Large-scale dynamics of winds originated from black hole accretion flows: (II) Magnetohydrodynamics

Winds from black hole accretion disks are essential ingredients in understanding the coevolution between the supermassive black hole and its host galaxy. The great difference of dynamical ranges from small-scale accretion disk simulations to large-scale or cosmological simulations places barriers to track wind kinematics. In the first paper of this series, we have studied the dynamics of disk winds from the outer edge of the accretion disk toward galaxy scales in the hydrodynamical framework. In this paper, we further incorporate magnetic fields to understand the wind dynamics by adopting one-dimensional magnetohydrodynamical (MHD) model, with boundary conditions set for hot accretion flows. The geometry of poloidal magnetic field is prescribed as a straight line with an angle $\theta=45^\circ$ from the rotational axis, and the strength satisfies the divergence free condition. The wind solution is achieved through requesting gas to pass through the slow, Alfv\'{e}n and fast magneto-sonic points smoothly. Physical quantities are found to show a power-law dependence on cylindrical radius $R$ beyond the fast magneto-sonic point, for which $\rho \propto R^{-2}, v_{\rm p}\propto {\rm const.}, v_{\rm \phi}\propto R^{-1}, B_{\rm \phi}\propto R^{-1},$ and $\beta \propto \rho^{\gamma-1}$. The magnetization of wind is dominant in determining the wind properties. The wind is accelerated to a greater terminal velocity with strong magnetization ($v_{\rm Ap0}>1$) compared to the hydrodynamical case, which the magnetic pressure gradient dominates and the centrifugal potential converts to the kinetic energy. The dependance of wind physical quantities on magnetization, temperature, field line angular velocity, and adiabatic index is also discussed.