Spectral and Imaging Diagnostics of Spatially Extended Turbulent Electron Acceleration and Transport in Solar Flares

Abstract

Solar flares are efficient particle accelerators with a large fraction of released magnetic energy (10%–50%) converted into energetic particles such as hard X-ray producing electrons. This energy transfer process is not well constrained, with competing theories regarding the acceleration mechanism(s), including MHD turbulence. We perform a detailed parameter study examining how various properties of the acceleration region, including its spatial extent and the spatial distribution of turbulence, affect the observed electron properties, such as those routinely determined from X-ray imaging and spectroscopy. Here, a time-independent Fokker–Planck equation is used to describe the acceleration and transport of flare electrons through a coronal plasma of finite temperature. Motivated by recent nonthermal line broadening observations that suggested extended regions of turbulence in coronal loops, an extended turbulent acceleration region is incorporated into the model. We produce outputs for the density-weighted electron flux, a quantity directly related to observed X-rays, modeled in energy and space from the corona to chromosphere. We find that by combining several spectral and imaging diagnostics (such as spectral index differences or ratios, energy or spatial-dependent flux ratios, and electron depths into the chromosphere) the acceleration properties, including the timescale and velocity dependence, can be constrained alongside the spatial properties. Our diagnostics provide a foundation for constraining the properties of acceleration in an individual flare from X-ray imaging spectroscopy alone, and can be applied to past, current, and future observations including those from RHESSI and Solar Orbiter.

The Efficiency of Electron Acceleration during the Impulsive Phase of a Solar Flare

“…Equation (3)) depends rather sensitively on the the values of both E o and δ, it is possible that a much lower value of n nth , comparable with that deduced from HXR and EUV observations, is also consistent with the observed microwave emission. Interestingly, the selfconsistent simulations of electron acceleration during magnetic reconnection in a macroscale system (Arnold et al 2021), as well as spatially extended turbulent electron acceleration (Stores et al 2023), also suggest that the instantaneous number density of nonthermal electrons remains small.…”

Exploring the Origin of Solar Energetic Electrons. I. Constraining the Properties of the Acceleration Region Plasma Environment

“…power law) is injected and transported through a hot over-dense region. Paper II will perform more realistic simulation where electrons are accelerated out of different thermal plasma using a turbulent diffusion model (similar to Stores et al 2023), with the resulting shape of the spectra also dependent on the plasma properties of the acceleration region, and producing a smoother spectral transition from thermal to nonthermal if this region exists within the 1-20 keV data. As mentioned, we purposely used higher temperatures and higher densities akin to hot flaring loops to show the types of spectra and diagnostics we may expect to see if such electrons are being produced in regions identical to HXR-emitting electrons.…”

A Modeling Investigation for Solar Flare X-Ray Stereoscopy with Solar Orbiter/STIX and Earth-orbiting Missions

“…Following previous works (Jeffrey et al 2014(Jeffrey et al , 2019Kontar et al 2015;Stores et al 2023), the evolution of an electron flux F in energy E [erg], cosine of the pitch angle (β), cos m b = , and distance along the guiding magnetic field z [cm], from a coronal loop apex to the chromosphere can be modeled using a time-independent Fokker-Planck equation (see Equation (1)). This takes into account the processes that alter electron properties, including their directivity, e.g., Coulomb collisions (represented by the last two terms on the right-hand side (rhs) of Equation (1)) and turbulent scattering (represented by the first term on the rhs of Equation (1)) from magnetic fluctuations using a diffusion coefficient D μμ , often chosen to be isotropic for simplicity, i.e., as shown by Jeffrey et al (2020):…”