🔭 astrophysics

Shock properties for solar energetic particle events with signatures of inverse velocity arrival

This study analyzes 26 solar energetic particle events exhibiting inverse velocity arrival using data from Solar Orbiter and Parker Solar Probe, revealing that the phenomenon results from evolving magnetic connectivity shifting from weak shock flanks to stronger shock apices, which delays high-energy particle arrival and hardens the energy spectrum.

Original authors: A. Kouloumvakos, D. Lario, G. M. Mason, A. Vourlidas, R. C. Allen, N. Wijsen, X. Chen, Z. Ding, I. C. Jebaraj, P. Riley, D. J. McComas, C. M. S. Cohen, E. Paouris, S. Raptis, L. Rodríguez-García, Z. G

Published 2026-04-16

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CC BY 4.0

Original authors: A. Kouloumvakos, D. Lario, G. M. Mason, A. Vourlidas, R. C. Allen, N. Wijsen, X. Chen, Z. Ding, I. C. Jebaraj, P. Riley, D. J. McComas, C. M. S. Cohen, E. Paouris, S. Raptis, L. Rodríguez-García, Z. G. Xu, G. D. Berland, G. C. Ho, D. G. Mitchell, E. C. Roelof, J. Rodriguez-Pacheco, M. E. Hill, R. F. Wimmer-Schweingruber

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the Sun as a giant, chaotic kitchen. Every now and then, it throws a massive "explosion party" called a Coronal Mass Ejection (CME). Think of this as a giant, invisible shockwave of air rushing out from the oven, sweeping up everything in its path.

Usually, when this shockwave hits a spaceship (like our solar observatories, Solar Orbiter or Parker Solar Probe), the particles it carries arrive in a predictable order: the fast, high-energy particles (the "sprinters") arrive first, followed by the slower, lower-energy ones (the "marathon runners"). This is called normal velocity dispersion. It's like a race where the fastest runners cross the finish line first.

The Mystery: The "Nose-Like" Surprise

But sometimes, something weird happens. The scientists noticed a strange pattern in the data: the "sprinters" (high-energy particles) actually arrived later than the "marathon runners."

In the data charts, this looks like a concave curve or a "nose" sticking out. The researchers call this Inverse Velocity Arrival (IVA). It's as if the slow runners crossed the finish line first, and the fast runners were stuck in traffic, arriving much later.

The Investigation: How the Shockwave Moves

The authors of this paper acted like cosmic detectives. They looked at 26 of these "nose" events and tried to figure out why the fast particles were delayed. They used 3D modeling to reconstruct the shape and speed of the shockwaves traveling through space.

Here is what they found, explained with some everyday analogies:

1. The "Side Door" vs. The "Front Door"

Imagine the shockwave is a giant, expanding balloon.

The Apex (Front): The very front of the balloon is moving fast and is very strong.
The Flanks (Sides): The sides of the balloon are moving slower and are weaker.

The scientists found that for these "nose" events, the spaceship wasn't connected to the Front Door (the strong, fast part) right away. Instead, the magnetic "wires" connecting the Sun to the spaceship were initially plugged into the Side Doors (the flanks) of the shockwave.

2. The "Moving Connection"

Here is the key twist: The shockwave doesn't just sit still; it expands and moves.

At the start: The spaceship is connected to the weak, slow-moving sides of the shockwave. The particles here are being accelerated slowly.
As time passes: As the shockwave expands, the magnetic connection shifts. The spaceship's "wire" slides from the weak sides toward the strong, fast front of the shockwave.

3. Why the "Sprinters" Arrive Late

This explains the mystery!

Early on: The spaceship is connected to the weak sides. It starts picking up the low-energy particles (the marathon runners) because they are easy to catch.
Later on: The connection shifts to the strong front. Now, the shockwave is powerful enough to accelerate the high-energy particles (the sprinters). But because the connection to this strong area happened later, the sprinters take longer to get ready and reach the spaceship.

It's like a factory assembly line that starts slow on the side of the building and then moves to the main, high-speed production line in the center. The first products (low energy) come out quickly, but the high-quality, high-speed products (high energy) only start coming out once the line moves to the main room.

The Big Picture

The paper concludes that these "nose" events happen because of a changing relationship between the spaceship and the shockwave.

The Shockwave: It gets stronger as it moves away from the Sun.
The Connection: The spaceship's magnetic link moves from the weak edges to the strong center.

This combination means the high-energy particles have to wait for the "connection" to move to the "strong zone" before they can be launched.

Why Does This Matter?

Understanding this helps scientists predict space weather. If we know how these shockwaves behave and how they connect to Earth or our satellites, we can better predict when dangerous high-energy radiation will arrive. It turns out that the "traffic jam" of particles isn't a glitch; it's a clue about how the Sun's shockwaves grow and how they interact with the magnetic highways of space.

In short: The high-energy particles weren't late because they were slow; they were late because the "on-ramp" to the highway they were traveling on didn't open until later in the journey!

1. Problem Statement

Solar Energetic Particle (SEP) events are traditionally characterized by velocity dispersion, where higher-energy particles arrive before lower-energy ones. However, recent observations by Solar Orbiter and Parker Solar Probe have identified a distinct subset of events exhibiting Inverse Velocity Arrival (IVA). In these events, high-energy particles arrive later than mid-energy particles, creating a concave ("nose-like") shape in the energy spectrogram.

While previous studies suggested that IVA might result from specific magnetic connectivity (e.g., western flank connections) or time-dependent acceleration, a comprehensive analysis linking the 3D evolution of shock properties to the temporal evolution of magnetic connectivity and the resulting SEP spectral characteristics was lacking. The central scientific question is: What specific shock dynamics and magnetic connectivity changes drive the formation of IVA signatures?

