Constraining the Solution to the Last Parsec Problem with Pulsar Timing

TL;DR

This paper explores how pulsar timing arrays can constrain the physics of supermassive black-hole binaries, potentially distinguishing gravitational-wave-driven evolution from other dynamical effects even without a detection.

Contribution

It introduces Bayesian methods to differentiate between gravitational-wave emission and other effects in PTA data, providing constraints on binary evolution models without requiring a detection.

Findings

Non-detection can disfavor gravitational-wave-dominated evolution with odds of 30:1.

Constraints can be placed on dynamical effects even with weak signals.

Results suggest models may overestimate binary populations or other effects dominate at PTA frequencies.

Abstract

The detection of a stochastic gravitational-wave signal from the superposition of many inspiraling supermassive black holes with pulsar timing arrays (PTAs) is likely to occur within the next decade. With this detection will come the opportunity to learn about the processes that drive black-hole-binary systems toward merger through their effects on the gravitational-wave spectrum. We use Bayesian methods to investigate the extent to which effects other than gravitational-wave emission can be distinguished using PTA observations. We show that, even in the absence of a detection, it is possible to place interesting constraints on these dynamical effects for conservative predictions of the population of tightly bound supermassive black-hole binaries. For instance, if we assume a relatively weak signal consistent with a low number of bound binaries and a low black-hole-mass to galaxy-mass correlation, we still find that a non-detection by a simulated array, with a sensitivity that should be reached in practice within a few years, disfavors gravitational-wave-dominated evolution with an odds ratio of $\sim$30:1. Such a finding would suggest either that all existing astrophysical models for the population of tightly bound binaries are overly optimistic, or else that some dynamical effect other than gravitational-wave emission is actually dominating binary evolution even at the relatively high frequencies/small orbital separations probed by PTAs.