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Numerical simulations of black hole hot accretion flows have shown theexistence of strong wind. Those works focus only on the region close to blackhole thus it is unknown whether or where the wind production stops at largeradii. To address this question, Bu et al. (2016) have performed hydrodynamic(HD) simulations by taking into account the gravitational potential of both theblack hole and the nuclear star clusters. The latter is assumed to be $\propto\sigma^2 \ln(r)$, with $\sigma$ being the velocity dispersion of stars and $r$be the distance from the center of the galaxy. It was found that when thegravity is dominated by nuclear stars, i.e., outside of radius $R_A\equivGM_{\rm BH}/\sigma^2$, winds can no longer be produced. That work, however,neglects the magnetic field, which is believed to play a crucial dynamical rolein the accretion and thus must be taken into account. In this paper, we revisitthis problem by performing magneto-hydrodynamical (MHD) simulations. We confirmthe result of Bu et al. (2016), namely wind can't be produced at the region of$R>R_A$. Our result, combined with the results of Yuan et al. (2015), indicatesthat the formula describing the mass flux of wind $\dot{M}_{\rmwind}=\dot{M}_{\rm BH}(r/20r_s)$ can only be applied to the region where theblack hole potential is dominant. Here $\dot{M}_{\rm BH}$ is the mass accretionrate at the black hole horizon and the value of $R_A$ is similar to the Bondiradius.

Magneto-hydrodynamical Numerical simulation of wind production from black hole hot accretion flows at very large radii