Proton Temperature Anisotropy Across Interplanetary Shocks: A Statistical Analysis with WIND observations

Abstract

Interplanetary (IP) shocks efficiently modify the proton temperature anisotropy of the solar wind. Analyzing ~800 IP shocks observed by the Wind spacecraft from 1997-2024, we present a statistical study of upstream and downstream proton temperature anisotropy and its dependence on shock geometry, compression, and distance from the shock. We find that (1) quasi-perpendicular shocks produce a pronounced enhancement of perpendicular temperature downstream (Tperp > Tpara), whereas parallel shocks remain near isotropic downstream due to typically stronger upstream Tpara; (2) comparisons with the Chew-Goldberger-Low (CGL) double-adiabatic model reveal geometry-dependent deviations. CGL overestimates downstream perpendicular heating and underestimates parallel heating at quasi-perpendicular shocks, with the opposite trend at quasi-parallel shocks, highlighting the importance of non-adiabatic processes beyond simple compression; (3) Shock-driven anisotropy is strongly localized near the shock and gradually relaxes toward typical solar wind conditions farther downstream as the shock's influence diminishes; and (4) downstream anisotropy is regulated by kinetic instabilities, with quasi-perpendicular shocks constrained by proton cyclotron and mirror instabilities and quasi-parallel shocks limited by the parallel firehose instability. Together, these results show that the evolution of temperature anisotropy at interplanetary shocks is controlled by shock geometry, localized processes, and instability driven regulation.

Figures (6)

• Figure 1: Upstream $A_\mathrm{u}$ (left panel) and downstream $A_\mathrm{d}$ (right panel) proton temperature anisotropy, defined as $A = T_\perp/T_\parallel$, as a function of shock obliquity $\theta\,(^\circ)$. Fast-forward (FF) shocks are shown in red and fast-reverse (FR) shocks in blue. Each dot represents the binned mean anisotropy within a $5^\circ$ shock-obliquity bin, and the error bar denote the standard error of the mean. The lower two panels show the number distribution of FF shocks (red) and FR shocks (blue) in each $\theta$ bin corresponding to the upper panels.
• Figure 2: Comparison of observed downstream-to-upstream proton temperature ratios with CGL predictions. Panels (a) and (b) show the parallel ($T_{\parallel d}/T_{\parallel u}$) and perpendicular ($T_{\perp d}/T_{\perp u}$) temperature ratios, respectively, with markers color-coded by shock obliquity. The dashed line denotes the temperature ratio predicted by the CGL double-adiabatic model based on magnetic-field and density compression. Deviations from this line indicate the influence of non-adiabatic and kinetic processes across the shock. Panels (c) and (d) show the relative change in temperature anisotropy, $A_d/A_u$, as a function of the magnetic compression ratio $r_B$ for quasi-parallel (c) and quasi-perpendicular (d) shocks, respectively.
• Figure 3: Probability distributions of proton temperature anisotropy $A$ at different time intervals relative to the shock front. The left and right panels show upstream and downstream distributions, respectively. Distributions are computed for increasing time windows from the shock: blue (0–1 min), orange (1–10 min), and green dashed (10–60 min). Shorter intervals reveal stronger anisotropy near the shock, while longer intervals approach more isotropic solar wind conditions.
• Figure 4: Statistical distribution of ($T_\perp/T_\parallel$, $\beta_\parallel$) upstream and downstream of Fast-Forward shocks. The black Dashed or Dotted lines indicate theoretical thresholds for various instabilities with growth rate $\gamma = 10^{-3}\,\omega_{cp}$. (Dotted: Mirror instability; Dashed: Proton cyclotron instability; Dash-dot: Parallel fire hose instability; Dash-dot-dot: Oblique fire hose instability) The top panels show the 0–1 min interval immediately near the shock, while the bottom panels show the 1–10 min interval farther from the shock. These time windows correspond to those used in Figure \ref{['fig:dist']}. Red contours represent the density distribution, and its levels span from 10% to 50% of the maximum value with equal spacing.
• Figure 5: Similar to Figure \ref{['fig:Ins1_FF']}, but showing the instability distributions for Fast-Reverse (FR) shocks.