Are we there yet? Time to detection of nanohertz gravitational waves based on pulsar-timing array limits

TL;DR

Current pulsar timing array limits suggest detection of nanohertz gravitational waves is challenging with small arrays but feasible within a decade with large, expanding arrays, despite environmental effects and merger rate uncertainties.

Contribution

This paper provides a quantitative analysis of detection prospects for nanohertz gravitational waves using pulsar timing arrays, highlighting the importance of large arrays for successful detection.

Findings

Large arrays have an ~80% chance of detection within 10 years.

Small arrays face discouraging prospects of detection in the next two decades.

Detection probability remains high even under extreme environmental and merger rate assumptions.

Abstract

Decade-long timing observations of arrays of millisecond pulsars have placed highly constraining upper limits on the amplitude of the nanohertz gravitational-wave stochastic signal from the mergers of supermassive black-hole binaries ($\sim 10^{-15}$ strain at $f = 1/\mathrm{yr}$). These limits suggest that binary merger rates have been overestimated, or that environmental influences from nuclear gas or stars accelerate orbital decay, reducing the gravitational-wave signal at the lowest, most sensitive frequencies. This prompts the question whether nanohertz gravitational waves are likely to be detected in the near future. In this letter, we answer this question quantitatively using simple statistical estimates, deriving the range of true signal amplitudes that are compatible with current upper limits, and computing expected detection probabilities as a function of observation time. We conclude that small arrays consisting of the pulsars with the least timing noise, which yield the tightest upper limits, have discouraging prospects of making a detection in the next two decades. By contrast, we find large arrays are crucial to detection because the quadrupolar spatial correlations induced by gravitational waves can be well sampled by many pulsar pairs. Indeed, timing programs which monitor a large and expanding set of pulsars have an $\sim 80\%$ probability of detecting gravitational waves within the next ten years, under assumptions on merger rates and environmental influences ranging from optimistic to conservative. Even in the extreme case where $90\%$ of binaries stall before merger and environmental coupling effects diminish low-frequency gravitational-wave power, detection is delayed by at most a few years.