Dissipation of magnetic flux in primordial gas clouds

We report on the strength of the seed magnetic flux of the accretion disk surrounding Population III stars. The magnetic field in accretion disks might play an important role in the transport of angular momentum because of the turbulence induced by magnetorotational instability (MRI). On the other hand, since the primordial star-forming clouds contain no heavy elements or grains, they experience a very different thermal history and magnetic-field-dissipation history in the course of their gravitational contraction from those in the present-day star-forming molecular clouds. In order to assess the magnetic field strength in the accretion disk of Population III stars, we calculate the thermal history of the primordial collapsing clouds and investigate the coupling of the magnetic field with the primordial gas. As a result, we find that the magnetic field strongly couples with the primordial gas cloud throughout the collapse, i.e., the magnetic field is frozen to the gas, as long as the initial field strength satisfies B less than or similar to 10(-5)(N-H/10(3) cm(-3)) 0.55 G.