Coherence of Supermassive Black Hole Binary Demographics with the nHz Stochastic Gravitational Wave Background

TL;DR

This work connects electromagnetic constraints on SMBHB demographics to the nanohertz SGWB detected by pulsar timing arrays by building an AGN-based population model anchored to the X-ray AGN luminosity function and dual AGN observations. It computes the SGWB via a four-stage merger timescale and a mass-resolution approach that uses a BH mass function derived from AGN activity, incorporating gas-driven migration and eccentricity effects. The Baseline model, which employs a luminosity-dependent dual AGN fraction, reproduces the PTA SGWB measurements, whereas a galaxy-pair–driven model overproduces power at the lowest frequencies, highlighting the importance of EM constraints. The results suggest gas accretion and eccentricity critically shape the SGWB spectrum and demonstrate a consistent picture where SMBHBs dominate the nHz background, with significant implications for multi-messenger observations and future GW probes.

Abstract

We present a refined estimation of the stochastic gravitational wave background (SGWB) based on observed dual active galactic nuclei (AGNs) together with AGN X-ray luminosity functions, in light of recent Pulsar Timing Array detections of an nHz SGWB. We identify a characteristic luminosity dependence in dual AGN fractions by compiling recent observational datasets, providing crucial constraints on supermassive black hole binary (SMBHB) populations. Our AGN-based model reproduces the current SGWB measurements within PTA observational uncertainties of $2 - 4 σ$ uncertainties, demonstrating consistency between electromagnetic and gravitational wave observations. These findings establish SMBHBs as the dominant source of the nHz gravitational wave signal, providing crucial insights into their demographics and evolution.

Figures (4)

• Figure 1: Dual AGN fraction as a function of bolometric luminosity and inferred black hole mass assuming $\lambda = 0.1$. Data points represent measurements from various surveys: COSMOS (circles) 2024arXiv240514980L, SDSS (thin diamonds) 2011ApJ...737..101L, Chandra (squares) 2012ApJ...746L..22K, Subaru HSC (diamonds) 2020ApJ...899..154S, Gaia (pentagons) Shen:2022cmp, and JWST (hexagons) 2023arXiv231003067P. Lines show our baseline model (blue solid, fitted to data) and predictions from galaxy merger rates (orange dashed, "Weigel+18" 2018MNRAS.476.2308W).
• Figure 2: The broadband SGWB energy density spectrum. Model predictions using our baseline dual AGN fraction (blue solid) and galaxy pair-based fraction (orange dashed) are compared with the posterior distribution of the SGWB spectrum from NANOGrav 15yr (blue) NANOGrav:2023gor, EPTA DR2 (orange) EPTA:2023fyk, and PPTA DR3 (green) Reardon:2023gzh measurements. The black dot-dashed curve shows a galaxy merger model fitted for the NANOGrav signals Bi:2023tib. Grey curves show sensitivity limits for future detectors LISA 2021arXiv210801167B, Taiji Chen:2023zkb, and TianQin TianQin:2015yph.
• Figure 3: The SGWB energy density spectrum enlarged at PTA frequency regimes, illustrating the impact of varying the accretion rate during the gaseous decay phase. The dash-dotted red, solid blue, and dotted green curves represent models with Eddington accretion rates $\mathcal{\dot{M}} = 1,0.1$ (Baseline), and $0.01$ respectively. The dashed purple curve shows the scenario without gas decay. The orange dashed curve corresponds to the galaxy pair model. The posterior distribution of the observed SGWB spectrum is also shown in the same format as Fig. \ref{['fig:SGWB']}. All parameters other than $\mathcal{\dot{M}}$ are assumed to be fiducial.
• Figure 4: The energy density spectrum of the SGWB in the nHz GW regime, illustrating the impact of varying the initial eccentricity at the inspiral phase. The dotted (orange), dashed (green), solid (blue), dash-dotted (red), and dotted (purple) curves represent models with initial eccentricities $e_0=0.1,0.3, 0.57\ (\rm Baseline), 0.7$, and $0.9$, respectively. The posterior distribution of the observed SGWB spectrum is also shown in the same way as in Fig. \ref{['fig:SGWB']}. All parameters other than $e_0$ are assumed to be fiducial as $(a_0, \mathcal{\dot{M}}, \rho_0)=(10\ \rm{kpc}, 0.1, 10.0\ M_{\odot}/ \rm{pc}^3)$.