On the Propagation and Damping of Alfvenic Fluctuations in the Outer Solar Corona and Solar Wind

Abstract

We analyze \textit{Parker Solar Probe} and \textit{Solar Orbiter} observations to investigate the propagation and dissipation of Alfvénic fluctuations from the outer corona to 1~AU. Conservation of wave-action flux provides the theoretical baseline for how fluctuation amplitudes scale with the Alfvén Mach number $M_a$, once solar-wind acceleration is accounted for. Departures from this scaling quantify the net balance between energy injection and dissipation. Fluctuation amplitudes follow wave-action conservation for $M_a < M_a^{b}$ but steepen beyond this break point, which typically lies near the Alfvén surface ($M_a \approx 1$) yet varies systematically with normalized cross helicity $σ_c$ and fluctuation scale. In slow, quasi-balanced streams, the transition occurs at $M_a \lesssim 1$; in fast, imbalanced wind, WKB-like scaling persists to $M_a \gtrsim 1$. Outer-scale fluctuations maintain wave-action conservation to larger $M_a$ than inertial-range modes. The turbulent heating rate $Q$ is largest below $M_a^{b}$, indicating a preferential heating zone shaped by the degree of imbalance. Despite this, the Alfvénic energy flux $F_a$ remains elevated, and the corresponding damping length $Λ_d = F_a/Q$ remains sufficiently large to permit long-range propagation before appreciable damping occurs. Normalized damping lengths $Λ_d/H_A$, where $H_A$ is the inverse Alfvén-speed scale height, are near unity for $M_a \lesssim M_a^{b}$ but decline with increasing $M_a$ and decreasing $U$, implying that incompressible reflection-driven turbulence alone cannot account for the observed dissipation. Additional damping mechanisms -- such as compressible effects -- are likely required to account for the observed heating rates across much of the parameter space.

Figures (10)

• Figure 1: Two-dimensional distributions of key solar-wind parameters. ($\alpha$) Mass flux, $M_f$, and ($\beta$) plasma $\beta$, $\beta$, plotted as functions of heliocentric distance $R$ (horizontal axis) and Alfvén Mach number $M_a$ (vertical axis). The color scale indicates the magnitude of each quantity, while black contour lines trace the data-point density; inline labels mark the number of intervals per bin. ($\gamma$) Alfvén Mach number, $M_a$, shown as a function of $R$ and solar-wind speed $U$. Dotted lines correspond to isothermal Parker-wind velocity profiles fitted to quantile boundaries within each of the $N_x = 100$ logarithmically spaced radial bins. In each bin, the data are divided into four equal-sized quantiles, $Q_i(R)$ for $i = 1,\dots,4$, and the fitted profiles $U_i(R)$ serve as radial-dependent thresholds for classifying the solar wind into four distinct acceleration regimes.
• Figure 2: Parametric representation of $\sigma^{\perp}_r$ and $\sigma^{\perp}_c$ as functions of $M_a$. Each marker denotes the median within one of 30 logarithmically spaced $M_a$ bins, with horizontal and vertical error bars indicating the interquartile range (25th-75th percentiles). Circles are used for bins with $M_a \leq 1$, while squares denote bins with $M_a > 1$. Panels (a-d) correspond to the four quartiles of the solar wind acceleration profiles (see Appendix \ref{['Appendix:methods']}). The logarithmic color scale encodes the bin-centered value of $M_a$. Horizontal dashed gray lines indicate contours of constant Elsässer increment alignment angle, defined by $\cos\, \theta_{z^{\pm}} = \sigma^{\perp}_{r}/\sqrt{1 - (\sigma^{\perp}_{c})^{2}}$, while vertical dash-dotted gray lines mark contours of constant velocity-magnetic field increment alignment angle, defined by $\cos\, \theta_{ub} = \sigma^{\perp}_{c}/\sqrt{1 - (\sigma^{\perp}_{r})^{2}}$.
• Figure 3: Wave-action flux spectra as a function of spacecraft-frame frequency $f_{\mathrm{sc}}$, binned by $M_a$. Panels ($\alpha$) and ($\beta$) show the spectral wave-action flux for outward- ($E_{S^{o}}$) and inward-propagating ($E_{S^{i}}$) wavepackets, respectively. Median spectra are computed within logarithmically spaced $M_a$ bins, with solid lines denoting sub-Alfvénic intervals ($M_a < 1$) and dotted lines corresponding to super-Alfvénic intervals ($M_a \geq 1$). Reference power-law slopes are indicated for comparison. Panel ($\gamma$) displays the total wave-action flux, $\mathcal{E}_{S^{\ast}}$, as a function of $M_a$ for selected frequencies. Colored points denote median values with quartile error bars; the corresponding frequencies are indicated by the colorbar, with the reference frequency marked by the white line.
• Figure 4: Power in ($\alpha$) outward-propagating, $\mathcal{P}_{o}$, and ($\beta$) inward-propagating, $\mathcal{P}_{i}$, Elsässer fluctuations, and ($\gamma$) total wave-action flux, $\mathcal{S}^\ast$, computed at a fixed increment scale $\tilde{\ell}=1024 \ d_i$ and plotted versus $M_a$. Curves show means in logarithmic $M_a$ bins, evaluated separately for the four speed quantiles $Q_i(R)$ listed in Table \ref{['tab:parker_fit']}. In ($\alpha$), dashed lines are best-fit WKB profiles $\propto M_a/(M_a+1)^2$ over $M_a<1$; in ($\gamma$), they indicate the median $\mathcal{S}^\ast$ over the same range. Black contours denote sampling density at $[0.5\sigma,~1\sigma,~2\sigma,~3\sigma]$.
• Figure 5: ($\alpha$) Volumetric heating rates, $Q$, estimated using the Cr09 model (solid lines) and the CH09 model (scatter points), plotted as a function of the Alfvén Mach number, $M_a$. The proton-only component, $Q_p$, from the Cr09 model is shown with dotted lines. For clarity, profiles corresponding to different solar-wind speed bins are vertically offset by factors of $10^n$, where $n = 0$ (dark blue) denotes the slowest wind bin and $n = 3$ (light blue) the fastest; offset values are indicated by the reference bars on the side. ($\beta$) Alfvén-wave energy flux. ($\gamma$) Turbulent damping length, $\Lambda_d = F_a / Q_{\mathrm{Cr09}}$. The inset figure illustrates $\Lambda_d$ normalized by the inverse Alfvén-speed scale height, $\left[ \frac{d}{dR} \ln V_{a}^{1/2} \right]^{-1}$.