A Bayesian method to set upper limits on the strength of a periodic gravitational wave signal from the remnant of SN1987A: possible applications in LIGO searches

TL;DR

This paper introduces a Bayesian Markov chain Monte Carlo method to determine the detection limits and upper bounds for periodic gravitational wave signals from neutron stars, with applications to LIGO data for SN1987A.

Contribution

It develops a Bayesian model comparison approach that automatically incorporates Occam's Razor to set upper limits on gravitational wave signals, improving detection assessments.

Findings

Provides a way to estimate upper limits on gravitational wave strength.

Quantifies detection probability for narrow-band signals.

Applicable to LIGO data for long observation times.

Abstract

We present a method that assesses the theoretical detection limit of a Bayesian Markov chain Monte Carlo search for a periodic gravitational wave signal emitted by a neutron star. Inverse probability yields an upper limit estimate for the strength when a signal could not be detected in an observed data set. The proposed method is based on Bayesian model comparison that automatically quantifies Occam s Razor. It limits the complexity of a model by favoring the most parsimonious model that explains the data. By comparing the model with a signal from a pulsar to the null model that assumes solely noise, we derive the detection probability and an estimate for the upper limit that a search, for example, for a narrow-band emission for SN1987a, might yield on data at the sensitivity of LIGO data for an observation time of one year.