🔭 astrophysics

The impact of Solar magnetic field configurations on the production of gamma rays at the Solar disk

This study utilizes the CRPropa framework with realistic magnetic field configurations to model solar gamma-ray and neutrino production from Galactic cosmic rays, revealing that magnetic mirroring and field topology significantly influence emission characteristics and predicting a slightly higher flux at solar minimum, though simulated values remain below current observations.

Original authors: Julien Dörner, Frederic Effenberger, Horst Fichtner, Julia Becker Tjus, Meng Jin, Wei Liu, Vahe' Petrosian

Published 2026-03-19

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Julien Dörner, Frederic Effenberger, Horst Fichtner, Julia Becker Tjus, Meng Jin, Wei Liu, Vahe' Petrosian

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 not just as a blazing ball of fire, but as a massive, invisible magnetic maze.

For decades, astronomers have known that the Sun acts like a cosmic "lightbulb," glowing faintly in high-energy gamma rays. This light isn't coming from the Sun's own nuclear furnace; it's actually a byproduct of Galactic Cosmic Rays (GCRs)—high-speed particles from deep space crashing into the Sun's atmosphere.

Think of these cosmic rays as billiard balls zooming through space. When they hit the "cushions" of the Sun's atmosphere (the gas and plasma), they smash into atoms and create a shower of new particles, including gamma rays (the light we see) and neutrinos (ghostly particles that pass right through everything).

The Mystery

Here's the problem: When scientists first tried to calculate how bright this "Sun-light" should be, their math predicted a very dim glow. But when telescopes like Fermi-LAT and HAWC looked at the Sun, they saw a glow six times brighter than expected.

Even stranger, the brightness changes over time. It gets brighter when the Sun is "sleepy" (solar minimum) and dimmer when the Sun is "active" and stormy (solar maximum). This didn't make sense with the old models. It suggested that the Sun's magnetic field was doing something tricky to the incoming cosmic rays, acting like a traffic cop or a funhouse mirror.

The New Study: Mapping the Maze

In this paper, the authors (a team of physicists from Germany, Sweden, and the US) decided to build a super-computer simulation to solve this mystery. They used a tool called CRPropa to track billions of these "billiard balls" as they tried to navigate the Sun's magnetic maze.

They tested two main types of magnetic maps:

The "Simple" Map (DQCS): A smooth, organized magnetic field, like a neat grid of lanes. This represents the Sun when it's quiet.
The "Real" Map (PFSS): A messy, chaotic field based on actual data from the Sun during both its quiet and stormy phases. This is like a grid where lanes are constantly shifting, merging, and twisting.

What They Discovered

The simulation revealed that the Sun's magnetic field acts like a giant mirror and a trap.

The Mirror Effect (Magnetic Mirroring): As a cosmic ray dives toward the Sun, the magnetic field gets stronger. If the particle is coming in at the wrong angle, the field acts like a mirror, bouncing it back before it ever hits the atmosphere.
- The Analogy: Imagine trying to run down a hallway that gets narrower and narrower. If you run straight, you might get stuck. But if you run at a slight angle, the walls might bounce you back out before you reach the end.
The Trap: When the magnetic field is organized (during solar minimum), it creates "loops" that trap particles, keeping them bouncing around in the lower atmosphere for longer. The longer they bounce, the more likely they are to crash into an atom and create gamma rays.
The Chaos: During solar maximum, the magnetic field is a tangled mess. It's harder for particles to get trapped in neat loops, so they either bounce back too early or crash through without interacting as much. This explains why the gamma-ray glow is actually fainter during stormy times.

The "Missing" Light

Even with this new, sophisticated map of the magnetic maze, the authors' simulation still predicted a glow that was about 10 times dimmer than what telescopes actually see.

So, what's missing? The authors suggest three "secret ingredients" that could boost the brightness to match reality:

Heavier Particles: They only simulated protons (hydrogen nuclei). But cosmic rays also include heavier stuff like carbon and iron. These are like bowling balls compared to the billiard balls; they create bigger splashes (more gamma rays) when they hit.
The Parker Spiral: The magnetic field between the Earth and the Sun isn't perfectly straight; it's a spiral. This might steer more particles toward the Sun than the simulation assumed.
Denser Atmosphere: The Sun's atmosphere might be denser in specific spots than the simple model assumed, giving the particles more "targets" to hit.

