The magnetic field of a magnetohydrodynamic disk wind: Water maser observations and simulations

Our goal is to measure and model the magnetic field distribution in the disk wind of the young stellar object (YSO) IRAS 21078+5211. We performed sensitive global Very Long Baseline Interferometry observations of the polarized emission of the 22 GHz water masers tracing individual streamlines of the magnetohydrodynamic (MHD) disk wind in IRAS 21078+5211. Our resistive-radiative-gravito-MHD simulations of a jet around a forming massive star are able to reproduce the maser kinematics in the inner jet cavity. We measure a weak level of 0.3%-3.2% of linear and circular polarization in 24 and 8 water masers, respectively. The detected polarized masers sample the direction and the strength of the magnetic field along five distinct streamlines within the inner 100 au region of the disk wind. Along the four streamlines at smaller radii from the jet axis (<25 au), the sky-projected direction of the magnetic field forms, in most cases, a small offset angle of<30$^{\circ}$ with the tangent to the streamline. Along the stream at larger radii (50-100 au), the magnetic field is sampled at only three separated positions, and it is found to be approximately perpendicular to the streamline tangent at heights of approximately 10 and 40 au, and parallel to the tangent at about 70 au. According to our simulations, the magnetic field lines should coincide with the flow streamlines in the inner jet cavity. The small tilt in the magnetic field direction observed along the inner streams can be well explained by Faraday rotation, assuming a realistic low level of ionization for the molecular shell of the jet of namely 10$^{-2}$. The magnetic field amplitudes measured from maser circular polarization are all within a relatively small range of 100-700 mG, which is in good agreement with the simulation results and consistent with reduced magnetic diffusivity in the jet cavity owing to efficient shock ionization.