Angular Momentum Transport in Magnetized Accretion Disks via the Magnetorotational Instability

Mathematics – Logic

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Scientific paper

Angular momentum transport in magnetized accretion disks is due to turbulence driven by the magnetorotational instability (MRI). The physical properties of the gas that set the turbulent saturation level, and thus the angular momentum transport, are not well constrained. This has important implications for phenomenological models that aim to tie accretion theory to observations. We investigate the possible role of physical dissipation, i.e., viscosity and resistivity, through numerical simulations of a local co-rotating patch of an accretion disk using the conservative magnetohydrodynamics code, Athena. We first examine the saturation of the MRI in the absence of dissipation terms, relying on grid-scale dissipation of the turbulent energy. The results are analyzed in terms of Fourier transfer functions to quantify the numerical dissipation of Athena prior to the addition of physical viscosity and resistivity. We find that turbulent energy injected at large scales dissipates in less than an orbital timescale and that magnetic dissipation dominates over kinetic. The effective numerical magnetic Prandtl number (i.e., the ratio of viscosity to resistivity) is approximately 2, independent of resolution or initial magnetic field geometry. The second set of simulations investigates the impact of constant shear viscosity and Ohmic resistivity on the turbulence in the presence of a net azimuthal field within the domain. We find that while an increased Prandtl number leads to increased turbulence, the turbulence decays away for a resistivity larger than a critical value, which is on order cH/1000. In local simulations without a mean magnetic field, the turbulence decays if the Prandtl number is less than unity. Finally, we describe simulations that include temperature-dependent viscosity and resistivity and the potential applications of such simulations to explaining dwarf novae or state transitions in X-ray binaries. We acknowledge support from NASA and the Virginia Space Grant Consortium.

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