The Ghostly Sidekick: Neutrinos

The paper also looked at neutrinos. Every time a cosmic ray makes a gamma ray, it usually makes a neutrino too. But while gamma rays get absorbed by the Sun (like light hitting a wall), neutrinos are ghosts. They can pass right through the Sun and escape.

The authors calculated how many of these ghostly neutrinos should be reaching Earth. They found that the number is just below what the IceCube telescope (a giant detector buried in Antarctic ice) can currently see. This suggests that with a little more data or a slightly more sensitive detector, we might soon "see" the Sun in neutrinos for the first time!

The Bottom Line

This paper is a major step forward. It proves that the Sun's magnetic field is the conductor of the orchestra, dictating where and how bright the gamma-ray light shines. While we still need to find the missing ingredients to match the exact brightness, we now have a much better map of the magnetic maze that guides these cosmic rays.

In short: The Sun isn't just a passive target; its magnetic field actively shepherds cosmic rays, trapping some to create a bright glow and bouncing others away. It's a cosmic game of pinball, and we are finally learning the rules.

1. Problem Statement

The Sun emits a steady flux of high-energy gamma rays resulting from the interaction of Galactic Cosmic Rays (GCRs) with the solar atmosphere. However, observations by Fermi-LAT and HAWC have revealed a gamma-ray flux significantly higher (by a factor of 6–10) than early theoretical predictions (e.g., Seckel et al. 1991). Furthermore, observations show unexpected temporal variations (anti-correlated with solar activity), spectral features (a dip at 30–50 GeV and a steepening above 500 GeV), and spatial anisotropies (enhanced polar and equatorial components).

Previous models attempting to explain these discrepancies have either:

Assumed spherically symmetric atmospheres, ignoring large-scale coronal magnetic fields.
Focused only on small-scale turbulent structures without global context.
Failed to account for the complex topology of the solar magnetic field (dipole, quadrupole, current sheets) and its evolution over the solar cycle.

The core problem is to quantify how large-scale solar magnetic field configurations influence the trajectories of GCRs, their trapping efficiency, and the resulting spatial and spectral distribution of gamma rays, to explain the gap between simulation and observation.

2. Methodology

The authors utilized the CRPropa 3.2 framework to simulate the propagation and interaction of charged particles in magnetic fields.

Simulation Setup:
- Volume: Defined between the solar surface ( $r = 1 R_\odot$ ) and a source surface ( $r = 2.5 R_\odot$ ).
- Particles: Primary GCR protons injected isotropically at the outer boundary.
- Interactions: Hadronic interactions ( $p + p \to \pi^0 \to \gamma\gamma$ ) modeled using the Kafexhiu et al. (2014) cross-section and Orusa et al. (2022, 2023) differential cross-sections. Secondary particles are treated as catastrophic losses.
- Atmosphere: A chromospheric density profile (Avrett & Loeser 2008) extended to the source surface using a radial slope from Kontar et al. (2019).
Magnetic Field Configurations:
- Baseline Model: A Dipole + Quadrupole + Current Sheet (DQCS) model (Banaszkiewicz et al. 1998), representing a simplified, ordered field.
- Realistic Models: Potential Field Source Surface (PFSS) extrapolations derived from Helioseismic and Magnetic Imager (HMI) synoptic maps for specific Carrington Rotations (CR):
  - CR 2224: Solar Minimum (ordered field).
  - CR 2154 & 2157: Solar Maximum (chaotic, active field).
Injection Spectra:
- Mono-energetic: $E = 1, 100, 10^4$ GeV to isolate energy-dependent transport effects.
- Realistic: A power-law spectrum reweighted to match the Local Interstellar Spectrum (LIS) from 1 GeV to 1 PeV.
Filtering:
- Gamma rays were categorized into three datasets based on their trajectory relative to the Sun: Outgoing (reflected by magnetic mirroring), Passing (produced far enough from the surface to escape without hitting the disk), and All (total production).

