Gravitational-wave Measurement of the M BH – M bulge Intrinsic Scatter at High Redshift

The observed gravitational-wave background (GWB) spectrum is higher in amplitude than model predictions by a factor of 2–3. Using a semi-analytic model, we evaluate the effect of a high-scatter supermassive black hole (SMBH) scaling relation ( M BH – M bulge ) on models of the nanohertz GWB. By implementing an intrinsic scatter of the M BH – M bulge relation, which is larger at higher redshift, but matches local observations, we find that the amplitude of GWB models increases to be consistent with the low-frequency end of the GWB spectrum. This amplitude increase is not uniform across frequencies, a strongly evolving scatter preferentially increases the number density of the most massive SMBHs which, in the GWB spectrum, minimizes the strength of the low-frequency turnover. Our models with positively evolving intrinsic scatter can reproduce the electromagnetically observed overmassive SMBHs at 4 < z < 6 without changing the M BH – M bulge normalization though we find that including moderate normalization evolution marginally improves fits to the GWB data. We conclude that the M BH – M bulge relation which best describes the available GWB and electromagnetic data sets has intrinsic scatter that evolves as ε ( z ) = ε 0 + ( 0.56 ± 0.4 ) log 10 ( 1 + z ) and normalization that evolves as α ( z ) = α 0 (1 + z ) 0.84±0.35 . The results of this work imply that the M BH – M bulge relation we see today is not universal throughout cosmic time and that a diversity of seeding models and growth mechanisms may be at play in the early stages of SMBH–galaxy evolution.