Inferring MBH​–Mbulge evolution from the gravitational-wave background

Matt, Cayenne; et al. [NANOGrav Collaboration]

Abstract

We test the impact of an evolving supermassive black hole mass scaling relation (MBH​–Mbulge​) on the predictions for the gravitational-wave background (GWB). The observed GWB amplitude is 2–3 times higher than predicted by astrophysically informed models, which suggests the need to revise the assumptions in those models. We compare a semi-analytic model’s ability to reproduce the observed GWB spectrum with a static versus evolving-amplitude MBH​–Mbulge​ relation. We additionally consider the influence of the choice of galaxy stellar mass function (GSMF) on the modeled GWB spectra. Our models are able to reproduce the GWB amplitude with either a large number density of massive galaxies or a positively evolving MBH​–Mbulge​ amplitude (i.e., the MBH​/Mbulge​ ratio was higher in the past). If we assume that the MBH​–Mbulge​ amplitude does not evolve, our models require a GSMF that implies an undetected population of massive galaxies (M⋆​ ≥ 10^11 M_⊙ at z > 1). When the MBH​–Mbulge​ amplitude is allowed to evolve, we can model the GWB spectrum with all fiducial values and an MBH​–Mbulge​ amplitude that evolves as α(z) = α0​ (1 + z)^1.04±0.5.