Radial Transport of Large-Scale Magnetic Fields in Accretion Disks. II. Relaxation to Steady States

We study the time evolution of a large-scale magnetic flux threading an accretion disk. Induction equation of the mean poloidal field is solved under the standard viscous disk model. Magnetic flux evolution is controlled by the two timescales: One is the timescale of the inward advection of the magnetic flux, tau_{adv}. This is induced by the dragging of the flux by the accreting gas. The other is the outward diffusion timescale of the magnetic flux tau_{dif}. We consider diffusion due to the Ohmic resistivity. These timescales can be significantly different from the disk viscous timescale tau_{disk}. The behaviors of the magnetic flux evolution is quite different depending on the magnitude relationship of the timescales tau_{adv}, \tau_{dif}, and tau_{disk}. The most interesting phenomena occurs when tau_{adv} << tau_{dif}, tau_{disk}. In such a case, the magnetic flux distribution approaches a quasi-steady profile much faster than the viscous evolution of the gas disk, and also the magnetic flux has been tightly bundled to the inner part of the disk. In the inner part, although the poloidal magnetic field becomes much stronger than the interstellar magnetic field, the field strength is limited to the maximum value that is analytically given by our previous work (Okuzumi et al. 2014, ApJ, 785, 127). We also find a condition for that the initial large magnetic flux, which is a fossil of the magnetic field dragging during the early phase of star formation, survives for a duration in which significant gas disk evolution proceeds.