Non-ideal MHD Effects in Protoplanetary Disks

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Non-ideal MHD effects play a significant role on the dynamics of protoplanetary disks (PPDs), hence affect the processes of planet formation and migration. In particular, the onset and saturation level of the magnetorotational instability (MRI) depend critically on non-ideal MHD processes including Ohmic resistivity, Hall effect and ambipolar diffusion (AD), with the latter two effects poorly explored in the literature. We perform 3D unstratified shearing-box simulations of the MRI with AD using a variety of magnetic configurations and AD coefficients. We find that the MRI becomes inefficient when the neutral-ion collision frequency falls below the orbital frequency, and sustained MRI turbulence requires weak magnetic field in the AD dominated regime. We further show preliminary results on the non-linear evolution of the MRI in the Hall-dominated regime. Incorporating all the constraints obtained from the simulations, we present a general framework to estimate the level of turbulence, the MRI-driven accretion rate and the corresponding magnetic field strength in PPDs. We find that the entire outer disk with radius larger than 10-20 AU is likely to be MRI-active, while MRI proceeds through the surface layer in the inner disk. Tiny grains such as polycyclic aromatic hydrocarbons promote accretion compared with sub-micron grains due to their own conductivity. Our predicted accretion rate in the inner disk, however, is insufficient to account for the observed accretion rate in a large fraction of T-Tauri stars, calling for additional mechanisms such as magnetized wind for angular momentum transport, or stronger sources of ionization. On the other hand, the predicted accretion rate at larger disk radii is consistent with the observed range in transitional disks.

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