Inferring M BH – M bulge Evolution from the Gravitational-wave Background

Abstract We test the impact of an evolving supermassive black hole mass scaling relation ( M BH – M bulge ) 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 M BH – M bulge 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 M BH – M bulge amplitude (i.e., the M BH / M bulge ratio was higher in the past). If we assume that the M BH – M bulge 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 M BH – M bulge amplitude is allowed to evolve, we can model the GWB spectrum with all fiducial values and an M BH – M bulge amplitude that evolves as α ( z ) = α 0 (1 + z ) 1.04±0.5 .