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Supermassive black hole binaries, cosmic strings, relic gravitational waves from inflation, and first order phase transitions in the early universe are expected to contribute to a stochastic background of gravitational waves in the 10^(-9) Hz-10^(-7) Hz frequency band. Pulsar timing arrays (PTAs) exploit the high precision timing of radio pulsars to detect signals at such frequencies. Here we present a time-domain implementation of the optimal cross-correlation statistic for stochastic background searches in PTA data. Due to the irregular sampling typical of PTA data as well as the use of a timing model to predict the times-of-arrival of radio pulses, time-domain methods are better suited for gravitational wave data analysis of such data. We present a derivation of the optimal cross-correlation statistic starting from the likelihood function, a method to produce simulated stochastic background signals, and a rigorous derivation of the scaling laws for the signal-to-noise ratio of the cross-correlation statistic in the two relevant PTA regimes: the weak signal limit where instrumental noise dominates over the gravitational wave signal at all frequencies, and a second regime where the gravitational wave signal dominates at the lowest frequencies.
Observations have revealed that nearly all galaxies contain supermassive black holes (SMBHs) at their centers. When galaxies merge, these SMBHs form SMBH binaries (SMBHBs) that emit low-frequency gravitational waves (GWs). The incoherent superpositio
A low-frequency gravitational-wave background (GWB) from the cosmic merger history of supermassive black holes is expected to be detected in the next few years by pulsar timing arrays. A GWB induces distinctive correlations in the pulsar residuals --
The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has recently reported strong statistical evidence for a common-spectrum red-noise process for all pulsars, as seen in their 12.5-yr analysis for an isotropic stochastic gravi
We search for isotropic stochastic gravitational-wave background (SGWB) in the International Pulsar Timing Array second data release. By modeling the SGWB as a power-law, we find very strong Bayesian evidence for a common-spectrum process, and furthe
We search for an isotropic stochastic gravitational-wave background (GWB) in the newly released $11$-year dataset from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). While we find no significant evidence for a GWB, we pl