We study the flow structure in 3D magnetohydrodynamic (MHD) simulations of accretion onto Sagittarius A* via the magnetized winds of the orbiting Wolf-Rayet stars. These simulations cover over 3 orders of magnitude in radius to reach $approx$ 300 gravitational radii, with only one poorly constrained parameter (the magnetic field in the stellar winds). Even for winds with relatively weak magnetic fields (e.g., plasma $beta$ $sim$ $10^6$), flux freezing/compression in the inflowing gas amplifies the field to $beta$ $sim$ few well before it reaches the event horizon. Overall, the dynamics, accretion rate, and spherically averaged flow profiles (e.g., density, velocity) in our MHD simulations are remarkably similar to analogous hydrodynamic simulations. We attribute this to the broad distribution of angular momentum provided by the stellar winds, which sources accretion even absent much angular momentum transport. We find that the magneto-rotational instability is not important because of i) strong magnetic fields that are amplified by flux freezing/compression, and ii) the rapid inflow/outflow times of the gas and inefficient radiative cooling preclude circularization. The primary effect of magnetic fields is that they drive a polar outflow that is absent in hydrodynamics. The dynamical state of the accretion flow found in our simulations is unlike the rotationally supported tori used as initial conditions in horizon scale simulations, which could have implications for models being used to interpret Event Horizon Telescope and GRAVITY observations of Sgr A*.
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