Convection-Driven Multi-Scale Magnetic Fields Determine the Observed Solar-Disk Gamma Rays

The solar disk is a continuous source of GeV–TeV gamma rays. The emission is thought to originate from hadronic Galactic cosmic rays (GCRs) interacting with the gas in the photosphere and uppermost convection zone after being reflected by solar magnetic fields. Despite this general understanding, existing theoretical models have yet to match observational data. At the photosphere and the uppermost convection zone, granular convection drives a multi-scale magnetic field, forming a larger-scale filamentary structure while also generating turbulence-scale Alfvén wave turbulence. Here, we demonstrate that the larger-scale filamentary field shapes the overall gamma-ray emission spectrum, and the Alfvén wave turbulence is critical for further suppressing the gamma-ray emission spectrum below $\sim 100$GeV. For a standard Alfvén wave turbulence level, our model’s predicted spectrum slope from 1GeV to 1~TeV is in excellent agreement with observations from Fermi-LAT and HAWC, an important achievement. The predicted absolute flux is a factor of 2–5 lower than the observed data; we outline future directions to resolve this discrepancy. The key contribution of our work is providing a new theoretical framework for using solar disk gamma-ray observations to probe hadronic GCR transport in the lower solar atmosphere.

💡 Research Summary

The paper tackles the long‑standing puzzle of the Sun’s steady GeV–TeV gamma‑ray emission from the solar disk. While it is widely accepted that Galactic cosmic rays (GCRs) – primarily protons and helium nuclei – penetrate the low solar atmosphere, interact with dense gas, and produce neutral pions that decay into gamma rays, existing models have struggled to reproduce the observed spectral shape, absolute flux, and the anti‑correlation with the solar cycle. The authors argue that the key missing ingredient is a realistic, multi‑scale description of the magnetic environment in the photosphere and the uppermost convection zone, where granular convection simultaneously creates large‑scale filamentary structures and drives Alfvén‑wave turbulence on much smaller scales.

The study builds on a previous “Paper I” that modeled only the small‑scale filamentary flux tubes and sheets. Here the authors extend the magnetic model to three components: (1) a network‑scale magnetic field that spans from roughly 700 km above the photosphere up into the corona, with horizontal extents of a few megameters; (2) the small‑scale filamentary fields (few hundred kilometers) generated by flux expulsion at granule edges; and (3) Alfvén‑wave turbulence generated by counter‑propagating waves launched by granular motions. The turbulence cascade is modeled using reduced magnetohydrodynamics (RMHD) on seven open field lines, while the mean field geometry is obtained from quasi‑linear Grad‑Shafranov solutions, yielding an “inverted wine‑bottle” shape where magnetic flux tubes narrow at low heights and fan out higher up.

To assess the impact on GCR transport, the authors perform full three‑dimensional test‑particle simulations that include the Lorentz force, pitch‑angle scattering from the turbulent component, and realistic energy‑dependent hadronic cross sections (σ_pp ≈ 3 × 10⁻²⁶ cm²). They adopt the Kafexhiu et al. (2014) gamma‑ray production model, allowing predictions down to 0.1 GeV. By varying the turbulence amplitude δB/B₀ (0.1, 0.3, 1.0) they find that a standard turbulence level (δB/B₀ ≈ 0.3) reproduces the observed spectral slope remarkably well: from 1 GeV to ~100 GeV the model yields dNγ/dEγ ∝ E⁻²·⁴, and from 100 GeV to 1 TeV it steepens to ≈ E⁻³·¹, matching the combined Fermi‑LAT and HAWC measurements (Fermi‑LAT reports ≈ E⁻²·², HAWC ≈ E⁻³·⁰). The filamentary network provides the primary magnetic mirroring that confines GCRs near the interaction layer (z ≈ ‑100 km to +400 km), while the Alfvén turbulence suppresses low‑energy gamma rays by increasing pitch‑angle diffusion and reducing the probability of deep penetration.

Despite the success in reproducing the spectral shape, the absolute gamma‑ray flux remains a factor of 2–5 below observations. The authors discuss several plausible reasons: (i) the model does not yet incorporate the solar‑cycle‑dependent strengthening of large‑scale fields, which could enhance mirroring during solar minimum; (ii) additional turbulence in the chromosphere and low corona (above 5 Mm) may further scatter GCRs; (iii) spatial variations in the local interstellar GCR spectrum are not accounted for. They propose future work that couples high‑resolution magnetograms (e.g., DKIST, Solar Orbiter) with the multi‑scale framework, includes electron‑proton mixed composition effects, and explores direct measurements of Alfvén turbulence levels.

In summary, the paper presents a comprehensive, physics‑based model that unifies filamentary magnetic structures and Alfvén‑wave turbulence to explain the solar‑disk gamma‑ray emission. It demonstrates that the observed hard spectrum arises from the interplay of large‑scale magnetic mirroring and small‑scale turbulent scattering, and it opens a new avenue for using solar gamma rays as a probe of GCR transport and the fine‑scale magnetic topology of the Sun’s lower atmosphere.