Placing limits on the stochastic gravitational-wave background using European Pulsar Timing Array data

TL;DR

This paper sets upper limits on the amplitude of the stochastic gravitational-wave background using European Pulsar Timing Array data, employing Bayesian methods to model the background as a Gaussian process and considering different spectral slopes.

Contribution

It introduces a Bayesian algorithm to constrain the GWB amplitude as a function of spectral slope using PTA data, improving previous limits and accounting for multi-telescope data integration.

Findings

95% confidence upper limit on A is 6×10⁻¹⁵ for α=-2/3

Limit is 1.8 times lower than previous PTA results from 2006

Method incorporates multi-telescope data for future PTA collaborations

Abstract

Direct detection of low-frequency gravitational waves ($10^{-9} - 10^{-8}$ Hz) is the main goal of pulsar timing array (PTA) projects. One of the main targets for the PTAs is to measure the stochastic background of gravitational waves (GWB) whose characteristic strain is expected to approximately follow a power-law of the form $h_c(f)=A (f/\hbox{yr}^{-1})^{\alpha}$, where $f$ is the gravitational-wave frequency. In this paper we use the current data from the European PTA to determine an upper limit on the GWB amplitude $A$ as a function of the unknown spectral slope $\alpha$ with a Bayesian algorithm, by modelling the GWB as a random Gaussian process. For the case $\alpha=-2/3$, which is expected if the GWB is produced by supermassive black-hole binaries, we obtain a 95% confidence upper limit on $A$ of $6\times 10^{-15}$, which is 1.8 times lower than the 95% confidence GWB limit obtained by the Parkes PTA in 2006. Our approach to the data analysis incorporates the multi-telescope nature of the European PTA and thus can serve as a useful template for future intercontinental PTA collaborations.