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

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 $\sim 3\sigma$.