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

TL;DR

Li et al. develop a multi-scale magnetic-field framework for the solar atmosphere that combines network-field/flux tubes, intergranular sheets, and Alfvén-wave turbulence to model GeV–TeV gamma-ray emission produced by hadronic GCRs. By simulating GCR propagation along seven open field lines with a magnetostatic background augmented by RMHD turbulence, they reproduce the observed spectral slope across $1~ ext{GeV}$ to $1~ ext{TeV}$ and demonstrate that the emission is shaped by filamentary structures and Alfvénic scattering, with turbulence primarily suppressing the $<100$ GeV flux. The work provides a new theoretical framework for using solar-disk gamma rays to probe hadronic GCR transport in the lower solar atmosphere and identifies key limitations, including flux underestimation and the need for coupled-field turbulence to explain TeV-time variability and solar-cycle modulation. This model advances the link between solar magnetic structuring and high-energy emission, offering pathways to refine hadronic interaction inputs and to test GCR transport in the inner heliosphere.

Abstract

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 1~GeV 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.

Figures (16)

• Figure 1: Schematic (not to scale) illustrating open magnetic network structure and Alfvén wave turbulence. (a) and (b) are partially inspired by figures in 2011ApJ...736....3V, 2005ApJS..156..265C. (c) is inspired by 2009SSRv..144..317W. Panels (a)--(c) depict progressively larger viewing areas. (a) A flux tube emerges from the photosphere, with kilo-Gauss vertical magnetic fields at the footpoint (gray patch). Convective motions from granules (red arrows) in the uppermost convection zone and photosphere jostle the flux tubes, launching Alfvén waves upward. (b) Individual flux tubes expand laterally with increasing height. At heights of 600--800 km, a bundle of tubes merge to form a network element. (c) Formed by field lines (solid lines) from network elements, a magnetic network further expands laterally with height and merges with adjacent networks. Portions of the Alfvén waves launched from the footpoints transmit (T) through this height range, while others are reflected (R). These counter-propagating Alfvén waves generate an energy cascade. The outer edge of each network is a canopy that separates the magnetic network from the weak-field sub-canopy domain. The internetwork region, located between network elements, contains closed magnetic loops ("small-scale canopies") that enclose the granules.
• Figure 2: (a) Stereo-A HI image (195 Å) of an active region close to the equator and to the East limb observed on 2007 December 09 at 06:35:30 UT. Seven open network field lines (F1 to F7) are randomly selected using the potential field extrapolation. Different colors are chosen to aid visualization. Positive and negative polarities are indicated by red and green, respectively. (b) SOHO/MDI magnetogram observed on 2007 December 09 at 06:23:30 UT. White and black represent positive and negative polarities, respectively. The line colors in both panels are chosen solely for visual clarity and do not carry any physical or categorical meaning.
• Figure 3: Background magnetic field strength $B_0$ for the seven magnetic network field lines calculated from the 3D MHD model.
• Figure 4: Magnetic power spectra (top row) and magnetic fluctuation amplitude (bottom row) within Network F2 case, shown for three $\Delta v_\mathrm{rms}$ conditions.
• Figure 5: Solar atmosphere profiles used in this work.