  These Faraday rotation calculations of hot, thick accretion flows are
motivated by the measured steady rotation measure (RM) of $\approx -6 \times
10^5$ rad m$^{-2}$ from Sgr A*. In our numerical simulations, the quasi-steady
state structure of the accretion flow, and the RM it produces, depends on the
initial magnetic field. In spite of this dependence, we can draw several robust
conclusions about Faraday rotation produced by geometrically thick accretion
disks: i) the time averaged RM does not depend that sensitively on the viewing
angle, but the stability of the RM can. Equatorial viewing angles show
significant variability in RM (including sign reversals), while polar viewing
angles are relatively stable if there is a large scale magnetic field threading
the disk at large radii. ii) Most of the RM is produced at small radii for
polar viewing angles while all radii contribute significantly near the midplane
of the disk. Our simulations confirm previous analytic arguments that the
accretion rate onto Sgr A* must satisfy $\dot M_{\rm in} \ll \dot M_{\rm Bondi}
\sim 10^{-5} \mpy$ in order to not over-produce the measured RM. We argue that
the steady RM $\approx -6 \times 10^5$ rad m$^{-2}$ from Sgr A* has two
plausible explanations: 1) it is produced at $\sim 100$ Schwarzschild radii,
requires $\dot{M}_{\rm in} \approx 3 \times 10^{-8} M_\odot$ yr$^{-1}$, and we
view the flow at an angle of $\sim 30^\circ$ relative to the rotation axis of
the disk; in our simulations, the variation in RM across a finite-sized source
is sufficient to depolarize the emission below $\approx$ 100 GHz, consistent
with observations. 2) Alternatively, the RM may be produced in the relatively
spherical inflowing plasma near the circularization radius at $\sim 10^3-10^4$
Schwarzschild radii.
