Proper Motion and Natal Kick in the Galactic Black Hole X-ray Binary AT2019wey

Understanding the formation mechanisms of stellar-mass black holes in X-ray binaries (BHXBs) remains a fundamental challenge in astrophysics. The natal kick velocities imparted during black hole formation provide crucial constraints on these formation channels. In this work, we present a new-epoch very long baseline interferometry (VLBI) observation of the Galactic BHXB AT2019wey carried out in 2023. Combining with archival VLBI data from 2020, we successfully measure the proper motion of AT2019wey over a 3-year timescale, namely $0.78\pm0.12$~\masyr\ in right ascension and $-0.42\pm0.07$~\masyr\ in declination. Employing the measured proper motion, we estimate its peculiar velocity and the potential kick velocity (PKV), through Monte Carlo simulations incorporating uncertainties of its distance and radial velocity. The estimated PKV distributions and height above the Galactic plane suggest that AT2019wey's black hole likely formed through a supernova explosion rather than direct collapse.