Gravitational-wave background from supermassive black holes without merger trees: Tidally regulated mergers and direct inference from the NANOGrav 15 yr data
Abstract
We present a semi-analytic framework that computes the gravitational-wave background (GWB) from supermassive black hole (SMBH) binaries by direct integration of an N-body-recalibrated extended Press-Schechter accretion kernel, bypassing Monte Carlo merger trees entirely. The calculation is resolution-free and fast enough to be sampled directly against pulsar-timing data with no emulator or precomputed model bank. Between halo accretion and black-hole binary formation, we couple the satellite's simulation-calibrated tidal mass loss continuously to Chandrasekhar dynamical friction. Satellites below a sharp, nearly redshift-independent mass-ratio threshold, ξ≃ 0.04, are stripped faster than they sink and stall: their drag collapses onto the stellar core, and 38% of accreted satellites are unmerged by z=0. Combining this population model with per-binary stellar-hardening turnovers and eccentric spectra, we sample the five-parameter posterior directly against the NANOGrav 15 yr Hellings-Downs-correlated free spectrum, excluding the $15.8$ nHz bin, whose excess power a subsequent chromatic-noise reanalysis attributes to pulsar noise. The data prefer a black-hole mass normalization +0.31+0.20−0.23 dex above the locally calibrated black-hole-bulge mass relation, consistent with earlier indications that the nanohertz background is loud relative to local SMBH calibrations and robust to the delay model, merger kernel, local mass calibration, and its redshift evolution. The spectrum is compatible with, but does not require, eccentric binaries or dense stellar environments.
Related
- Bridging the Population Synthesis of Supermassive Binary Black Holes and the Gravitational Wave Background
- Higher-order statistics of the stochastic gravitational wave background from supermassive black hole binaries
- Constraints on Supermassive Black Hole Binaries from the Lack of Resolvable Sources in the NANOGrav 15-yr Dataset
- Nanohertz Gravitational-Wave Constraints on Supermassive Binary Black Holes at Cosmic Dawn
- Detector orientation matters: Consequences for gravitational-wave background detectability
BibTeX
@misc{ando2026gravitationalwave,
title = {{Gravitational-wave background from supermassive black holes without merger trees: Tidally regulated mergers and direct inference from the NANOGrav 15 yr data}},
author = {Shin'ichiro Ando},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06220},
eprint = {2610.06220},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06220},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gravitational-wave background from supermassive black holes without merger trees: Tidally regulated mergers and direct inference from the NANOGrav 15 yr data
AU - Shin'ichiro Ando
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06220
UR - https://arxiv.org/abs/2610.06220
AB - We present a semi-analytic framework that computes the gravitational-wave background (GWB) from supermassive black hole (SMBH) binaries by direct integration of an N-body-recalibrated extended Press-Schechter accretion kernel, bypassing Monte Carlo merger trees entirely. The calculation is resolution-free and fast enough to be sampled directly against pulsar-timing data with no emulator or precomputed model bank. Between halo accretion and black-hole binary formation, we couple the satellite's simulation-calibrated tidal mass loss continuously to Chandrasekhar dynamical friction. Satellites below a sharp, nearly redshift-independent mass-ratio threshold, ξ≃ 0.04, are stripped faster than they sink and stall: their drag collapses onto the stellar core, and 38% of accreted satellites are unmerged by z=0. Combining this population model with per-binary stellar-hardening turnovers and eccentric spectra, we sample the five-parameter posterior directly against the NANOGrav 15 yr Hellings-Downs-correlated free spectrum, excluding the $15.8$ nHz bin, whose excess power a subsequent chromatic-noise reanalysis attributes to pulsar noise. The data prefer a black-hole mass normalization +0.31^+0.20_−0.23 dex above the locally calibrated black-hole-bulge mass relation, consistent with earlier indications that the nanohertz background is loud relative to local SMBH calibrations and robust to the delay model, merger kernel, local mass calibration, and its redshift evolution. The spectrum is compatible with, but does not require, eccentric binaries or dense stellar environments.
ER -