Is GN-z11 powered by a super-Eddington massive black hole?

Abstract: Observations of $z \sim 6$ quasars powered by super-massive black holes (SMBHs, $M_{\rm BH} \sim 10^{8-10}\, M_\odot$) challenge our current understanding of early black hole formation and evolution. The advent of the James Webb Space Telescope (JWST) has enabled the study of massive black holes (MBHs, $M_{\rm BH}\sim 10^{6-7} \ \mathrm{M}_\odot$) up to $z\sim 11$, thus bridging the properties of $z\sim 6$ quasars to their ancestors. JWST spectroscopic observations of GN-z11, a well-known $z=10.6$ star forming galaxy, have been interpreted with the presence of a super-Eddington (Eddington ratio $\equiv \,\lambda_{\rm Edd}\sim 5.5$) accreting MBH. To test this hypothesis we use a zoom-in cosmological simulation of galaxy formation and BH co-evolution. We first test the simulation results against the observed probability distribution function (PDF) of $\lambda_{\rm Edd}$ found in $z\sim 6$ quasars. Then, we select in the simulation those BHs that satisfy the following criteria: (a) $10 < z < 11 $, (b) $M_{\rm BH} > 10^6 \ \mathrm{M}_\odot$. Finally we apply the Extreme Value Statistics to the PDF of $\lambda_{\rm Edd}$ resulting from the simulation and find that the probability of observing a $z\sim 10-11$ MBH, accreting with $\lambda_{\rm Edd} \sim 5.5$, in the volume surveyed by JWST, is very low ($<0.5\%$). We compare our predictions with those in the literature and further discuss the main limitations of our work. Our simulation cannot explain the JWST observations of GN-z11. This might be due to (i) missing physics in simulations, or (ii) uncertainties in the data analysis.