Constraining astrophysical observables of Galaxy and Supermassive Black Hole Binary Mergers using Pulsar Timing Arrays

TL;DR

This paper develops an analytic model linking galaxy and black hole merger observables to gravitational wave background predictions, and explores how pulsar timing array data can constrain supermassive black hole binary populations and merger physics.

Contribution

It introduces a comprehensive astrophysical inference framework using PTA data to constrain SMBHB merger rates, properties, and galaxy relations, incorporating observational priors and simulations.

Findings

Current PTA non-detections do not significantly constrain SMBHB models.

Future PTA detections can tightly constrain SMBHB merger rates and properties.

Non-detection at certain levels challenges existing galaxy and SMBHB merger theories.

Abstract

We present an analytic model to describe the supermassive black hole binary (SMBHB) merger rate in the Universe with astrophysical observables: galaxy stellar mass function, pair fraction, merger timescale and black hole - host galaxy relations. We construct observational priors and compute the allowed range of the characteristic spectrum $h_c$ of the gravitational wave background (GWB) to be $10^{-16}<h_c<10^{-15}$ at a frequency of $f=1/{\rm yr}$. We exploit our parametrization to tackle the problem of astrophysical inference from Pulsar Timing Array (PTA) observations. We simulate a series of upper limits and detections and use a nested sampling algorithm to explore the parameter space. Corroborating previous results, we find that the current PTA non-detection does not place significant constraints on any observables; however, either future upper limits or detections will significantly enhance our knowledge of the SMBHB population. If a GWB is not detected at a level of $h_c(f=1/{\rm yr})=10^{-17}$, our current understanding of galaxy and SMBHB mergers is disfavoured at a $5\sigma$ level, indicating a combination of severe binary stalling, over-estimating of the SMBH -- host galaxy relations, and extreme dynamical properties of merging SMBHBs. Conversely, future detections of a Square Kilometre Array (SKA)-type array will allow to constrain the normalization of the SMBHB merger rate in the Universe, the time between galaxy pairing and SMBHB merging, the normalization of the SMBH -- host galaxy relations and the dynamical binary properties, including their eccentricity and density of stellar environment.