Abstract

Context. Observations of z similar to 6 quasars powered by supermassive black holes (SMBHs; MBH similar to 10(8 - 10) M-circle dot) challenge our current understanding of early black hole (BH) formation and evolution. The advent of the James Webb Space Telescope (JWST) has enabled the study of massive BHs (MBHs; MBH similar to 10(6 - 7) M-circle dot) up to z similar to 11, thus bridging the properties of z similar to 6 quasars to their ancestors. Aims. The 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 equivalent to lambda(Edd) similar to 5.5) accreting MBH. To test this hypothesis, we used a zoom-in cosmological simulation of galaxy formation and BH co-evolution. Methods. We first tested the simulation results against the observed probability distribution function (PDF) of lambda(Edd) found in z similar to 6 quasars. Then, in the simulation we selected the BHs that satisfy the following criteria: (a) 10 < z < 11, (b) MBH > 10(6) M-circle dot. Next, we applied the extreme value statistics to the PDF of lambda(Edd) resulting from the simulation. Results. We find that the probability of observing a z similar to 10 - 11 MBH accreting with lambda(Edd) similar to 5.5 in the volume surveyed by JWST is very low (< 0.2%). We compared our predictions with those in the literature, and discussed the main limitations of our work. Conclusions. Our simulation cannot explain the JWST observations of GN-z11. This might be due to: (i) poor resolution and statistics in simulations, (ii) simplistic sub-grid models (e.g. BH accretion and seeding), (iii) uncertainties in the data analysis and interpretation.