# Dependence of Hall Coefficient on Grain Size and Cosmic Ray Rate and Implication for Circumstellar Disk Formation

## TL;DR

This study investigates how the Hall coefficient, influenced by dust grain size and cosmic ray ionization, affects the formation and size of circumstellar disks during star formation.

## Contribution

It provides a quantitative analysis of the dependence of the Hall effect on dust and cosmic rays, and estimates resulting disk sizes using an analytic model.

## Key findings

- Disk sizes range from 3 to 100 au depending on parameters.
- Hall effect significantly influences disk formation, especially with small dust grains.
- Disk growth occurs mainly during the main accretion phase.

## Abstract

The Hall effect plays a significant role in star formation because it induces rotation in the infalling envelope, which in turn affects the formation and evolution of the circumstellar disk. The importance of the Hall effect varies with the Hall coefficient, and this coefficient is determined by the fractional abundances of charged species. These abundance values are primarily based on the size and quantity of dust grains as well as the cosmic ray intensity, which respectively absorb and create charged species. Thus, the Hall coefficient varies with both the properties of dust grains and the cosmic ray rate (or ionization source). In this study, we explore the dependence of the Hall coefficient on the grain size and cosmic ray ionization rate using a simplified chemical network model. Following this, using an analytic model, we estimate the typical size of a circumstellar disk induced solely by the Hall effect. The results show that the disk grows during the main accretion phase to a size of ${\sim}$ 3 - 100 au, with the actual size depending on the parameters. These findings suggest that the Hall effect greatly affects circumstellar disk formation, especially in the case that the dust grains have a typical size of ${\sim}$ 0.025 ${\mu}$m - 0.075 ${\mu}$m.