Dissipation of Magnetic Flux in Primordial Gas Clouds

We report the strength of seed magnetic flux of accretion disk surroundingthe PopIII stars. The magnetic field in accretion disk might play an importantrole in the transport of angular momentum because of the turbulence induced byMagneto-Rotational Instability (MRI). On the other hand, since the primordialstar-forming clouds contain no heavy elements and grains, they experience muchdifferent thermal history and different dissipation history of the magneticfield in the course of their gravitational contraction, from those in thepresent-day star-forming molecular clouds. In order to assess the magneticfield strength in the accretion disk of PopIII stars, we calculate the thermalhistory of the primordial collapsing clouds, and investigate the coupling ofmagnetic field with primordial gas. As a result, we find that the magneticfield strongly couple with primordial gas cloud throughout the collapse, i.e.the magnetic field are frozen to the gas as far as initial field strengthsatisfies $ B\lesssim 10^{-5}(n_{\rm H}/10^3{\rm cm^{-3}})^{0.55}{\rm G}$.Comment: 23 pages, 10 figures, accepted for publication in Ap