Application of asymptotic expansions for maximum likelihood estimators' errors to gravitational waves from binary mergers: the network case

TL;DR

This paper presents the most accurate analytical assessment of gravitational wave parameter estimation errors from binary mergers, highlighting the impact of network geometry and SNR, and demonstrating the limitations of simplified Fisher matrix approaches.

Contribution

It introduces an asymptotic expansion method for more precise uncertainty estimates in gravitational wave parameter inference, surpassing traditional Fisher matrix approximations.

Findings

Network geometry significantly affects sky localization accuracy.

Expanding the detector network improves angular resolution by about three times.

Simplified Fisher matrix methods can underestimate uncertainties by a factor of ~7.

Abstract

This paper describes the most accurate analytical frequentist assessment to date of the uncertainties in the estimation of physical parameters from gravitational waves generated by non spinning binary systems and Earth-based networks of laser interferometers. The paper quantifies how the accuracy in estimating the intrinsic parameters mostly depends on the network signal to noise ratio (SNR), but the resolution in the direction of arrival also strongly depends on the network geometry. We compare results for 6 different existing and possible global networks and two different choices of the parameter space. We show how the fraction of the sky where the one sigma angular resolution is below 2 square degrees increases about 3 times when transitioning from the Hanford (USA), Livingston (USA) and Cascina (Italy) network to possible 5 sites ones (while keeping the network SNR fixed). The technique adopted here is an asymptotic expansion of the uncertainties in inverse powers of the signal to noise ratio where the first order is the inverse Fisher information matrix. We show that a common approach to use simplified parameter spaces and only the Fisher information matrix can largely underestimate the uncertainties (by a factor ~7 for the one sigma sky uncertainty in square degrees at a network SNR of ~15).