Faraday rotation in global accretion disk simulations: Implications for Sgr A

We calculate Faraday rotation in global axisymmetric MHD simulations of geometrically thick accretion flows. These calculations are motivated by the measured rotation measure (RM) ≈ -6 × 10⁵ rad m^-2 from Sgr A* in the Galactic center, which appears to have been stable over the past ≈7 yr. In our numerical simulations, the quasi-steady state structure of the accretion flow, as well as the RM it produces, depends on the initial magnetic field threading the accreting material. In spite of this dependence, we can draw several robust conclusions about Faraday rotation produced by geometrically thick accretion disks: (1) the time-averaged RM does not depend that sensitively on the viewing angle through the accretion flow, 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. (2) 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 M_in ≪ M_Bondi ∼ 10 ^-5 M⊙ yr^-1 in order to not overproduce the measured RM. We argue that the steady RM ≈ -6 × 10⁵ rad m ^-2 from Sgr A* has two plausible explanations: (1)It is produced at∼100 Schwarzschild radii, requires M_in ≈ 3 × 10^-8 M⊙ yr^-1, and we view the flow at an angle of ∼30° relative to the rotation axis of the disk. (2) Alternatively, the RM may be produced in the relatively spherical inflowing plasma near the circularization radius at ∼ 10³-10⁴ Schwarzschild radii. Time variability studies of the RM can distinguish between these two possibilities.