Multi-spacecraft constraints on relativistic solar energetic particle transport in the widespread 28 October 2021 event

This study utilizes multi-spacecraft observations and numerical simulations to demonstrate that the widespread 28 October 2021 relativistic solar energetic particle event was governed by a narrow injection region coupled with efficient cross-field diffusion, resulting in parallel mean free paths within the Palmer consensus range and perpendicular mean free paths of approximately 1–10% of the parallel values.

The Gist

Here is an explanation of the paper, translated into everyday language with some creative analogies.

The Big Picture: A Solar "Super-Storm"

Imagine the Sun as a giant, chaotic factory. On October 28, 2021, this factory had a massive explosion (a solar flare) and shot out a huge cloud of gas (a coronal mass ejection). This event, known as GLE73, was so powerful that it accelerated particles (protons and electrons) to near the speed of light.

These particles didn't just stay near the Sun; they rained down on Earth and were detected by spacecraft scattered all over the solar system. The big mystery for scientists was: How did these particles spread out so widely and so quickly?

The Mystery: The "Impossible" Spread

Think of the solar system like a giant, invisible highway system made of magnetic lines (the "Parker Spiral"). Usually, particles travel like cars stuck in a single lane, following these magnetic lines from the Sun to Earth.

However, on this day, the particles were detected by spacecraft that were not on the same "lane" as the explosion.

• One spacecraft (STEREO-A) was right next to the "highway" leading from the explosion.
• Another (Solar Orbiter) was a bit further away.
• Earth was even further down a different lane.
• And incredibly, particles were even detected on Mars, which was on the opposite side of the Sun from the explosion!

If particles only followed the magnetic lanes, Mars should have been safe. But it wasn't. This meant the particles were somehow jumping lanes, crossing the "traffic" to get to places they shouldn't have been able to reach.

The Investigation: The Cosmic Detective Work

The scientists in this paper acted like detectives trying to solve a crime scene. They had three main questions:

1. How slippery is the road? (How easily do particles slide along the magnetic lines?)
2. How good are they at jumping lanes? (How easily do they cross from one magnetic line to another?)
3. How big was the explosion site? (Did the particles come out of a tiny pinhole or a wide-open door?)

To answer this, they used computer simulations. They built a virtual solar system and tried to "replay" the event millions of times, tweaking the rules until their virtual particles matched what the real spacecraft actually saw.

The Findings: What They Discovered

1. The "Lane Jumping" (Cross-Field Diffusion)

The scientists found that the particles were incredibly good at "lane jumping."

• The Analogy: Imagine a crowd of people running down a long hallway. Usually, they stay in their assigned row. But on this day, the crowd was so energetic and the hallway so turbulent that people were constantly bumping into each other and shuffling sideways into neighboring rows.
• The Result: The particles didn't just follow the magnetic lines; they diffused (spread out) sideways. For protons, they jumped about 5–10% of the distance they traveled forward. For electrons, it was a bit less (1–3%), but still significant enough to reach Mars.

2. The Size of the "Door" (Injection Region)

The scientists wanted to know if the explosion happened over a huge area of the Sun or a tiny spot.

• The Analogy: Imagine a sprinkler. If you turn on a wide sprinkler, water hits a large area immediately. If you use a tiny nozzle, the water hits a small spot, but if the wind is strong, it can still blow the mist far away.
• The Result: The "nozzle" was actually quite small (less than 20 degrees wide). The particles didn't start out spread across the whole Sun. Instead, they started in a tight, concentrated bundle. The reason they ended up everywhere was because of that "lane jumping" (diffusion) we mentioned earlier.

3. The Timing

The particles arrived at the different spacecraft at times that perfectly matched the explosion.

• The Analogy: It's like a starting gun firing. The runners (particles) left the starting line at the exact moment the gun went off.
• The Result: The particles were accelerated by the flare and the shockwave of the CME almost instantly. There was no long delay; they were launched and then immediately began their chaotic journey across the solar system.

Why This Matters

This study is like figuring out how a specific type of smoke spreads through a building.

