Semianalytical Approach for Sky Localization of Gravitational Waves

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.

15 pages, 8 figures

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