On the Grain-Modified Magnetic Diffusivities in Protoplanetary Disks

• Published in: arXiv.org
• Main Authors: Xu, Rui, Xue-Ning Bai
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 23.11.2015
• Subjects: Ambipolar diffusion; Diffusion effects; Disks; Field strength; Fluid dynamics; Fluid flow; Gas dynamics; Grains; Hall effect; Ionization; Kelvin-Helmholtz instability; Magnetic fields; Magnetohydrodynamics; Phenomenology; Physics - Earth and Planetary Astrophysics; Planet formation; Polarity; Protoplanetary disks; Protoplanets
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1511.07199

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 (\(\eta_O, \eta_H\) and \(\eta_A\)) largely control the disk gas dynamics. The presence of grains not only strongly reduces disk ionization fraction, but also modify the scalings of \(\eta_H\) and \(\eta_A\) with magnetic field strength. We derive analytically asymptotic expressions of \(\eta_H\) and \(\eta_A\) in both strong and weak field limits and show that towards strong field, \(\eta_H\) can change sign (at a threshold field strength \(B_{\rm th}\)), mimicking a flip of field polarity, and AD is substantially reduced. Applying to PPDs, we find that when small \(\sim0.1\) (\(0.01\))\(\mu\)m grains are sufficiently abundant [mass ratio \(\sim0.01\) (\(10^{-4}\))], \(\eta_H\) can change sign up to \(\sim2-3\) scale heights above midplane at modest field strength (plasma \(\beta\sim100\)) 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 \(B_{\rm th}\). Together with previous studies, we conclude by discussing the grain-abundance-dependent phenomenology of PPD gas dynamics.