Semianalytical Approach for Sky Localization of Gravitational Waves

TL;DR

This paper introduces a semianalytical Bayesian method for rapid sky localization of gravitational wave sources, significantly reducing computational complexity while maintaining accuracy, demonstrated on simulated data and real events like GW170817.

Contribution

A novel semianalytical approach that simplifies Bayesian sky localization of gravitational waves, requiring only one-fold numerical integration, improving speed without sacrificing accuracy.

Findings

Median 90% confidence area of ~100 deg^2 at O2 sensitivity

Localization of GW170817 within an 11 deg^2 50% confidence region

Comparable performance to existing localization tools like Bayestar

Abstract

Rapid sky localization of gravitational wave sources is crucial to enable prompt electromagnetic follow-ups. In this article, we present a novel semianalytical approach for sky localization of gravitational waves from compact binary coalescences. We use the Bayesian framework with an analytical approximation to the prior distributions for a given astrophysical model. We derive a semianalytical solution to the posterior distribution of source directions. This method only requires one-fold numerical integral that marginalizes over the merger time, compared to the five-fold numerical integration otherwise needed in the Bayesian localization method. The performance of the method is demonstrated using a set of binary neutron stars (BNS) injections on Gaussian noise using LIGO-Virgo's design and O2 sensitivity. We find the median of 90% confidence area in O2 sensitivity to be $\mathcal{O}(10^2) ~\mathrm{deg}^2$, comparable to that of the existing LIGO-Virgo online localization method Bayestar and parameter estimation toolkit LALInference. In the end, we apply this method to localize the BNS event GW170817 and find the 50% (90%) confidence region of 11 $\mathrm{deg}^2$ (50 $\mathrm{deg}^2$). The detected optical counterpart of GW170817 resides within our 50% confidence area.