Quantifying the Effects of Parameters in Widespread SEP Events with EPREM

This study utilizes the uncoupled Energetic Particle Radiation Environment Model (EPREM) to systematically analyze how variations in physical parameters, such as diffusion and shock profile, influence the morphology and longitudinal spread of simulated widespread solar energetic particle events, revealing conditions under which flux may diminish at large longitudinal distances from the shock origin.

The Gist

Imagine the Sun is a massive, active lighthouse in the middle of a dark ocean. Sometimes, it sneezes out a giant cloud of energetic particles (like protons) that race through space. These are called Solar Energetic Particles (SEPs).

For a long time, scientists thought these sneezes were like a flashlight beam: if you were standing in the beam, you got blasted; if you were to the side, you were safe. But recently, we've discovered that sometimes, these sneezes are more like a giant, expanding fog that covers the entire solar system, hitting spaceships on opposite sides of the Sun at the same time. This is called a "widespread SEP event."

This paper is like a virtual weather lab where scientists built a computer simulation to figure out why this fog spreads so far and what changes the weather.

The Virtual Lab: EPREM

The scientists used a tool called EPREM. Think of EPREM as a super-advanced video game engine for space weather. Instead of playing a game, it solves complex math equations to track how billions of tiny particles move through the solar wind (the "wind" blowing from the Sun).

Usually, this tool needs a massive, complex 3D map of the Sun's magnetic field to work. But for this experiment, the scientists simplified things. They created a "toy model" of a shockwave (the leading edge of the solar sneeze) that moves outward like a perfect cone. They then ran 8 different simulations to see how changing the "rules" of the game changed the outcome.

The 8 Experiments: Tweaking the Dials

The scientists took their "baseline" simulation (the standard setting) and tweaked one specific "dial" in seven other versions. Here is what they tested, using everyday analogies:

1. The "Cross-Wind" Test (Perpendicular Diffusion)

• The Concept: Imagine particles are cars driving on a highway (magnetic field lines). Usually, they stay in their lane. But sometimes, they drift sideways into other lanes.
• The Experiment: They turned off the "drifting" ability.
• The Result: Without drifting, the "fog" stayed tightly packed in the highway lane. Spaceships far away from the shockwave (90 degrees or more) saw almost nothing. This proved that sideways drifting is the main reason the fog spreads so wide to hit ships on the other side of the Sun.

2. The "Road Condition" Test (Mean Free Path)

• The Concept: Imagine the space between particles is like a road. A "short mean free path" is a road full of potholes and traffic jams (particles bump into things often). A "long mean free path" is a smooth, empty highway.
• The Experiment: They made the road smoother (longer mean free path) and also changed how bumpy the road gets as you get farther from the Sun.
• The Result:
  • Smoother roads: Particles escaped the acceleration zone faster but with less energy. It was like a sprinter who runs out of the gate too quickly and gets tired before finishing the race.
  • Bumpier roads (near the Sun): Particles got stuck in the acceleration zone longer, getting super-charged (high energy) before escaping. This created a "sweet spot" for high-energy particles but fewer low-energy ones.

3. The "Shockwave Strength" Test (Shock Profile)

• The Concept: Imagine a shockwave is a wall. A "hard" shock is a brick wall; a "soft" shock is a thick curtain.
• The Experiment: They turned the brick wall into a curtain (a gradual, soft shock).
• The Result: The curtain didn't push the particles as hard. The result was a much weaker "fog." The high-energy particles barely made it out, and the widespread event almost disappeared. This tells us that strong, sharp shockwaves are needed to create the massive, widespread events we see in real life.

What Did They Learn?

By comparing these 8 simulations, the scientists learned that the "widespread" nature of these solar events isn't magic; it's physics.

1. Sideways Drifting is Key: If particles couldn't drift sideways across magnetic field lines, the "fog" would never reach the other side of the Sun.
2. The Shape of the Shock Matters: A gentle, gradual shockwave creates a weak event. A sharp, sudden shockwave creates a powerful, widespread event.
3. The "Road" Changes Everything: How easily particles move through space (the mean free path) determines whether we get a flood of low-energy particles or a few super-fast, high-energy ones.

Why Does This Matter?

This isn't just about math. It's about safety.

• Astronauts: If we are sending people to Mars, we need to know if a solar sneeze will hit them. If the "fog" spreads widely, astronauts on the far side of the Sun aren't safe just because they are "behind" the Sun.
• Satellites: High-energy particles can fry electronics. Knowing how these events spread helps engineers build better shields.

In short: The scientists built a virtual solar system, turned the dials on the physics, and discovered that sideways drifting and strong shockwaves are the secret ingredients that turn a local solar sneeze into a system-wide storm. This helps us predict when and where the next "solar storm" will hit, keeping our technology and future astronauts safe.

Technical Summary

1. Problem Statement

Solar Energetic Particle (SEP) events pose significant radiation hazards to astronauts and spacecraft electronics. A specific class of events, known as "widespread SEP events," involves particles being observed by multiple spacecraft separated by large longitudinal distances (sometimes >90° or even 360°) from the source.

• The Challenge: The physical mechanisms driving this extreme longitudinal spread are not fully understood. Observations often show particle onset times and flux profiles that do not correlate simply with magnetic connectivity to the Coronal Mass Ejection (CME)-driven shock.
• The Gap: While models exist, there is a need to isolate and quantify how specific physical parameters (diffusion coefficients, mean free paths, shock profiles) influence the morphology of these widespread events, particularly in the absence of complex Magnetohydrodynamic (MHD) coupling.

