Probing the assembly history and dynamical evolution of massive black hole binaries with pulsar timing arrays

TL;DR

This paper investigates how pulsar timing array detections of gravitational waves can reveal detailed astrophysical information about massive black hole binary populations, including their evolution, mass distribution, and eccentricity.

Contribution

It introduces a physically motivated model linking the gravitational wave background spectrum to MBHB population parameters, enabling extraction of astrophysical insights from PTA data.

Findings

Current upper limits constrain the MBHB merger rate.

Future detections can differentiate between population models.

Spectral features can reveal MBHB mass function and eccentricity.

Abstract

We consider the inverse problem in pulsar timing array (PTA) analysis, investigating what astrophysical information about the underlying massive black hole binary (MBHB) population can be recovered from the detection of a stochastic gravitational wave background (GWB). We employ a physically motivated model that connects the GWB spectrum to a series of parameters describing the underlying redshift evolution of the MBHB mass function and to the typical eccentricity they acquire while interacting with the dense environment of post merger galactic nuclei. This allows the folding in of information about the spectral shape of the GWB into the analysis. The priors on the model parameters are assumed to be uninformative and consistent with the current lack of secure observations of sub-parsec MBHBs. We explore the implications of current upper limits as well as of future detections with a variety of PTA configurations. We confirm our previous finding that current upper limits can only place an upper bound on the overall MBHB merger rate. Depending on the properties of the array, future detections can also constrain several MBHB population models at different degrees of fidelity. In particular, a simultaneous detection of a steepening of the spectrum at high frequency and a bending at low frequency will place strong constraints on both the MBHB mass function and on the typical eccentricity of inspiralling MBHBs, providing insights on MBHB astrophysics unlikely to be achievable by any other means.