2. Methodology

The authors employed a multi-instrumental and modeling approach to investigate 26 IVA-SEP events observed between 2018 and 2025.

Data Sources:
- SEP Data: Energetic Particle Detector (EPD) suite on Solar Orbiter and Integrated Science Investigation of the Sun (IS $\odot$ IS) on Parker Solar Probe.
- Coronal Data: White-light coronagraphs (SOHO/LASCO, STEREO-A/SECCHI) and EUV imagers (SDO/AIA, STEREO-A/EUVI, Solar Orbiter/EUI) to identify associated Coronal Mass Ejections (CMEs) and flares.
Event Selection:
- Identified 26 events with clear "nose-like" spectrograms.
- Filtered for events with clear CME/flare associations and sufficient data for 3D reconstruction.
- Final analysis focused on 19 events where shock properties could be fully reconstructed.
3D Shock Modeling:
- Used the PyThea software package to perform 3D kinematic reconstruction of shock fronts using an ellipsoidal geometric model.
- Fitted shock fronts to white-light imagery from multiple vantage points (STEREO-A, SOHO).
- Derived height-time profiles and shock speeds for the shock apex and the COBPOINTs (Connecting with the OBserver POINTs).
Magnetic Connectivity & MHD Simulations:
- Modeled magnetic field lines using nominal Parker spirals (adjusted with measured solar wind speeds where available).
- Calculated the intersection of these field lines with the evolving 3D shock surface (COBPOINTs).
- Utilized Magnetohydrodynamic (MAS) simulations to derive background coronal plasma parameters (density, temperature, magnetic field) to calculate shock parameters (Mach number, compression ratio) at the COBPOINTs.
Analysis:
- Correlated the transition energy ( $E_t$ , the energy where IVA begins) with mean shock parameters (speed, Mach number, compression ratio) and the central separation angle ( $\lambda$ ) between the shock apex and the COBPOINT.

3. Key Contributions

Systematic Catalog: Established a list of 26 IVA-SEP events observed below 1 AU, providing the first systematic statistical analysis of their shock properties.
3D Kinematic Reconstruction: Successfully reconstructed the 3D evolution of shock fronts associated with IVA events, moving beyond 1D or 2D approximations.
Connectivity Evolution Mapping: Demonstrated that the magnetic connection of observers to the shock is not static; it evolves from the shock flanks toward the apex during the event.
Shock Strength Evolution: Quantified the transition of connected shock regions from sub-critical (weak) to super-critical (strong) states over time.

4. Key Results

Magnetic Connectivity Location:
- IVA-SEP events predominantly occur when the spacecraft is magnetically connected to the western flanks of the CME-driven shock.
- The mean central separation angle ( $\lambda$ ) between the shock apex and the COBPOINT ranges from $\sim30^\circ$ to $110^\circ$ , indicating connections are primarily near the flanks rather than the apex.
Shock Speed and Strength:
- The mean shock speed at the COBPOINTs is $\sim882$ km/s, significantly lower than the apex speed ( $\sim1140$ km/s) and lower than speeds typical for large, high-energy SEP events.
- Temporal Evolution: Initially, the connected regions are often sub-critical (Mach number $M_{fms} < 1.5$ ) or even non-shocks. As the shock expands and the magnetic connection shifts toward the apex, the connected regions strengthen, becoming super-critical.
Correlation with Transition Energy ( $E_t$ ):
- A positive correlation was found between the transition energy ( $E_t$ ) and the shock speed at the COBPOINTs (Pearson $r = 0.57$ ).
- Similar positive trends were observed with the fast magnetosonic Mach number ( $M_{fms}$ ) and density compression ratio.
- A weak anti-correlation exists between $E_t$ and the $\lambda$ -angle, suggesting higher transition energies are associated with connections closer to the apex (smaller $\lambda$ ).
Spectral Hardening:
- The observed progressive hardening of the SEP energy spectrum (delayed arrival of high-energy particles) is consistent with the time-dependent Diffusive Shock Acceleration (DSA) process occurring as the connected shock region strengthens from sub-critical to super-critical.

5. Significance

This study provides a unified physical explanation for the formation of IVA-SEP signatures, resolving the debate between source effects and propagation effects:

Mechanism of IVA: The "nose-like" signature is driven by the spatial and temporal evolution of the shock. Observers initially connect to weak flank regions where acceleration is inefficient (producing lower-energy particles first). As the shock expands and the magnetic footpoint shifts toward stronger regions (closer to the apex), the acceleration efficiency increases, allowing higher-energy particles to be accelerated and arrive later.
Role of DSA: The results strongly support time-dependent Diffusive Shock Acceleration as the primary mechanism. The delay in high-energy particle arrival is a direct consequence of the time required for the shock to strengthen at the specific magnetic field line connected to the observer.
Predictive Capability: The findings suggest that the occurrence of IVA events is spatially dependent (favoring western connections) and dynamically dependent on the shock's evolution. This improves the ability to predict SEP spectral profiles based on CME kinematics and magnetic topology.
Future Implications: The study underscores the necessity of combining multi-point observations with 3D MHD modeling to disentangle the complex interplay between shock dynamics, magnetic connectivity, and particle transport in the heliosphere.

In conclusion, the paper establishes that IVA-SEP events are not anomalies but natural outcomes of evolving CME-driven shocks interacting with the Parker spiral magnetic field, where the observer samples a shock front that is strengthening over time.