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The Hall effect plays a significant role in star formation because it inducesrotation in the infalling envelope, which in turn affects the formation andevolution of the circumstellar disk. The importance of the Hall effect varieswith the Hall coefficient, and this coefficient is determined by the fractionalabundances of charged species. These abundance values are primarily based onthe size and quantity of dust grains as well as the cosmic ray intensity, whichrespectively absorb and create charged species. Thus, the Hall coefficientvaries with both the properties of dust grains and the cosmic ray rate (orionization source). In this study, we explore the dependence of the Hallcoefficient on the grain size and cosmic ray ionization rate using a simplifiedchemical network model. Following this, using an analytic model, we estimatethe typical size of a circumstellar disk induced solely by the Hall effect. Theresults 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. Thesefindings suggest that the Hall effect greatly affects circumstellar diskformation, especially in the case that the dust grains have a typical size of${\sim}$ 0.025 ${\mu}$m - 0.075 ${\mu}$m.

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