3. Key Contributions

First Production Maps: The paper presents the first spatial maps of gamma-ray production locations on the solar surface, resolved by magnetic field configuration and energy.
Global Magnetic Topology: It demonstrates that large-scale field structures (dipole/quadrupole/current sheets) and their evolution over the solar cycle are critical determinants of gamma-ray yield and morphology, not just small-scale turbulence.
Neutrino Estimation: The study provides the first estimate of the expected high-energy neutrino flux from the Sun based on these gamma-ray production models, comparing it to IceCube limits.
Quantification of Discrepancies: It systematically quantifies how magnetic mirroring and field topology affect the spectral shape and flux normalization, identifying specific mechanisms (e.g., pitch-angle dependence) that reduce the flux in simulations compared to observations.

4. Key Results

A. Magnetic Mirroring and Trapping

Energy Dependence: Low-energy GCRs ( $< 100$ GeV) are efficiently trapped in closed magnetic loops, increasing their column density and interaction probability. High-energy GCRs ( $> 1$ TeV) have large gyroradii, averaging over field structures and penetrating deeper or escaping more easily.
Pitch Angle: Magnetic mirroring preferentially selects forward-directed particles. Particles with perpendicular pitch angles are mirrored before reaching the dense chromosphere, suppressing gamma-ray production. This effect is more pronounced in ordered fields (Solar Minimum/DQCS).

B. Spatial Distribution

Solar Minimum (Ordered Fields): Gamma-ray production is concentrated at the poles (open field lines connecting to the interplanetary medium) and specific latitudinal bands (e.g., $|b| \approx 15^\circ$ in DQCS due to quadrupole loops).
Solar Maximum (Chaotic Fields): Production becomes more filamentary and localized. Active regions appear as "voids" in gamma-ray production because strong magnetic fields push mirroring points to higher, less dense atmospheric layers.
High Energy: At TeV energies, the distribution becomes more homogeneous as GCRs can traverse complex field lines to reach the surface almost anywhere.

C. Spectral Properties

Spectral Breaks: The "outgoing" selection (requiring mirroring) shows a spectral break around 10 GeV and a steepening above 300–500 GeV, consistent with observations.
Flux Normalization: The simulated baseline flux is 1–2 orders of magnitude lower than Fermi-LAT and HAWC observations.
- Solar Minimum simulations predict slightly higher fluxes than Solar Maximum due to more efficient trapping in ordered fields.
- The spectral slope for "all" gamma rays follows the injected proton spectrum, while "outgoing" gamma rays show a harder spectrum below the break.

D. Neutrino Flux

Using the delta-approximation, the authors estimate the neutrino flux.
The total flux is dominated by "behind-the-limb" events (neutrinos produced toward the Sun that traverse the solar interior).
The predicted flux is roughly 5 times lower than current IceCube upper limits, suggesting that a detection is plausible with future data and detector upgrades (IceCube-Gen2).

5. Significance and Future Outlook

Explaining the Flux Gap: While the baseline model underpredicts the flux, the authors identify three mechanisms that could bridge the gap:
1. Heavier Nuclei: Including He, C, and Fe in GCRs could increase flux by a factor of ~2.
2. Parker Field Mirroring: Pre-mirroring in the heliosphere (between Earth and Sun) could alter the pitch-angle distribution, increasing the flux by up to a factor of 2.
3. 3D Density Coupling: Realistic 3D MHD models coupling magnetic topology with gas density could yield higher local densities, increasing interaction rates by a factor of 3 or more.
Multi-Messenger Astronomy: The study establishes a robust link between solar magnetic topology, gamma-ray morphology, and neutrino production.
Future Work: The authors call for multi-scale models combining global PFSS fields with small-scale turbulent structures and 3D MHD density profiles. They also highlight the need for higher angular resolution observations to distinguish between polar and equatorial production mechanisms.

In conclusion, this work confirms that the solar magnetic field is the primary regulator of the solar gamma-ray signal, dictating where and when GCRs interact with the atmosphere. While current models capture the qualitative features (spectral breaks, spatial anisotropy), quantitative agreement with observations requires incorporating heavier nuclei, heliospheric transport effects, and realistic 3D atmospheric densities.