Generation and Expansion-Driven Growth of Switchbacks in the Outer Solar Corona and Solar Wind

TL;DR

The paper investigates magnetic-field switchbacks observed by the Parker Solar Probe and Solar Orbiter near the Alfvén surface to determine whether sub-Alfvénic intervals can host switchbacks. It demonstrates that conditioning on the instantaneous Alfvén Mach number $M_a^{\mathrm{Inst}}$ and using short, co-moving backgrounds biases deflection statistics, and that treating $M_a$ as a bulk-stream property with a Parker-spiral or long background reference recovers a substantial sub-Alfvénic SB population, aligning with expansion-driven amplification. The results reveal two regimes: for $M_a \lesssim 1$, deflection growth is rapid with weak scale dependence, while for $M_a \gtrsim 1$, small-scale deflections saturate and large-scale rotations continue to grow due to turbulence; this is consistent with wave-action conservation and scale-dependent dissipation. Overall, the study supports a formation pathway in which coronal Alfvénic fluctuations are amplified by expansion through the sub-Alfvénic corona and then reshaped by turbulent decay in the super-Alfvénic wind, unifying in-situ generation with expansion-driven physics.

Abstract

We analyze \emph{Parker Solar Probe} and \emph{Solar Orbiter} measurements of magnetic-field reversals (``switchbacks'') across the Alfvén surface ($M_a\simeq 1$), where $M_a$ is the Alfvén Mach number. The reported ``sub-Alfvénic switchback dropout'' follows from two diagnostic biases: conditioning on an instantaneous $M_a$, which is transiently elevated above unity by radial-velocity enhancements during large-amplitude Alfvénic rotations, and short-window local-mean backgrounds that partially track these rotations and suppress deflection angles. Treating $M_a$ as a bulk-stream property via rolling medians and referencing deflections to event-independent backgrounds -- a Parker-spiral direction or a sufficiently long rolling median -- recovers sub-Alfvénic switchbacks systematically. The mean deflection $\langle θ\rangle$ separates into two regimes with $M_a$. For $M_a \lesssim 1$, $\langle θ\rangle$ rises rapidly with weak dependence on the background window, consistent with expansion-driven amplification of Alfvénic fluctuations. For $M_a \gtrsim 1$, the evolution becomes scale dependent: large-scale $\langle θ\rangle$ continues to grow with $M_a$ at reduced rate, while small-scale growth saturates, consistent with turbulent decay and dissipation. Collectively, these results indicate that switchbacks need not originate only in the super-Alfvénic solar wind. Instead, they are consistent with a formation pathway in which coronal fluctuations are amplified by large-scale expansion through the sub-Alfvénic regime, with subsequent propagation into the super-Alfvénic wind where turbulent decay modifies their scale-dependent properties.

Figures (3)

• Figure 1: Mass-flux proxy $\dot{M}$ in the $(R,M_a)$ plane, where $R\equiv r/R_{\odot}$ and $r$ is heliocentric distance. Colors show the binned mean $\langle \dot{M}\rangle$ (log scale), and black contours indicate the sample-count levels used to delineate regions with sufficient statistics. The top and right margins show one-dimensional profiles of the $M_a$-conditioned diagnostics (definitions in Appendix \ref{['app:wkb_theta_ps:diagnostics']}): $\mathcal{Y}_{PS}\equiv \dot{M}\,2(U^{\mathrm{Bulk}})^2\!\left(1-\langle \cos\Theta_{PS}\rangle_{w}\right)$ (black) and $\mathcal{X}_{PS}\equiv \dot{M}\,(U^{\mathrm{Bulk}})^2(\delta B_{PS}/B_0)^2$ (colored), averaged over $M_a$ (top) and over $R$ (right), respectively. The dotted curve shows the best-fit WKB profile $\alpha\,g(M_a)$ with $g(M_a)=M_a^3/(M_a+1)^2$ over the fitted $M_a$ range.
• Figure 2: Conditional PDFs $P(\theta\,|\,M_a)$ of the magnetic-field deflection angle $\theta$ (definitions in Appendix \ref{['Appendix:Methods']}, Sections \ref{['app:Ma_defs']} and \ref{['app:def_angles']}). Panels $(\alpha)$ and $(\beta)$ measure $\theta$ relative to a local background field defined by a dynamic window of scale $\ell^\ast$: Panel $(\alpha)$ uses a local-mean background ($\theta_{\mathrm{mea}}$, $\ell^\ast=2^{10}\,d_i$) and Panel $(\beta)$ uses a local-median background ($\theta_{\mathrm{med}}$, $\ell^\ast=2^{14}\,d_i$). Panel $(\gamma)$ measures $\theta$ relative to the Parker-spiral direction ($\theta_{PS}$) as the reference. Color encodes the $M_a$ bin (top color bar). Solid (dotted) curves condition on the bulk-stream (instantaneous) Mach number, $M_a^{\mathrm{Bulk}}$ ($M_a^{\mathrm{Inst}}$). Curve thickness denotes $M_a<1$ (thin) and $M_a>1$ (thick) using the same Mach-number definition used to condition each curve. Shaded regions mark $\theta<90^\circ$.
• Figure 3: Average deflection angle $\langle \theta_{\mathrm{med}} \rangle$ as a function of $M_a$. Colored curves indicate deflection angles estimated relative to a local, scale-dependent background magnetic field $\mathbf{B}^{\mathrm{med}}_{\ell^\ast}(t)$, with the scale $\ell^\ast$ parametrized by the smoothing window width shown in the colorbar (definitions in Appendix \ref{['Appendix:Methods']}, Section \ref{['app:def_angles']}).