Effects of the Hubble Parameter on the Cosmic Growth of the First Quasars

TL;DR

This study investigates how the value of the Hubble parameter influences models of early supermassive black hole growth, revealing that current Hubble estimates favor heavy seed formation scenarios over light ones.

Contribution

The paper quantifies the impact of Hubble parameter variations on black hole growth models and constrains seed mass and Eddington ratio using quasar data and MCMC analysis.

Findings

Hubble parameter variations cause >300% change in predicted quasar mass at z=6.

Current Hubble estimates favor heavy seed formation scenarios with seed masses >10^4 M_sun.

Light seed formation scenarios are statistically rejected at ~3 sigma.

Abstract

Supermassive black holes (SMBHs) play a crucial role in the evolution of galaxies and are currently detected up to $z\sim 7.5$. Theories describing black hole (BH) growth are challenged by how rapidly seeds with initial mass $M_{\bullet} \lesssim 10^5 \, \mathrm{M_{\odot}}$, formed at $z \sim 20-30$, grew to $M_{\bullet} \sim 10^9 \, \mathrm{M_{\odot}}$ by $z\sim 7$. Here we study the effects of the value of the Hubble parameter, $H_0$, on models describing the early growth of BHs. First, we note that the predicted mass of a quasar at $z=6$ changes by $> 300$% if the underlying Hubble parameter used in the model varies from $H_0 = 65$ to $H_0 = 74$ km s$^{-1}$Mpc$^{-1}$, a range encompassing current estimates. Employing an MCMC approach based on priors from $z \gtrsim 6.5$ quasars and on $H_0$, we study the interconnection between $H_0$ and the parameters describing BH growth: seed mass $M_i$ and Eddington ratio $f_{\rm Edd}$. Assuming an Eddington ratio of $f_{\rm Edd} = 0.7$, in agreement with previous estimates, we find $H_0 = 73.6^{+1.2}_{-3.3}$ km s$^{-1}$Mpc$^{-1}$. In a second analysis, allowing all the parameters to vary freely, we find $\log(M_{i}/\mathrm{M_{\odot}}) > 4.5$ (at 95% CL), $H_0 = 74^{+1.5}_{-1.4}$ km s$^{-1}$Mpc$^{-1}$ and $f_{\rm Edd}=0.77^{+0.035}_{-0.026}$ at 68% CL. Our results on the typical Eddington ratio are in agreement with previous estimates. Current values of the Hubble parameter strongly favour heavy seed formation scenarios, with $M_i \gtrsim 10^4 \, \mathrm{M_{\odot}}$. In our model, with the priors on BH masses of quasars used, light seed formation scenarios are rejected at $\sim 3\sigma$.