Gravitational wave burst source direction estimation using time and amplitude information

In this article we study two problems that arise when using timing and amplitude estimates from a network of interferometers (IFOs) to evaluate the direction of an incident gravitational wave burst. First, we discuss an angular bias in the least squares timing-based approach that becomes increasingly relevant for moderate to low signal-to-noise ratios. We show how estimates of the arrival time uncertainties in each detector can be used to correct this bias. We also introduce a stand-alone parameter estimation algorithm that can improve the arrival time estimation and provide root-sum-squared strain amplitude (hrss) values for each site. In the second part of the paper we discuss how to resolve the directional ambiguity that arises from observations in three non co-located IFOs between the true source location and its mirror image across the plane containing the detectors. We introduce a new, exact relationship among the hrss values at the three sites that, for sufficiently large signal amplitudes, determines the true source direction regardless of whether or not the signal is linearly polarized. Both the algorithm estimating arrival times, arrival time uncertainties, and hrss values and the directional follow-up can be applied to any set of gravitational wave candidates observed in a network of three non co-located IFOs. As a case study we test the methods on simulated waveforms embedded in simulations of the noise of the LIGO and Virgo detectors at design sensitivity.