Hierarchical Inference of the Supermassive Black Hole Binary Merger Rates from Joint Searches using Pulsar Timing Arrays
Abstract
Gravitational-wave searches do more than identify individual sources - they provide a way to infer the underlying astrophysical populations that produce them. Currently, Pulsar Timing Arrays (PTAs) constrain the supermassive black-hole binary (SMBHB) merger-rate density through both the stochastic gravitational-wave background (SGWB) and searches for individual SMBHB signals. The latter implies converting source upper limits into rate upper limits using detection efficiencies estimated empirically. We instead develop a hierarchical Bayesian framework that places the SMBHB merger-rate density model directly inside the PTA likelihood. The unknown catalog of individual SMBHB merger signals is modeled as a Poisson point process on source-parameter space, so that the number of merger signals is inferred from the data rather than imposed by a detection threshold. We describe two computational routes: a catalog-marginal likelihood based on analyses with fixed numbers of candidate sources, and an explicit transdimensional sampling approach that jointly samples population hyperparameters, latent merger signals, and noise. We validate the method with a toy merger-only population model and then apply it to an astrophysical SMBHB merger-rate density model that jointly predicts the SGWB amplitude and the expected merger-catalog size. In simulations, an individual merger signal adds complementary information to the SGWB and can tighten constraints on the merger-rate population.
Related
- Red noise and evolving signals: a complete frequentist approach to supermassive black hole binary searches with pulsar timing arrays
- Gravitational-wave background from supermassive black holes without merger trees: Tidally regulated mergers and direct inference from the NANOGrav 15 yr data
- Physics-based phenomenological modeling of binary black hole hierarchical formation 2: Autodifferentiable functional inference of hierarchical compact-binary populations
- Unifying spatial correlation with hierarchical population inference to constrain the AGN channel for binary black hole mergers
- Hierarchical Population Inference with Normalizing Flows for Binary Black Holes
BibTeX
@misc{tomson2026hierarchical,
title = {{Hierarchical Inference of the Supermassive Black Hole Binary Merger Rates from Joint Searches using Pulsar Timing Arrays}},
author = {Sharon Mary Tomson and Rutger van Haasteren and Boris Goncharov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09086},
eprint = {2609.09086},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09086},
note = {CC0},
}
RIS
TY - UNPB
TI - Hierarchical Inference of the Supermassive Black Hole Binary Merger Rates from Joint Searches using Pulsar Timing Arrays
AU - Sharon Mary Tomson
AU - Rutger van Haasteren
AU - Boris Goncharov
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09086
UR - https://arxiv.org/abs/2609.09086
AB - Gravitational-wave searches do more than identify individual sources - they provide a way to infer the underlying astrophysical populations that produce them. Currently, Pulsar Timing Arrays (PTAs) constrain the supermassive black-hole binary (SMBHB) merger-rate density through both the stochastic gravitational-wave background (SGWB) and searches for individual SMBHB signals. The latter implies converting source upper limits into rate upper limits using detection efficiencies estimated empirically. We instead develop a hierarchical Bayesian framework that places the SMBHB merger-rate density model directly inside the PTA likelihood. The unknown catalog of individual SMBHB merger signals is modeled as a Poisson point process on source-parameter space, so that the number of merger signals is inferred from the data rather than imposed by a detection threshold. We describe two computational routes: a catalog-marginal likelihood based on analyses with fixed numbers of candidate sources, and an explicit transdimensional sampling approach that jointly samples population hyperparameters, latent merger signals, and noise. We validate the method with a toy merger-only population model and then apply it to an astrophysical SMBHB merger-rate density model that jointly predicts the SGWB amplitude and the expected merger-catalog size. In simulations, an individual merger signal adds complementary information to the SGWB and can tighten constraints on the merger-rate population.
ER -