The Influences of Outflow on the Dynamics of Inflow
  Both numerical simulations and observations indicate that in an advection-dominated accretion flow most of the accretion material supplied at the outer boundary will not reach the inner boundary. Rather, they are lost via outflow. Previously, the influence of outflow on the dynamics of inflow is taken into account only by adopting a radius-dependent mass accretion rate $\dot{M}=\dot{M}_0 (r/r_{\rm out})^s$ with $s>0$. In this paper, based on a 1.5 dimensional description to the accretion flow, we investigate this problem in more detail by considering the interchange of mass, radial and azimuthal momentum, and the energy between the outflow and inflow. The physical quantities of the outflow is parameterized based on our current understandings to the properties of outflow mainly from numerical simulations of accretion flows. Our results indicate that under reasonable assumptions to the properties of outflow, the main influence of outflow has been properly included by adopting $\dot{M}=\dot{M}_0 (r/r_{\rm out})^s$. 
Fu-Guo Xie (1), Feng Yuan (1) ((1) Shao)