2. Methodology

The authors utilized the Energetic Particle Radiation Environment Model (EPREM), a code that solves the focused transport equation (FTE) on a Lagrangian grid co-moving with the solar wind.

• Simulation Mode: The study used an "uncoupled" version of EPREM (v0.14.0). Instead of ingesting data from a complex external MHD model (like BATS-R-US or Enlil), EPREM internally generated an idealized cone-shock propagating radially through a homogeneous background solar wind.
• Experimental Design:
  • Baseline Run: A reference simulation using a set of physically motivated parameters.
  • Variations: Seven additional simulation runs were performed, each altering a single parameter while keeping others fixed to the baseline.
• Key Parameters Varied:
  • Perpendicular Diffusion: Ratio of perpendicular to parallel diffusion coefficients ($\kappa_\perp/\kappa_\parallel$), set to 0 in one run.
  • Mean Free Path ($\lambda_\parallel$):
    • Reference value at 1 AU ($\lambda_{\parallel0}$).
    • Rigidity dependence power-law index ($\chi$).
    • Radial dependence power-law index ($\beta$).
    • Dependence on magnetic field strength ($|\vec{B}|$).
  • Shock Profile: The gradient of the shock front ($\Gamma_s$), varying from a sharp step function to a gradual transition.
• Observation Setup: 16 point observers were placed at radial distances of 0.5 AU and 1.0 AU, distributed azimuthally from $0^\circ$ (shock origin) to $\pm 90^\circ$ and $180^\circ$ relative to the shock.

3. Key Contributions

• Parameter Sensitivity Analysis: The study provides a systematic quantification of how individual physical parameters alter SEP flux profiles in widespread events, isolating variables that are often coupled in observational data.
• Validation of Diffusion Mechanisms: It explicitly demonstrates the distinct roles of parallel vs. perpendicular diffusion in populating magnetic field lines far from the shock origin.
• Model-Data Comparison: The authors compare their baseline simulation results against observational data from the April 17, 2021, widespread SEP event (involving BepiColombo, PSP, Solar Orbiter, and STEREO-A) to validate the model's ability to reproduce real-world flux profiles.
• Open Science: The authors made the analysis code, EPREM source code, and simulation input/output files publicly available, facilitating reproducibility and future community analysis.

4. Key Results

The simulations revealed complex flux profiles dependent on the interplay of diffusion, acceleration, and transport:

• Perpendicular Diffusion ($\kappa_\perp$):
  • Critical Role: It is the primary mechanism allowing particles to reach observers located $\ge 90^\circ$ from the shock origin.
  • Result: When $\kappa_\perp$ was set to zero, fluxes at $180^\circ$ and $90^\circ$ (especially for high-energy protons) dropped to negligible levels. High-energy particles ($>50$ MeV) at $+90^\circ$ were almost entirely sustained by perpendicular diffusion.
• Mean Free Path ($\lambda_\parallel$):
  • Reference Value ($\lambda_{\parallel0}$): Increasing the reference mean free path allowed protons to escape acceleration regions earlier with lower energies, resulting in earlier arrival times but lower peak fluxes for high-energy particles.
  • Magnetic Field Dependence ($\beta$):
    • High $\beta$ (strong inverse dependence on $|\vec{B}|$): Protons in regions of high magnetic field (near the shock) had shorter mean free paths, allowing for greater acceleration before escape. This increased high-energy flux ($>50$ MeV) but reduced low-energy flux.
    • Low $\beta$: Allowed protons to escape earlier with lower energies, increasing low-energy flux but reducing high-energy flux.
  • Rigidity Dependence ($\chi$): Higher rigidity dependence shifted the energy spectrum, generally reducing flux at lower energies and increasing it at higher energies.
• Shock Profile ($\Gamma_s$):
  • Softer Shock: Reducing the shock gradient (making it more gradual) significantly reduced fluxes across all energies, particularly for high-energy protons ($>50$ MeV). This was attributed to a reduced effective compression ratio experienced by particles crossing the shock.
• Longitudinal Spread:
  • All simulations showed significant longitudinal spread, but the magnitude and energy dependence of this spread were highly sensitive to the parameters.
  • Observers on the "eastern" flank (connected to the shock origin via the Parker spiral) generally saw more impulsive, connected profiles, while "western" flank observers saw more gradual profiles sustained by diffusion.

5. Significance and Implications

• Understanding Widespread Events: The study confirms that widespread SEP events are not solely a result of the shock geometry but are heavily dependent on the state of the solar wind (turbulence, magnetic field strength) and the diffusion properties of the particles.
• Predictive Capability: By tuning parameters like $\lambda_\parallel$ and $\kappa_\perp$, the model can be adjusted to match specific observational events, aiding in the prediction of radiation hazards for future missions (e.g., Artemis, Mars missions).
• Model Limitations & Future Work: The authors note that the idealized cone shock lacks the deceleration dynamics of real CMEs and does not model flux ropes or cavities. Future versions of EPREM will incorporate one-way coupling to external MHD models to capture these realistic dynamics.
• Scientific Insight: The results suggest that the "morphology" of an observed SEP event (e.g., impulsive vs. gradual, high vs. low energy dominance) serves as a diagnostic tool for inferring the physical state of the interplanetary medium through which the CME propagated.

In conclusion, this paper establishes a foundational framework for using EPREM to deconstruct the physics of widespread SEP events, demonstrating that accurate modeling requires precise constraints on diffusion coefficients and shock profiles to explain the complex flux variations observed by multi-spacecraft constellations.