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Spinning up black holes with super-critical accretion flows

We study the process of spinning up black holes by accretion from slim disks in a wide range of accretion rates. We show that for super-Eddington accretion rates and low values of the viscosity parameter alpha (\lesssim 0.01) the limiting value of the dimensionless spin parameter a_* can reach values higher than a_*=0.9978 inferred by Thorne (1974) in his seminal study. For \mdot=10\mdot_{Edd} and alpha=0.01 spin equilibrium is reached at a_*=0.9994. We show that the equilibrium spin value depends strongly on the assumed value of alpha. We also prove that for high accretion rates the impact of captured radiation on spin evolution is negligible.