Time-domain Implementation of the Optimal Cross-Correlation Statistic for Stochastic Gravitational-Wave Background Searches in Pulsar Timing Data

Abstract

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.

12 pages, 3 figures, submitted to Physical Review D

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• Expected properties of the first gravitational wave signal detected with pulsar timing arrays
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• Quality over Quantity: Optimizing pulsar timing array analysis for stochastic and continuous gravitational wave signals
• Supermassive Black Hole Binary Environments: Effects on the Scaling Laws and Time to Detection for the Stochastic Background
• Gravitational wave non-linearities and pulsar-timing array angular correlations
• A Detection of Red Noise in PSR J1824$-$2452A and Projections for PSR B1937+21 using NICER X-ray Timing Data
• A Parallelized Bayesian Approach To Accelerated Gravitational-Wave Background Characterization