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Supernova Explosions in Accretion Disks in Active Galactic Nuclei: Three-Dimensional Models

Supernova (SN) explosions can potentially affect the structure and evolution of circumnuclear disks in active galactic nuclei (AGN). Some previous studies have suggested that a relatively low rate of SN explosions can provide an effective value of alpha viscosity between 0.1 and 1 in AGN accretion disks within 1 pc scale. In order to test this possibility, we provide some analytic scalings of the evolution of a SN remnant embedded in a differentially rotating smooth disk. We calibrate our estimates using three-dimensional hydrodynamical simulations where the gas is modeled as adiabatic with index $γ$. Our simulations are suited to include the fact that a fraction of the momentum injected by the SN escapes from the disk into the corona. Based on these results, we calculate the contribution of SN explosions to the effective alpha viscosity, denoted by $α_{SNe}$, in a model AGN accretion disk, where accretion is driven by the local viscosity $α$. We find that for AGN galaxies with a central black hole of $~ 10^8M_{\cdot}$ and a disk with viscosity $α=0.1$, the contribution of SN explosions may be as large as $α_{SNe} \simeq 0.02$, provided that $α\gtrsim 1.1$. On the other hand, in the momentum conservation limit, which is valid when the push by the internal pressure of the SN remnant is negligible, we find $α_SNe \lesssim 6\times10^{-4}$.