On the Grain-Modified Magnetic Diffusivities in Protoplanetary Disks

Abstract

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 ( , O H h h , and A h ) largely control the disk gas dynamics. The presence of grains not only strongly reduces the disk ionization fraction, but also modifies the scalings of H h and A h with magnetic field strength. We analytically derive asymptotic expressions of H h and A h in both the strong and weak field limits and show that toward a strong field, H h can change sign (at a threshold field strength B th ), 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 )), H h can change sign up to ∼2-3 scale heights above the midplane at a modest field strength (plasma 100 b~) 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 B th . Together with previous studies, we conclude by discussing the grainabundance-dependent phenomenology of PPD gas dynamics.

Temperature Structure in the Inner Regions of Protoplanetary Disks: Inefficient Accretion Heating Controlled by Nonideal Magnetohydrodynamics

“…The diffusion coefficients are expressed in terms of the Hall parameters of individual charged species as is commonly done (e.g., Wardle 2007;Bai 2011). In regimes of interest (when small dust grains are scarce), the diffusion coefficients η O , η H , and η A can be found to be proportional to B 0 , B 1 , and B 2 respectively, with f dg (a/1µm) −2 < 1 (Xu & Bai 2016), where f dg and a are the dust-to-gas mass ratio and radius of small dust grains, respectively. This condition is generally satisfied in PPDs with grain growth, and is marginally satisfied in the simulations presented in this study.…”

Hall Effect–Mediated Magnetic Flux Transport in Protoplanetary Disks

“…Also note that h H can change sign for sufficiently strong magnetic field in the presence of charged grains (Xu & Bai 2016), and in that case, the direction of magnetic flux transport would be reversed.…”

Ionization and Dust Charging in Protoplanetary Disks

“…Here, α ∼ 10 −3 is the turbulent alpha-parameter (outside of the dead zone), c s = k B T /(2.3m p ) is the sound speed, and Ω K = GM * /R 3 is the Keplerian angular velocity. For the estimates, we assume that the magnetic diffusivity η O at high gas densities is determined by the Ohmic term (Xu & Bai 2016), which can be approximated by η O = 234(n g /n e ) T /K for a weakly ionized gas (Spitzer 1962;Armitage 2011). …”