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

Context. Observations of z∼6 quasars powered by supermassive black holes (SMBHs; MBH∼ 10-10 M⊙) 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∼ 106-7 M⊙) up to z∼ 11, thus bridging the properties of z∼ 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 ≡λEdd∼ 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 λEdd found in z∼ 6 quasars. Then, in the simulation we selected the BHs that satisfy the following criteria: (a) 10 < z < 11, (b) MBH > 106 M⊙. Next, we applied the extreme value statistics to the PDF of λEdd resulting from the simulation. Results. We find that the probability of observing a z∼ 10-11 MBH accreting with λEdd∼ 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.