Energetic Ceilings of Astrophysical Gravitational-Wave Backgrounds

TL;DR

This paper establishes a universal energy limit for astrophysical gravitational-wave backgrounds, applies it to various sources, and finds current observations are consistent with black hole populations near this ceiling.

Contribution

It introduces a population-agnostic scaling law that sets an absolute energetic ceiling for stochastic gravitational-wave backgrounds across all frequencies.

Findings

The energetic ceiling for supermassive black hole binaries is approximately 1.6 x 10^{-15} at 1 yr^{-1}.

Current GWB observations are consistent with being powered by ultramassive black holes.

The total astrophysical background cannot exceed a density parameter of about 10^{-7}.

Abstract

Every astrophysical stochastic gravitational wave (GWB) is limited by the amount of rest mass available to be converted into gravitational radiation. Here we derive a population-agnostic scaling law that places an absolute energetic ceiling on stochastic backgrounds across the entire GW frequency spectrum, from nanoHertz to kilohertz. We apply this framework to bound the backgrounds from supermassive black hole binaries, intermediate-mass black hole captures by supermassive black holes in AGN disks, extreme mass-ratio inspirals, binary neutron stars, Population III remnants, and stellar-mass binary black holes. We find that the energetic ceiling for supermassive black hole binaries is $A \leq 1.6^{+0.3}_{-0.3} \times 10^{-15}$ at a reference frequency of $1\,{\rm yr}^{-1}$. This astrophysical GWB ceiling is within $1\sigma$ with the GWB amplitude reported by NANOGrav, EPTA, and PPTA, implying that the current observed signal is consistent with being powered by a population of ultramassive black holes ($M_\bullet \gtrsim 10^{10}\,M_\odot$). Finally, we demonstrate that the total astrophysical background from all channels combined cannot exceed $\Omega_{\rm gw} \sim 10^{-7}$.