

Perturbative expression for PDFs based on network sensitivity asymmetry

Abstract

We analytically discuss probability distribution function (PDF) for inclinations of merging compact binaries whose gravitational waves are coherently detected by a network of ground based interferometers. The PDF would be useful for studying prospects of (1) simultaneously detecting electromagnetic signals (such as gamma-ray-bursts) associated with binary mergers and (2) statistically constraining the related theoretical models from the actual observational data of multi-messenger astronomy. Our approach is similar to Schutz (2011), but we explicitly include the dependence of the polarization angles of the binaries, based on the concise formulation given in Cutler and Flanagan (1994). We find that the overall profiles of the PDFs are similar for any networks composed by the second generation detectors (Advanced-LIGO, Advanced-Virgo, KAGRA, LIGO-India). For example, 5.1% of detected binaries would have inclination angle less than 10 degree with at most 0.1% 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 $\epsilon$ that characterises the asymmetry of network sensitivities to incoming two orthogonal polarization modes.