Reconstructing the Sun’s Alfvén surface and wind braking torque with Parker Solar Probe

The Alfvén surface -- where the solar wind exceeds the local Alfvén speed as it expands into interplanetary space -- is now routinely probed by NASA's Parker Solar Probe (PSP) in the near-Sun environment. The size of the Alfvén surface governs how efficiently the solar wind braking torque causes the Sun to spin-down. We aimed to characterise the size and evolution of the Alfvén surface as magnetic activity increased during solar cycle 25. The Alfvén surface was extrapolated from the solar wind mass and magnetic flux measured by the SWEAP and FIELDS instrument suites on board PSP. We accounted for the acceleration of the solar wind along Parker spiral magnetic field lines and used potential field source surface modelling to determine the sources of the solar wind. The longitudinally averaged Alfvén radius measured by PSP grew from 11 to 16 solar radii as solar activity increased. Accordingly, the solar wind angular momentum-loss rate grew from ∼1. 4times 10^ erg to 3times 10^ erg. Both the radial and longitudinal scans of the solar wind contained fluctuations of 10-40% from the average Alfvén radius in each encounter. Structure in the solar corona influenced the morphology of the Alfvén surface, which was smallest around the heliospheric current sheet and pseudo-streamers. At large scales, the Alfvén surface -- organised by the coronal magnetic field -- was highly structured and time-varying. The evolution of the solar corona over the solar cycle systematically shifted the magnetic connectivity of PSP and influenced our perception of the Alfvén surface. The Alfvén surface was 30% larger than in both thermally driven and Alfvén wave-driven wind simulations with the same mass-loss rate and open magnetic flux, but had a similar dependence on the wind magnetisation parameter.