  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*.
