Spatial and Spectral Characterization of the Gravitational-wave Background with the PTA Optimal Statistic

TL;DR

This paper introduces the Per-Frequency Optimal Statistic (PFOS), a computationally efficient method to analyze the gravitational-wave background spectrum with pulsar timing arrays, overcoming assumptions of previous methods and enabling new analyses.

Contribution

The paper extends the PTA Optimal Statistic by developing PFOS, which estimates the GWB spectrum frequency-by-frequency without assuming a power-law, and adapts recent generalizations for better accuracy in strong signal regimes.

Findings

PFOS accurately characterizes the GWB spectrum in various signal regimes.

Even with strong signals, the injected value remains within the 50th percentile of uncertainty in 41-45% of simulations.

PFOS achieves similar accuracy to Bayesian methods with less computational cost.

Abstract

Pulsar timing arrays (PTAs) have made tremendous progress and are now showing strong evidence for the gravitational-wave background (GWB). Further probing the origin and characteristics of the GWB will require more generalized analysis techniques. Bayesian methods are most often used but can be computationally expensive. On the other hand, frequentist methods, like the PTA Optimal Statistic (OS), are more computationally efficient and can produce results that are complementary to Bayesian methods, allowing for stronger statistical cases to be built from a confluence of different approaches. In this work we expand the capabilities of the OS through a technique we call the Per-Frequency Optimal Statistic (PFOS). The PFOS removes the underlying power-law assumption inherent in previous implementations of the OS, and allows one to estimate the GWB spectrum in a frequency-by-frequency manner. We have also adapted a recent generalization from the OS pipeline into the PFOS, making it capable of accurately characterizing the spectrum in the intermediate and strong GW signal regimes using only a small fraction of the necessary computational resources when compared with fully-correlated Bayesian methods, while also empowering many new types of analyses not possible before. We find that even in the strong GW signal regime, where the GWB dominates over noise in all frequencies, the injected value of the signal lies within the 50th-percentile of the PFOS uncertainty distribution in 41-45% of simulations, remaining 3$\sigma$-consistent with unbiased estimation.