• For Astronauts: If we know how these dangerous particles spread, we can better predict when they will hit a spaceship or a space station, keeping astronauts safe.
• For Technology: These particles can fry satellites and disrupt GPS. Knowing how they travel helps us protect our tech.
• For Science: It proves that the Sun's magnetic field is more "turbulent" and "messy" than we thought. It's not a set of straight, rigid rails; it's more like a swirling river where particles can drift sideways quite easily.

The Bottom Line

The October 28, 2021, solar storm was a massive event where particles were launched from a tiny, focused spot on the Sun. They managed to reach spacecraft all over the solar system (even Mars!) not because they started everywhere, but because the space between the Sun and the planets is full of magnetic turbulence that acts like a chaotic dance floor, allowing particles to jump lanes and spread out rapidly.

The scientists successfully recreated this "dance" on a computer, proving that a small explosion combined with a lot of sideways drifting explains the massive, widespread storm we observed.

Technical Summary

Here is a detailed technical summary of the paper "Multi-spacecraft constraints on relativistic solar energetic particle transport in the widespread 28 October 2021 event."

1. Problem Statement

Solar Energetic Particle (SEP) events, particularly those reaching relativistic energies (Ground Level Enhancements or GLEs), pose significant hazards to space infrastructure and human health. A major challenge in SEP physics is understanding how particles, accelerated in localized solar regions (flares/CMEs), spread across vast longitudinal distances (often >180°) in the heliosphere.

While standard models assume particles travel primarily along magnetic field lines (Parker spiral), widespread events suggest significant cross-field transport. Key open questions include:

• What are the magnitudes of parallel ($\lambda_{\parallel}$) and perpendicular ($\lambda_{\perp}$) mean free paths for both protons and electrons?
• Is the broad spatial distribution caused by a wide injection source (extended acceleration region) or efficient cross-field diffusion during transport?
• How do these transport parameters depend on particle rigidity?

This study focuses on the 28 October 2021 event (GLE73), a relativistic event where high-energy particles were detected by spacecraft at widely separated longitudes, including those magnetically disconnected from the source (e.g., Mars, Earth, Solar Orbiter, STEREO-A).

2. Methodology

The authors employed a multi-step inverse modeling approach combining observational data with numerical simulations:

• Data Sources: Multi-spacecraft observations from STEREO-A (STA), Solar Orbiter (SolO), Wind, SOHO, and GOES. Data included electron and proton fluxes across a wide energy range (electrons: 0.05–3.3 MeV; protons: 14.3–896 MeV) and pitch-angle distributions (PADs).
• 1D Focused Transport Modeling:
  • Used the 1D SEP-propagator model (van den Berg et al. 2020) to analyze the magnetically well-connected observer (STA).
  • Solved the Focused Transport Equation (FTE) to constrain the parallel mean free path ($\lambda_{\parallel}$), acceleration time ($t_a$), and escape time ($t_e$).
  • Assumed a time-dependent Reid–Axford injection profile and a Kolmogorov turbulence spectrum for pitch-angle scattering.
• 2D Cross-Field Diffusion Modeling:
  • Used the 2D SEP-propagator model (Strauss & Fichtner 2015) to simulate transport in the ecliptic plane (radial distance $r$ and heliographic longitude $\phi$).
  • Included cross-field diffusion via the Field Line Random Walk (FLRW) approximation, parameterized by the perpendicular mean free path ($\lambda_{\perp}$).
  • Modeled the injection source as a Gaussian distribution in longitude with a variable angular width ($\Delta\Phi$).
• Inverse Modeling Strategy:
  • Simulated flux profiles and anisotropies were compared against observations at all three observers (STA, SolO, Earth).
  • Parameters ($\lambda_{\parallel}$, $\lambda_{\perp}$, $\Delta\Phi$, injection time) were iteratively adjusted to minimize the difference between simulated and observed data (measured by $R^2$).
  • The study specifically tested the degeneracy between a "wide source + weak diffusion" scenario and a "narrow source + strong diffusion" scenario.

