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

TL;DR

This paper introduces a time-domain method for optimal cross-correlation in pulsar timing array data, improving gravitational wave background detection by accounting for irregular sampling and timing models.

Contribution

It presents a new time-domain implementation of the optimal cross-correlation statistic tailored for PTA data analysis, including derivations and scaling laws.

Findings

Derivation of the optimal cross-correlation statistic from the likelihood function

Method for generating simulated stochastic background signals

Scaling laws for signal-to-noise ratio in different PTA regimes

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.