The Role of Energy Diffusion in the Deposition of Energetic Electron Energy in Solar and Stellar Flares

Abstract

During solar flares, a large fraction of the released magnetic energy is carried by energetic electrons that transfer and deposit energy in the Sun's atmosphere. Electron transport is often approximated by a cold thick-target model (CTTM), assuming that electron energy is much larger than the temperature of the ambient plasma, and electron energy evolution is modeled as a systematic loss. Using kinetic modeling of electrons, we re-evaluate the transport and deposition of flare energy. Using a full collisional warm-target model (WTM), we account for electron thermalization and for the properties of the ambient coronal plasma such as its number density, temperature and spatial extent. We show that the deposition of non-thermal electron energy in the lower atmosphere is highly dependent on the properties of the flaring coronal plasma. In general, thermalization and a reduced WTM energy loss rate leads to an increase of non-thermal energy transferred to the chromosphere, and the deposition of non-thermal energy at greater depths. The simulations show that energy is deposited in the lower atmosphere initially by high energy non-thermal electrons, and later by lower energy non-thermal electrons that partially or fully thermalize in the corona, over timescales of seconds, unaccounted for in previous studies. This delayed heating may act as a diagnostic of both the injected non-thermal electron distribution and the coronal plasma, vital for constraining flare energetics.

Accelerated particle beams in a 3D simulation of the quiet Sun

“…This is because the target particles can be considered e↵ectively stationary, leading to a deterministic evolution of each accelerated particle. Je↵rey et al (2019) found that the cold-target approximation tends to underestimate the amount of energy deposited in the lower atmosphere compared to the results of a full warm-target model because the electrons that thermalise in the corona eventually will di↵use down to the lower atmosphere and deposit their energy there. However, this conclusion was based on work not including standard thermal conduction, and the inclusion of thermal conduction would mitigate some of the discrepancies between the cold-and warm-target models.…”

A User’s Guide to the Magnetically Connected Space Weather System: A Brief Review

“…Finally, it is known that particles are accelerated during solar flares, when the chromosphere is heated by energy deposition during the flare (Jeffrey et al, 2019). This source is generally interpreted as a signature of energy release near or above the loop top, which heats the plasma in the coronal loop and accelerates electrons that can escape from the primary acceleration site as beams.…”

Probing solar flare accelerated electron distributions with prospective X-ray polarimetry missions

“…Equation 1is a time-independent equation useful for studying solar flares where the electron transport time from the corona to the lower atmosphere is usually shorter than the observational time (i.e. most X-ray spectral observations have integration times of tens of seconds to minutes), but temporal information can be extracted (Jeffrey et al 2019).…”

“…For simplicity here, in each simulation we use a homogenous coronal number density and temperature. At the boundary with the chromosphere, the number density is set at n = 1 × 10 12 cm −3 but the number density rises to photospheric densities of n ≈ 10 17 cm −3 over ≈ 3 ′′ using the exponential density function shown Jeffrey et al (2019). At the chromospheric boundary, the temperature is set at T ≈ 0 MK so that the electron transport model becomes a cold target model (Brown 1971) where all E >> k B T .…”

“…For this the pitch-angle term in Equation (1) is multiplied by 2, compared to andJeffrey et al (2019).…”