Dependence of Hall coefficient on grain size and cosmic ray rate and implication for circumstellar disc formation

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 disc. 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 disc induced solely by the Hall effect. The results show that the disc grows during the main accretion phase to a size of ∼3-100 au, with the actual size depending on the parameters. These findings suggest that the Hall effect greatly affects circumstellar disc formation, especially in the case that the dust grains have a typical size of ∼0.025 − 0.075 μm.