On the Grain-Modified Magnetic Diffusivities in Protoplanetary Disks
Xu et al
Weakly ionized protoplanetary disks (PPDs) are subject to non-ideal-magnetohydrodynamic (MHD) effects including Ohmic resistivity, the Hall effect and ambipolar diffusion (AD), and the resulting magnetic diffusivities (ηO,ηH and ηA) largely control the disk gas dynamics. The presence of grains not only strongly reduces disk ionization fraction, but also modify the scalings of ηH and ηA with magnetic field strength. We derive analytically asymptotic expressions of ηH and ηA in both strong and weak field limits and show that towards strong field, ηH can change sign (at a threshold field strength Bth), mimicking a flip of field polarity, and AD is substantially reduced. Applying to PPDs, we find that when small ∼0.1 (0.01)μm grains are sufficiently abundant [mass ratio ∼0.01 (10−4)], ηH can change sign up to ∼2−3 scale heights above midplane at modest field strength (plasma β∼100) over a wide range of disk radii. Reduction of AD is also substantial towards the AD dominated outer disk and may activate the magneto-rotational instability. We further perform local non-ideal MHD simulations of the inner disk (within 10 AU) and show that with sufficiently abundant small grains, magnetic field amplification due to the Hall-shear instability saturates at very low level near the threshold field strength Bth. Together with previous studies, we conclude by discussing the grain-abundance-dependent phenomenology of PPD gas dynamics.