Semi-empirical Framework of Supermassive Black Hole Evolution: Highlighting a possible tension between Demographics and Gravitational Wave Background

TL;DR

This paper presents a semi-empirical model of supermassive black hole evolution, integrating observational data and Bayesian methods to explore growth mechanisms and potential tensions in gravitational wave background interpretations.

Contribution

It introduces a minimal-assumption, data-driven framework combining continuity and Smoluchowski equations to constrain black hole growth and merger rates using multiple observational datasets.

Findings

Black hole accretion parameters depend on local mass function estimates.

Binary black hole merger rate is constrained to be less than 10% of galaxy merger rate.

Possible tension exists between black hole demographics and gravitational wave background interpretations.

Abstract

The evolution of the supermassive Black Hole (BH) population across cosmic times remains a central unresolved issue in modern astrophysics, due to the many noticeable uncertainties in the involved physical processes that span a huge range of spatial, temporal and energy scales. Here we tackle the problem via a semi-empirical approach with minimal assumptions and data-driven inputs. This is based on a continuity plus Smoluchowski equation framework that allows to unitarily describe the two primary modes of BH growth: gas accretion and binary mergers. Key quantities related to the latter processes are incorporated through educated parameterizations, and then constrained in a Bayesian setup from joint observational estimates of the local BH mass function, of the large-scale BH clustering, and of the nano-Hz stochastic gravitational wave (GW) background measured from Pulsar Timimg Array (PTA) experiments. We find that the BH accretion-related parameters are strongly dependent on the local BH mass function determination: higher normalizations and flatter high-mass slopes in the latter imply lower radiative efficiencies and mean Eddington ratios with a stronger redshift evolution. Additionally, the binary BH merger rate is estimated to be a fraction $\lesssim 10^{-1}$ of the galaxy merger rate derived from galaxy pairs counts by \texttt{JWST}, and constrained not to exceed the latter at $\gtrsim 2\sigma$. Relatedly, we highlight hints of a possible tension between current constraints on BH demographics and the interpretation of the nano-Hz GW background as predominantly caused by binary BH mergers. Specifically, we bound the latter's contribution to $\lesssim 30-50\%$ at $\sim 3\sigma$, suggesting that additional astrophysical/cosmological sources are needed to explain the residual part of the signal measured by PTA experiments.