Determination of the Total Accelerated Electron Rate and Power Using Solar Flare Hard X-Ray Spectra

Abstract

Solar flare hard X-ray spectroscopy serves as a key diagnostic of the accelerated electron spectrum. However, the standard approach using the collisional cold thick-target model poorly constrains the lower-energy part of the accelerated electron spectrum, and hence the overall energetics of the accelerated electrons are typically constrained only to within one or two orders of magnitude. Here we develop and apply a physically self-consistent warm-target approach which involves the use of both hard X-ray spectroscopy and imaging data. The approach allows an accurate determination of the electron distribution low-energy cutoff, and hence the electron acceleration rate and the contribution of accelerated electrons to the total energy released, by constraining the coronal plasma parameters. Using a solar flare observed in X-rays by the RHESSI spacecraft, we demonstrate that using the standard cold-target methodology, the lowenergy cutoff (and hence the energy content in electrons) is essentially undetermined. However, the warm-target methodology can determine the low-energy electron cutoff with ∼7% uncertainty at the 3σ level and hence permits an accurate quantitative study of the importance of accelerated electrons in solar flare energetics.

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

“…The determination of these coronal plasma properties is vital for constraining electron transport and deposition. Figures taken from Kontar et al (2019).…”

Global Energetics of Solar Flares. VIII. The Low-energy Cutoff

“…The model has been tested with numerical simulations that include the effects of collisional energy diffusion, spatial transport and thermalization of fast electrons (Jeffrey et al 2014). The warm target model assumes a two-temperature target plasma (Kontar et al , 2019: the warm solar corona and the cold chromosphere. The warm corona is collisionally thick to electrons with energy E < √ 2KnL, where K = 2πe 4 ln Λ is a constant, n is the density of the coronal plasma, and L is the length of the warm target region.…”

“…Importantly, the warm target model uses the warm coronal plasma environment (its temperature, number density, and warm plasma extent) to constrain the properties of the accelerated electron distribution. In general, the low-energy cutoff should be determined by fitting the warm target model to the observed X-ray count spectrum (see Kontar et al 2019). An application of a simplified version of this warm target model to 191 M and X-class flares yielded a mean low-energy cutoff of ε wt = 6.2 ± 1.6 keV (Aschwanden et al 2016), which is significantly lower than the cross-over energy of ε co = 21 ± 6 keV.…”

“…It can be shown that the low-energy cutoff in a cold thick-target model is essentially undetermined (e.g. Ireland et al 2013;Kontar et al 2019), while it was shown that the warm target model can constrain the low-energy cutoff down to 7% at a 3-σ level (Kontar et al 2019).…”

“…One issue is that the plasma in a flare is highly inhomogeneous, ranging from the cold background corona values at the beginning of a flare (T cold ≈ 0.5 − 2 MK) to the hot chromospheric evaporation component (T hot ≈ 5 − 25 MK) at the flare peak time, causing some ambiguity about which temperature to attribute to the warm-plasma component that constrains the low-energy cutoff. In the warm target model, the deduction of the coronal plasma environment is crucial for constraining the low energy cutoff, and hence the nonthermal electron power (Kontar et al (2019).…”