3D Radiative MHD Modeling of Particle Beam Heating of the Solar Atmosphere

TL;DR

This study implements 3D radiative-MHD StellarBox simulations of electron-beam heating with $1\times10^{12}$ erg s$^{-1}$ cm$^{-2}$ flux and $E_C$ in the $10$–$25$ keV range, coupled to RH 1.5D NLTE synthesis of Fe I 6173 Å to compare with HMI white-light flare observations. The results show substantial upper-chromospheric heating and continuum enhancements up to a factor of $\sim 2.5$, driven by multiple shocks and chromospheric condensations, but the Fe I line core remains in absorption, indicating insufficient deep photospheric heating from these beams alone. Compared to 1D RADYN models, the 3D simulations exhibit more rapid heating, higher coronal temperatures ($\sim 1\times10^{7}$–$2\times10^{7}$ K), and faster post-impulsive cooling due to multidimensional transport and pre-existing structuring. The work suggests that deeper-penetrating particles (e.g., protons) or mixed electron-proton beams, along with cooler pre-flare atmospheres or umbral magnetic fields, may be required to reproduce the strongest WLF and helioseismic signatures observed, guiding future multi-component modeling efforts.

Abstract

While solar flares are primarily associated with enhanced ultraviolet and X-ray emission, a subset of flares exhibit significant continuum brightening in visible light and are classified as white-light flares (WLFs). Despite extensive observational and modeling efforts, the physical mechanisms responsible for the compact, short-lived photospheric brightenings in WLF kernels observed during the impulsive phase of solar flares remain uncertain. Thick-target electron-beam models typically deposit energy in the upper chromosphere, and their ability to reproduce the magnitude and spatial localization of photospheric continuum enhancements observed in white-light flare kernels remains an open question. To investigate the role of realistic atmospheric structuring and multidimensional transport in flare energy deposition, we perform three-dimensional radiative MHD simulations of electron-beam heating using the StellarBox code for beam fluxes of $10^{12}$ erg\,s$^{-1}$\,cm$^{-2}$ and low-energy cutoffs of 10--25\,keV. We then compute Fe\,I 6173\,Å~Stokes profiles using the RH 1.5D radiative transfer code for direct comparison with Helioseismic and Magnetic Imager (HMI) observations. The simulations produce strong upper-chromospheric heating, multiple shock fronts, and continuum enhancements up to a factor of 2.5 relative to pre-flare levels, comparable to continuum enhancements observed during strong X-class white-light flares. Comparison with one-dimensional RADYN simulations highlights the influence of fine-scale structuring on flare dynamics and continuum emission that arises in three-dimensional geometry.

Figures (11)

• Figure 1: Vertical x-z slices of $\log_{10}(T)$ for the B1 model for the $E_C$ = 10, 15, 20, and 25 keV beams at t = 14 s.
• Figure 2: Vertical x-z slices of $\log_{10}(\rho)$ for the B1 model for the $E_C$ = 10, 15, 20, and 25 keV beams at t = 14 s.
• Figure 3: Horizontal x-y slices at z = 10.00 Mm for $\log_{10}(\rho)$, $\log_{10}(P)$, $\log_{10}(T)$, and $v_r$ for the B1 model for the $E_C$ = 10 and 25 keV beams at t = 20 s.
• Figure 4: Time-distance plots of $\log_{10}(\rho)$ at z = 10.00 Mm for the B1 model for the $E_C$ = 10 and 25 keV beams. Distance is in the +x direction from the center of the beam impact.
• Figure 5: Time-distance plots of $v_r$ at z = 10.00 Mm for the B1 model for the $E_C$ = 10 and 25 keV beams. Distance is in the +x direction from the center of the beam impact.