Dynamical effects of the ambipolar diffusion in a protoplanetary disc

Abstract

ABSTRACT Several recent simulation works in the non-ideal magnetohydrodynamic (MHD) formalism have shown the importance of ambipolar diffusion (AD) within the protoplanetary discs (PPDs) at large radii. In this study, we model the time evolution of a polytropic PPD in the presence of the AD. In this regard, the non-ideal MHD equations are investigated in the outer region of a PPD where the magnetic field evolution is dominated by the AD. The self-similar solution technique is used for a polytropic fluid including the self-gravity and viscosity. The ambipolar diffusivity and its derivative are crucial for the formulation of this study. Hence, this variable is scaled by an important factor, that is the Elsasser number. The self-similar equations are derived, and the semi-analytical and numerical solutions are presented for the isothermal and polytropic cases. The analytical approach enables us to know the asymptotic behaviour of the physical variables in a PPD, such as the angular momentum and magnetic field. Furthermore, the coupling/decoupling of magnetic field with the angular momentum was discussed analytically to find a corresponding model for the angular momentum loss at large radii of a PPD. Regarding this approach, we found that the magnetic braking induced by the AD at large radii has a high potential to loss the angular momentum even if the turbulent viscosity is not efficient. Also, the sign and values of vertical velocity strongly depends on the sign and values of radial field in the polytropic case.