The response of a turbulent accretion disc to an imposed epicyclic shearing motion

Abstract

We excite an epicyclic motion, whose amplitude depends on the vertical position, $z$, in a simulation of a turbulent accretion disc. An epicyclic motion of this kind may be caused by a warping of the disc. By studying how the epicyclic motion decays we can obtain information about the interaction between the warp and the disc turbulence. A high amplitude epicyclic motion decays first by exciting inertial waves through a parametric instability, but its subsequent exponential damping may be reproduced by a turbulent viscosity. We estimate the effective viscosity parameter, ${\alpha }_{\mathrm{v}}$, pertaining to such a vertical shear. We also gain new information on the properties of the disc turbulence in general, and measure the usual viscosity parameter, ${\alpha }_{\mathrm{h}}$, pertaining to a horizontal (Keplerian) shear. We find that, as is often assumed in theoretical studies, ${\alpha }_{\mathrm{v}}$ is approximately equal to ${\alpha }_{\mathrm{h}}$ and both are much less than unity, for the field strengths achieved in our local box calculations of turbulence. In view of the smallness ($\sim 0.01$) of ${\alpha }_{\mathrm{v}}$ and ${\alpha }_{\mathrm{h}}$ we conclude that for $\beta =p_{\mathrm{gas}}/p_{\mathrm{mag}}\sim 10$ the timescale for diffusion or damping of a warp is much shorter than the usual viscous timescale. Finally, we review the astrophysical implications.

12 pages, 18 figures, MNRAS accepted

References in corpus (2)

• Linear and non-linear theory of a parametric instability of hydrodynamic warps in Keplerian discs
• Hydrodynamic Simulations of Propagating Warps and Bending Waves In Accretion Discs

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