Energetic Ceilings of Astrophysical Gravitational-Wave Backgrounds

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 $A\le 1.6_{-0.3}^{+0.3}\times {10}^{-15}$ at a reference frequency of $1{\mathrm{y}\mathrm{r}}^{-1}$. 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 ${\mathrm{\Omega }}_{\mathrm{g}\mathrm{w}}\sim {10}^{-7}$.