The evolution of the fossil large-scale magnetic field in turbulent accretion disks of young stars

We study the fossil large-scale magnetic field evolution in a turbulent accretion disk of young T Tauri star. The coefficient of turbulent viscosity is calculated according to the Shakura and Sunyaev model. The modeling is performed taking into account the weakening of the turbulence in the region of low ionization fraction ("dead" zone). The ionization structure is calculated taking into account thermal ionization, cosmic rays and radioactive elements, radiative recombinations and recombinations on dust grains. The magnetic field is calculated taking into account ambipolar diffusion. The simulations show that the magnetic field is frozen in gas and its strength is proportional to the gas surface density in the inner region of the disk, $R<0.2$ AU. The magnetic field strength increases from $10^2$ G to $10^3$ G in this region within 5 Myr. The outer boundary of the "dead" zone depends on the dust grain size and ranges from 30 AU for $a_g=0.1$ $\mu$m to 3 AU for $a_g=10^3$ $\mu$m. The size of the "dead" zone decreases with time. The magnetic field strength inside the "dead" zone remains practically constant at around $10^{-3}$–$10^{-4}$ G during the disk evolution.