Noise analysis of six pulsars and a limit on the gravitational wave background

Abstract The direct detection of ultra-low frequency gravitational waves (GWs, 10 −9 − 10 −6 Hz) using pulsar timing arrays (PTAs) is a significant application of millisecond pulsars. The initial detection of GWs in the nano-Hertz range will probably be an isotropic stochastic GW background (GWB) emitted by the combination of merging super-massive black hole binaries (SMBHBs). In this study, we utilize data from six pulsars collected with four European PTA (EPTA) telescopes to place an upper limit on the GWB amplitude A = 2.34 − 1.32 + 0.75 × 10 − 15 (95%) as a function of the spectral slope α = − 2/3, corresponding to a GWB generated by inspiraling SMBHBs. The posterior for the amplitude that we obtained from the six brightest EPTA pulsars is strongly consistent with previously published upper limits set by the three PTAs. We also compare the sensitivity of our reprocessed pulsar pulse times of arrival (ToAs) determined by the superior ToA creation method, which utilizes a combination of the best template generation algorithm and template-matching algorithm, with the ToAs determined by the EPTA groups. Our analysis shows that the reprocessed ToAs obtained with the superior ToA creation method yield narrower posteriors, indicating an overall increased sensitivity to GW.