Gravitational Wave Measurement of the $M_{\mathrm{BH}}$-$M_{\mathrm{bulge}}$ Intrinsic Scatter at High Redshift

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 ($M_{\mathrm{BH}}$-$M_{\mathrm{bulge}}$) on models of the nanohertz gravitational wave background (GWB). By implementing an intrinsic scatter of the $M_{\mathrm{BH}}$-$M_{\mathrm{bulge}}$ 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 $M_{\mathrm{BH}}$-$M_{\mathrm{bulge}}$ normalization though we find that including moderate normalization evolution marginally improves fits to the GWB data. We conclude that the $M_{\mathrm{BH}}$-$M_{\mathrm{bulge}}$ relation which best describes the available GWB and electromagnetic data sets has intrinsic scatter that evolves as $\epsilon (z)={\epsilon }_0+(0.56\pm 0.4){\log }_{10}(1+z)$ and normalization that evolves as $\hat{I}\pm (z)=\hat{I}{\pm }_0(1+z{)}^{0.84\pm 0.35}$. The results of this work imply that the $M_{\mathrm{BH}}$-$M_{\mathrm{bulge}}$ 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.

Accepted for publication in ApJ