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

TL;DR

This study reconstructs the Sun's Alfvén surface, $r_A$, using Parker Solar Probe measurements during solar cycle 25, linking in-situ solar wind data with coronal magnetic-field structure via Parker spiral physics and PFSS modelling. The Alfvén radius grows from ~11 to ~16 $R_\odot$ as activity increases, with fluctuations of 10–40% over both space and time; the corresponding solar wind angular momentum-loss rate rises from ~1×10^{30} erg to ~3×10^{30} erg, following the cycle. The results show that $r_A$ scales with wind magnetisation $\Upsilon_{\text{open}}$, but PSP measurements yield ~30% larger radii than 2.5D wind simulations for the same $\dot{M}$ and $\phi_{\text{open}}$, suggesting missing physics such as 3D geometry, time variability, or turbulence. The work highlights the complex, corrugated Alfvén surface shaped by coronal field evolution and underscores the value of combining in-situ measurements with global coronal models to test angular-momentum loss in Sun-like stars. Future missions extending measurements in latitude and remote sensing will further constrain the large-scale Alfvén-surface morphology and its role in stellar spin-down.

Abstract

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 onboard 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 $\sim$1.4$\times 10^{30}$ erg to 3$\times 10^{30}$ 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 pseudostreamers. The Alfvén surface was highly structured and time-varying however, at large-scales, organised by the coronal magnetic field. 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 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.

Figures (13)

• Figure 1: Summary of the hourly solar wind speed, Alfvén speed, and Alfvén Mach number measured by PSP from E04 to E20. Intervals containing sub-Alfvénic solar wind are highlighted in magenta. Left: Quantities displayed as a function of PSP's radial distance. PSP's inbound journey is on the left, the outbound journey on the right. Structure in the radial scans is quickly discerned in this view, but the longitudinal scans are compressed. Right: Quantities shown as a function of PSP's Carrington longitude. The radial scans are obscured, but the structure in each longitudinal scan is easily distinguished.
• Figure 2: Extrapolation of the solar wind along Parker spiral magnetic field lines for PSP encounters E04 and E06 (left), and E16 and E18 (right). The path of PSP is coloured red or blue according to the radial magnetic field polarity. Parker spiral magnetic field lines are coloured by solar wind speed using an acceleration of $\alpha=0.1$. The solid black lines show the Alfvén surface when averaged into bins of two degrees width in Carrington longitude. The dashed semi-circles represents the longitudinally averaged Alfvén radii.
• Figure 3: Evolution of the Alfvén radius extrapolated from PSP over solar cycle 25. The horizontal black ticks show PSP's closest approach in each encounter. The distribution of hourly extrapolations using $\alpha=0.1$ are shown with coloured histograms. The longitudinally averaged value for each encounter is indicated with a red marker. The associated red bars show the variation in the average due to different wind accelerations (from $\alpha=0$ to $\alpha=0.2$). The thin and thick grey lines represent the monthly and monthly smoothed sunspot number from WDC-SILSO.
• Figure 4: Same as Figure \ref{['fig:cycle']}, but now for the solar wind mass flux and magnetic flux. Both values have been multiplied by a factor of $4\pi$ to be used as an estimate for the global mass-loss rate and open magnetic flux.
• Figure 5: Fluctuations in the Sun's Alfvén radius during PSP's longitudinal and radial scans. Encounters are coloured by monthly sunspot number. Top left: PSP's trajectory in the Carrington frame from E04 to E20, when PSP was below 50 solar radii. The segments highlighted red at closest approach correspond to the longitudinal scans. The segments highlighted blue correspond to the radial scans, when PSP moved quasi radially in the Carrington frame. Top right: Markers, labelled by encounter, show the 50th percentile of the Alfvén radii measured during the longitudinal and radial scans. Vertical and horizontal lines represent the 25th to 75th percentiles during the longitudinal and radial scans, respectively. The solid line marks equality and the dashed lines highlight $\pm$ a third. The bottom panels show the longitudinal scan and radial scans decomposed with discrete Fourier transforms to identify the spatial and temporal scales associated with the variation of the Alfvén radius away from the average ($r_A-\langle r_A\rangle$). Thick solid lines show the averaged profile for all encounters except E04 and E05.