The Strength of the Sheared Magnetic Field in the Galactic's Circumnuclear Disk

Recent high-resolution 53 μm polarimetric observations from SOFIA/HAWC+ have revealed the inferred plane-of-the-sky magnetic field (B-field) orientation in the Galactic center's circumnuclear disk (CND). The B-field is mostly aligned with the steamers of ionized material falling onto Sgr A* at large, differential velocities (shear). In such conditions, estimating the B-field strength with the "classical" Davis-Chandrasekhar-Fermi (DCF) method does not provide accurate results. We derive a "modified" DCF method by solving the ideal-MHD equations from first principles considering the effects of a large-scale, shear flow on the propagation of a fast magnetosonic wave. In the context of the DCF approximation, both the value of the shear and its Laplacian affect the inferred B-field strength. Using synthetic polarization data from MHD simulations for a medium dominated by shear flows, we find that the "classical" DCF determines B-field strengths only within >50% of the true value where the "modified" DCF results are improved significantly (~3%-22%). Applying our "modified" DCF method to the CND revealed B-field strengths of 1-16 mG in the northern arm, 1-13 mG in the eastern arm, and 3-27 mG in the western arc at spatial scales ≲1 pc, with median values of 5.1 ± 0.8, 4.0 ± 1.2, and 8.5 ± 2.3 mG, respectively. The balance between turbulent gas energy (kinetic plus hydrostatic) and turbulent magnetic energy densities suggest that, along the magnetic-field-flow direction, magnetic effects become less dominant as the shear flow increases and weakens the B-field via magnetic convection. Our results indicate that the transition from magnetically to gravitationally dominated accretion of material onto Sgr A* starts at distances ~1 pc.