The Hall effect in accretion flows

TL;DR

This paper presents similarity solutions for accretion flows considering magnetic diffusion, highlighting the significant role of Hall diffusion in influencing flow structure and potentially resolving magnetic braking issues in star formation.

Contribution

It introduces two new power law similarity solutions for accretion flows with magnetic diffusion, emphasizing the impact of Hall diffusion even when weak.

Findings

Hall diffusion affects surface density, accretion rate, and angular momentum.

Solutions include a Keplerian disc and free fall onto the central object.

Hall diffusion may solve the magnetic braking catastrophe.

Abstract

Magnetic diffusion in accretion flows changes the structure and angular momentum of the accreting material. We present two power law similarity solutions for flattened accretion flows in the presence of magnetic diffusion: a secularly-evolving Keplerian disc and a magnetically-diluted free fall onto the central object. The influence of Hall diffusion on the solutions is evident even when this is small compared to ambipolar and Ohmic diffusion, as the surface density, accretion rate and angular momentum in the flow all depend upon the product \eta_H(B.\Omega), and the inclusion of Hall diffusion may be the solution to the magnetic braking catastrophe of star formation simulations.