Hall Effect in Protostellar Disc Formation and Evolution

TL;DR

This study investigates how the Hall effect influences protostellar disc formation and evolution, revealing that it leads to small discs and depends on grain size and ionization conditions, with implications for magnetic field diffusion.

Contribution

The paper demonstrates that Hall effect efficiency depends on grain size removal and ionization rate, and shows it results in small discs regardless of magnetic field polarity.

Findings

Hall effect becomes efficient when small grains are removed.

Discs formed are typically less than 20 AU in size.

Radial magnetic field diffusion is crucial for disc growth.

Abstract

The Hall effect is recently shown to be efficient in magnetized dense molecular cores, and could lead to a bimodal formation of rotationally supported discs (RSDs) in the first core phase. However, how such Hall dominated systems evolve in the protostellar accretion phase remains unclear. We carry out 2D axisymmetric simulations including Hall effect and Ohmic dissipation, with realistic magnetic diffusivities computed from our equilibrium chemical network. We find that Hall effect only becomes efficient when the large population of very small grains (VSGs: $\lesssim$10 nm) is removed from the standard MRN size distribution. With such an enhanced Hall effect, however, the bimodality of disc formation does not continue into the main accretion phase. The outer part of the initial $\sim$40 AU disc formed in the anti-aligned configuration (${\bf \Omega \cdot B}<0$) flattens into a thin rotationally supported Hall current sheet as Hall effect moves the poloidal magnetic field radially inward relative to matter, leaving only the inner $\lesssim$10--20 AU RSD. In the aligned configuration (${\bf \Omega \cdot B}>0$), disc formation is suppressed initially but a counter-rotating disc forms subsequently due to efficient azimuthal Hall drift. The counter-rotating disc first grows to $\sim$30 AU as Hall effect moves the magnetic field radially outward, but only the inner $\lesssim$10 AU RSD is long-lived like in the anti-aligned case. Besides removing VSGs, cosmic ray ionization rate should be below a few 10$^{-16}$ s$^{-1}$ for Hall effect to be efficient in disc formation. We conclude that Hall effect produces small $\lesssim$10--20 AU discs regardless of the polarity of the magnetic field, and that radially outward diffusion of magnetic fields remains crucial for disc formation and growth.