Weakly ionized protoplanetary disks (PPDs) are subject to nonideal magnetohydrodynamic (MHD) effects, including ohmic resistivity, the Hall effect, and ambipolar diffusion (AD), and the resulting magnetic diffusivities (, and ) largely control the disk gas dynamics. The presence of grains not only strongly reduces the disk ionization fraction, but also modifies the scalings of and with magnetic field strength. We analytically derive asymptotic expressions of and in both the strong and weak field limits and show that toward a strong field, can change sign (at a threshold field strength ), mimicking a flip of field polarity, and AD is substantially reduced. Applied to PPDs, we find that when small ~0.1 (0.01)μm grains are sufficiently abundant (mass ratio ~0.01 (10?4)), can change sign up to ~2–3 scale heights above the midplane at a modest field strength (plasma ) over a wide range of disk radii. The reduction of AD is also substantial toward the AD-dominated outer disk and may activate the magnetorotational instability. We further perform local nonideal MHD simulations of the inner disk (within 10 au) and show that, with sufficiently abundant small grains, the magnetic field amplification due to the Hall-shear instability saturates at a very low level near the threshold field strength . Together with previous studies, we conclude by discussing the grain-abundance-dependent phenomenology of PPD gas dynamics.
展开▼
