Faraday Rotation in Global Accretion Disk Simulations: Implications for Sgr A*

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.