Placing Limits on the Stochastic Gravitational-Wave Background Using European Pulsar Timing Array Data

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 chapter 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 inference method, 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.

The most beautiful thing we can experience is the mysterious.

It is the source of all true art and all science. He to whom this

emotion is a stranger, who can no longer pause to wonder and

stand rapt in awe, is as good as dead: his eyes are closed.

Albert Einstein.

This chapter is adapted from: R. van Haasteren et al. Placing limits on the stochastic gravitational-wave background using European Pulsar Timing Array data MNRAS (2011) 414(4): 3117-3128 By permission of Oxford University Press on behalf of the Royal Astronomical Society.