Energetic particle-mediated interplanetary shocks observed by Solar Orbiter

Technical Summary: Energetic Particle-Mediated Interplanetary Shocks Observed by Solar Orbiter

Problem and Context
In collisionless astrophysical plasmas, energetic particles are ubiquitous, yet the mechanisms driving their production remain a subject of debate since Fermi's seminal works. While collisionless shocks are recognized as efficient particle accelerators, a specific regime where energetic particle pressure ($P_{EP}$) dynamically dominates the upstream thermal ($P_{Th}$) and magnetic ($P_B$) pressures is theoretically predicted but rarely observed in the heliosphere. Previous observational hints near Earth and at the heliospheric termination shock, as well as analyses of Geotail and STEREO data, have suggested the existence of this regime. However, limitations in energy coverage and the lack of comprehensive in-situ characterization have prevented a detailed understanding of how accelerated particles modify shock structures and upstream plasma conditions.

Methodology
This study utilizes in-situ measurements from the Solar Orbiter mission to identify and characterize interplanetary (IP) shocks where energetic particles dynamically dominate the upstream pressure. The authors analyzed a sample of 152 shock events observed inside 1 au. For each event, the energetic particle pressure ($P_{EP}$) was computed for the 5 hours preceding and 1 hour following the shock passage. The calculation integrated proton differential flux ($j(E)$) over kinetic energies from $E_1 = 10$ keV to $E_2 = 100$ MeV, using the expression $P_{EP} \equiv (4\pi/3)(2m)^{1/2} \int_{E_1}^{E_2} \sqrt{E} j(E) dE$.

This computed $P_{EP}$ was compared against the sum of upstream magnetic pressure ($P_B = B^2/2\mu_0$) and thermal pressure ($P_{Th} = 2n_p k_B T_p$, assuming $T_e \simeq T_p$). The analysis focused on identifying intervals where $P_{EP} \ge P_B + P_{Th}$. The study further examined the evolution of plasma velocity, density, temperature, and magnetic field components in the shock rest frame to characterize the shock geometry (angle $\theta_{Bn}$), Mach numbers ($M_A$, $M_{fms}$), and the spatial extent of any resulting precursors.

Key Results
The analysis identified four specific shock events (S1–S4) satisfying the condition $P_{EP} \ge P_B + P_{Th}$ upstream of the shock. Key findings include:

• Shock Characteristics: All four events correspond to strong, fast shocks with speeds between $\sim600$ and $1000$ km s$^{-1}$. They occupy the high-Mach-number tail of the Solar Orbiter shock population, with Alfvénic Mach numbers ($M_A$) ranging from 6.3 to 8.1 and fast magnetosonic Mach numbers ($M_{fms}$) from 4.3 to 6.9.
• Occurrence Rate: These energetic particle-mediated events represent approximately 3% of the analyzed shock sample, indicating they occur only under extreme parameter conditions.
• Precursor Extent: The spatial extent of the energetic particle-dominated region (precursor) varies significantly, ranging from $\sim10^3$ to $\sim10^5$ ion inertial lengths ($d_i$). The duration of this regime ($\tau_{EP}$) spans from a few minutes (S2) to over 100 minutes (S3, S4).
• Dynamic Modifications: In several cases, the rise in $P_{EP}$ coincides with a decrease in the upstream bulk flow speed and ram pressure in the shock frame, consistent with the formation of an energetic particle pressure precursor that decelerates the incoming flow.
• Geometric Dependence: The extent of the precursor ($L_{EP}$) shows a clear dependence on shock geometry. Quasi-parallel shocks (smaller $\theta_{Bn}$) produce more extended precursors, allowing particles to escape farther upstream, while quasi-perpendicular shocks confine particles closer to the shock front.
• Seed Populations: Three of the four events occurred following large Solar Energetic Particle (SEP) events, suggesting that a substantial pre-existing "seed" population of energetic particles may facilitate the development of this regime.

Significance and Claims
The authors claim that these observations provide the first detailed description of energetic particle-mediated shocks using in-situ data, offering direct evidence that accelerated particles can dynamically modify the upstream medium and structure of IP shocks. The study highlights the critical coupling between energetic particles, upstream fluctuations, and shock structure.

The paper posits that these findings are essential for understanding particle acceleration at collisionless shocks, as they confirm theoretical predictions that strong shocks can generate upstream precursors that alter compression ratios and flow dynamics. While the authors note that similar upstream modifications are observed at Earth's bow shock, they emphasize that the events described here involve higher-energy particles and dynamic interplanetary environments. The work establishes that the energetic particle-mediated regime is a distinct, albeit rare, phenomenon occurring at the extreme end of the IP shock parameter space, linking shock strength and geometry directly to the efficiency of particle acceleration and the resulting modification of the shock environment.