Gravitational Wave Measurement of the Mbh-Mbulge Intrinsic Scatter at High Redshift

TL;DR

This study investigates how an evolving intrinsic scatter in the supermassive black hole (SMBH) mass-bulge relation at high redshift affects gravitational wave background models, reconciling observations with theoretical predictions.

Contribution

It introduces a semi-analytic model incorporating a redshift-dependent intrinsic scatter in the Mbh-Mbulge relation, improving GWB predictions and understanding SMBH evolution.

Findings

Evolving scatter increases GWB amplitude at low frequencies.

Models with positive scatter evolution match observed overmassive SMBHs at high redshift.

Normalization evolution further improves fit to GWB data.

Abstract

The observed 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 (Mbh-Mbulge) on models of the nanoHertz gravitational wave background (GWB). By implementing an intrinsic scatter of the Mbh-Mbulge 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 Mbh-Mbulge normalization though we find that including moderate normalization evolution improves fits to the GWB data. We conclude that the Mbh-Mbulge relation which best describes the available GWB and electromagnetic data sets has intrinsic scatter which evolves as epsilon(z) = epsilon_0 + (0.56 +/- 0.4) log10(1 + z) and normalization which evolves as alpha(z) = alpha_0 (1 + z)^(0.84 +/- 0.35). The results of this work imply that the Mbh-Mbulge 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.