How the super-Eddington regime affects black hole spin evolution in high-redshift galaxies

By performing three-dimensional hydrodynamical simulations of a galaxy in an isolated dark matter halo, we follow the evolution of the spin parameter $a$ of a black hole (BH) undergoing super-Eddington phases throughout its growth. This regime, suspected to be accompanied by powerful jet outflows, is expected to decrease the BH spin magnitude. We combine super-Eddington accretion with sub-Eddington phases (quasar and radio modes) and follow the BH spin evolution. Due to the low frequency of super-Eddington episodes, relativistic jets in this regime are not able to decrease the magnitude of the spin effectively, as thin disc accretion in the quasar mode inevitably increases the BH spin. The combination of super- and sub-Eddington accretion does not lead to a simple explicit expression for the spin evolution because of feedback from super-Eddington events. An analytical expression can be used to calculate the evolution for $a\lesssim0.3$, assuming the super-Eddington feedback is consistently weak. Finally, BHs starting with low spin magnitude are able to grow to the highest mass, and if they initially start misaligned with the galactic disc, they get a small boost of accretion through retrograde accretion.