3. Key Contributions

• Rigidity-Dependent Transport Parameters: Provided simultaneous constraints on $\lambda_{\parallel}$ and $\lambda_{\perp}$ for both electrons and protons across a wide rigidity range (0.2 MV to 1.6 GV) for a single widespread event.
• Resolution of Injection vs. Transport Degeneracy: Demonstrated that the observed multi-spacecraft profiles for GLE73 cannot be reproduced by a wide injection source with weak diffusion. The data uniquely requires a narrow injection region coupled with significant cross-field diffusion.
• Validation of 2D Models: Showed that 2D finite-difference models can effectively reproduce complex multi-point observations, including onset delays and anisotropy evolution, without requiring full 3D drift simulations for this specific event geometry.

4. Key Results

A. Transport Parameters

• Parallel Mean Free Path ($\lambda_{\parallel}$):
  • Electrons: $\sim 0.07–0.18$ AU.
  • Protons: $\sim 0.25–0.38$ AU.
  • These values generally fall within or slightly above the Palmer consensus range (0.08–0.3 AU), though high-rigidity protons exceed the upper limit.
  • A rigidity dependence was observed where $\lambda_{\parallel}$ generally increases with rigidity for protons, while low-rigidity electrons showed a trend opposite to standard expectations (potentially due to specific turbulence damping effects).
• Perpendicular Mean Free Path ($\lambda_{\perp}$):
  • Electrons: $\sim 0.0013–0.0036$ AU ($\sim 1–3\%$ of $\lambda_{\parallel}$).
  • Protons: $\sim 0.012–0.025$ AU ($\sim 5–10\%$ of $\lambda_{\parallel}$).
  • The ratio $\lambda_{\perp}/\lambda_{\parallel}$ increases slightly with rigidity, suggesting higher-energy particles diffuse more efficiently across field lines.

B. Injection Region Characteristics

• Size ($\Delta\Phi$): The injection region is relatively narrow, estimated at $\le 20^{\circ}$.
• Rigidity Dependence: The injection size decreases with increasing rigidity, converging to $\sim 5^{\circ}$ for the highest energy particles. This contradicts models suggesting a broad (e.g., $60^{\circ}$) shock acceleration region for the highest energies.
• Timing:
  • Electron release: $\sim 15:20$ UT.
  • Proton release: $\sim 15:27$ UT.
  • These align well with the parent X1.0 flare start (15:17 UT) and CME onset (15:25 UT), supporting a compact acceleration region near the flare site.

C. Anisotropy and Onset

• Anisotropy: High initial anisotropies were observed at well-connected locations (STA), decaying to isotropy within $\sim 3$ hours, consistent with pitch-angle scattering.
• Onset Delays: The model successfully reproduced the onset delays at magnetically disconnected observers (SolO, Earth) using the derived $\lambda_{\perp}$ values, confirming that cross-field diffusion is the dominant mechanism for spreading particles to these locations.

5. Significance and Implications

• Mechanism of Widespread Events: The study provides strong evidence that the broad longitudinal spread of SEPs in GLE73 is driven primarily by interplanetary cross-field diffusion rather than an extended coronal acceleration source. This supports the "compact source + efficient transport" paradigm.
• Modeling Constraints: The results highlight that assuming a wide injection source is insufficient to explain the specific time profiles and anisotropies observed in this event. Future models must prioritize accurate cross-field diffusion coefficients.
• Space Weather Forecasting: Understanding the specific $\lambda_{\perp}/\lambda_{\parallel}$ ratios and injection sizes improves the ability to forecast SEP arrival times and intensities at spacecraft with poor magnetic connectivity to the Sun.
• Future Directions: The authors note limitations regarding the 2D equatorial assumption (ignoring latitudinal drifts across the Heliospheric Current Sheet) and the need for better high-energy proton data from multiple spacecraft to refine transport models for the most hazardous radiation levels.

In conclusion, the paper establishes that the 28 October 2021 event was governed by a localized acceleration region and significant perpendicular diffusion, offering a refined physical picture of how relativistic particles traverse the heliosphere.