Large-scale dynamics of winds originated from black hole accretion flows: (I) Hydrodynamics

Winds from black hole accretion flows are ubiquitous. Previous works mainly focus on the launching of wind in the accretion flow scale. It still remains unclear how far the winds can propagate outward and what is their large-scale dynamics. As the first paper of this series, we study the large-scale dynamics of thermal wind beyond accretion scales via analytical and numerical methods. Boundary conditions, which are crucial to our problem, are analyzed and presented based on the small-scale simulations combined with observations of winds. Both black hole and galaxy potential are taken into account. For winds originated from hot accretion flows, we find that the wind can reach to large scales. The radial profiles of velocity, density, and temperature can be approximated by $v_r\approx v_{r0}, \rho\approx \rho_{0}(r/r_0)^{-2}$, and $T\approx T_0 (r/r_0)^{-2(\gamma-1)}$, where $v_{r0}, \rho_0, T_0$ are the velocity, density, and temperature of winds at the boundary $r_0(\equiv 10^3 r_g)$, $\gamma$ is the polytropic index. During the outward propagation, the enthalpy and the rotational energy compensate the increase of gravitational potential. For thin disks, we find that because the Bernoulli parameter is smaller, winds cannot propagate as far as the hot winds, but stop at a certain radius where the Bernoulli parameter is equal to the potential energy. Before the winds stop, the profiles of dynamical quantities can also be approximated by the above relations. In this case the rotational energy alone compensates the increase of the potential energy.