Efficiency of Super-Eddington Magnetically-Arrested Accretion

The radiative efficiency of super-Eddington accreting black holes (BHs) is explored for magnetically-arrested disks (MADs), where magnetic flux builds-up to saturation near the BH. Our three-dimensional general relativistic radiation magnetohydrodynamic (GRRMHD) simulation of a spinning BH (spin $a/M=0.8$) accreting at $\sim 50$ times Eddington shows a total efficiency $\sim 50\%$ when time-averaged and total efficiency $\gtrsim 100\%$ in moments. Magnetic compression by the magnetic flux near the rotating BH leads to a thin disk, whose radiation escapes via advection by a magnetized wind and via transport through a low-density channel created by a Blandford-Znajek (BZ) jet. The BZ efficiency is sub-optimal due to inertial loading of field lines by optically thick radiation, leading to BZ efficiency $\sim 40\%$ on the horizon and BZ efficiency $\sim 5\%$ by $r\sim 400r_g$ (gravitational radii) via absorption by the wind. Importantly, radiation escapes at $r\sim 400r_g$ with efficiency $η\approx 15\%$ (luminosity $L\sim 50L_{\rm Edd}$), similar to $η\approx 12\%$ for a Novikov-Thorne thin disk and beyond $η\lesssim 1\%$ seen in prior GRRMHD simulations or slim disk theory. Our simulations show how BH spin, magnetic field, and jet mass-loading affect the radiative and jet efficiencies of super-Eddington accretion.

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