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