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Abstract

A rotating, self-gravitating, disk of gas exhibits instabilities in the form of spiral waves. The waves transport angular momentum, giving the disk a source of internal viscosity. The mechanism of the waves is fairly well understood in linear theory, but the nonlinear consequences, such as the rate of angular momentum transport, depend on the amplitude of the spirals, making a numerical experiment useful. We describe N-body experiments of an accretion disk comprised of weakly self-gravitating particles in a background Keplerian potential. The heating effect of the spiral waves is offset by a radial drag force that keep the particles "cool." The numerical disk has an inner and outer boundary that respectively absorbs and emits angular momentum, similar to a viscosity measuring device or viscometer. The rate of angular momentum transfer dh/dt correlates with the self-gravity of the disk, f, such that dh/dt is proportional to f^7/2^. The rate of transport also shows a weak dependence on the boundary conditions of the disk. For a 1% self-gravitating disk, the implied accretion time scale, t_acc_ = h(dh/dt)^-1^, is 7 x 10^5^ rotation periods. The increased spiral activity in a 4% self-gravitating disk decreases the total accretion time to 4 x 10^3^ half-mass radius rotations. An imposed tidal force of a few percent only slightly enhances the viscosity. An autocorrelation analysis shows that the fundamental potential perturbations are the spiral wakes described by Julian and Toomre (1966). The peak overdensity of the spiral wakes is weakly related to the self-gravity, ~f^2/5^. The peak overdensity gradually increases with time, doubling in ~75 rotations, suggesting that the effective central mass of the wake is on the order of a few hundred particles. Applications to quasars and protoplanetary disks are briefly discussed.

Spiral wave viscosity in self-gravitating accretion disks

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Abstract

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