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. The induction equation of the mean poloidal field is solved under the standard viscous disk model. Magnetic flux evolution is controlled by two timescales: one is the timescale of the inward advection of the magnetic flux, τ 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 τ dif . We consider diffusion due to the Ohmic resistivity. These timescales can be significantly different from the disk viscous timescale τ disk . The behaviors of the magnetic flux evolution are quite different depending on the magnitude relationship of the timescales τ adv , τ dif , and τ disk . The most interesting phenomena occur when τ adv ≪ τ dif , τ 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 the magnetic flux has also 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. We also find a condition for the initial large magnetic flux, which is a fossil of the magnetic field dragging during the early phase of star formation that survives for a duration in which significant gas disk evolution proceeds.