Unveiling the gas kinematics at 10 AU scales in high-mass star-forming regions: Milliarcsecond structure of 6.7 GHz methanol masers

Context. High-mass stars play a prominent role in Galactic evolution, but their formation mechanism is still poorly understood. This lack of knowledge reflects the observational limitations of present instruments, whose angular resolution (at the typical distances of massive protostars) precludes probing circumstellar gas on scales of 1-100 AU, relevant for a detailed investigation of accretion structures and launch/collimation mechanims of outflows in high-mass star formation. Aims: This work presents a study of the milliarcsecond structure of the 6.7 GHz methanol masers at high-velocity resolution (0.09 km s-1) in four high-mass star-forming regions: G16.59-0.05, G23.01-0.41, IRAS 20126 + 4104, and AFGL 5142. Methods: We studied these sources by means of multi-epoch VLBI observations in the 22 GHz water and 6.7 GHz methanol masers, to determine the 3-D gas kinematics within a few thousand AU from the (proto)star. Our results demonstrate the ability of maser emission to trace kinematic structures close to the (proto)star, revealing the presence of fast wide-angle and/or collimated outflows (traced by the H2O masers), and of rotation and infall (indicated by the CH3OH masers). The present work exploits the 6.7 GHz maser data collected so far to investigate the milliarcsecond structure of this maser emission at high-velocity resolution. Results: Most of the detected 6.7 GHz maser features present an ordered (linear, or arc-like) distribution of maser spots on the plane of the sky, together with a regular variation in the spot LSR velocity (VLSR) with position. Typical values for the amplitude of the VLSR gradients (defined in terms of the derivative of the spot VLSR with position) are found to be 0.1-0.2 km s-1 mas-1. In each of the four target sources, the orientation and the amplitude of most of the feature VLSR gradients remain remarkably stable in time, on timescales of (at least) several years. We also find that the data are consistent with having the VLSR gradients and proper motion vectors in the same direction on the sky, considered the measurement uncertainties. In three (G16.59 - 0.05, G23.01 - 0.41, and IRAS 20126 + 4104) of the four sources under examination, feature gradients with the best determined (sky-projected) orientation divide into two groups directed approximately perpendicular to each other. Conclusions: The time persistency, the ordered angular and spatial distribution, and the orientation generally similar to the proper motions, altogether suggest a kinematical interpretation for the origin of the 6.7 GHz maser VLSR gradients. This work shows that the organized motions (outflow, infall, and rotation) revealed by the (22 GHz water and 6.7 GHz methanol) masers on large scales (~100-1000 AU) also persist to very small (~10 AU) scales. In this context, the present study demonstrates the potentiality of the mas-scale 6.7 GHz maser gradients as a unique tool for investigating the gas kinematics on the smallest accessible scales in proximity to massive (proto)stars