Multithermal Representation of the Kappa-Distribution of Solar Flare Electrons and Application to Simultaneous X-Ray and Euv Observations

Abstract

Acceleration of particles and plasma heating is one of the fundamental problems in solar flare physics. An accurate determination of the spectrum of flare energized electrons over a broad energy range is crucial for our understanding of aspects such as the acceleration mechanism and the total flare energy. Recent years have seen a growing interest in the kappa-distribution as representation of the total spectrum of flare accelerated electrons. In this work we present the kappa-distribution as a differential emission measure. This allows for inferring the electron distribution from X-ray observations and EUV observations by simultaneously fitting the proposed function to RHESSI and SDO/AIA data. This yields the spatially integrated electron spectra of a coronal source between less than 0.1 keV up to several tens of keV. The method is applied to a singleloop GOES C4.1 flare. The results show that the total energy can only be determined accurately by combining RHESSI and AIA observations. Simultaneously fitting the proposed representation of the kappa-distribution reduces the electron number density in the analysed flare by a factor of ∼ 30 and the total flare energy by a factor of ∼ 5 compared with the commonly used fitting of RHESSI spectra. The spatially integrated electron spectrum of the investigated flare between 0.043 keV and 24 keV is consistent with the combination of a low-temperature (∼ 2 MK) component and a hot (∼ 11 MK) kappa-like component with spectral index 4, reminiscent of solar wind distributions.

Nonequilibrium Processes in the Solar Corona, Transition Region, Flares, and Solar Wind (Invited Review)

“…In addition to that, Battaglia, Motorina, and Kontar (2015) found that fitting the combined RHESSI and AIA data together can be done by using a two-component ξ κ (T ) function, consisting of ξ These analyses show that taking account of the larger observed energy range provides tighter constraints on the mean electron flux spectrum present in the flare plasma. Additionally, approximating only a limited energy range (e.g., only RHESSI observations above several tens of keV) could in principle lead to misleading results on the nature of the non-thermal component present in the plasma.…”

“…It consist of two components, ξ hot (T ) and ξ cold (T ), shown in blue and purple, respectively. From Battaglia, Motorina, and Kontar (2015), c AAS. Reproduced with permission.…”

“…Battaglia, Motorina, and Kontar (2015) remedied this by using a κ-distribution instead (see Section 2 therein). The RHESSI 7-24 keV data for the loop source in the confined SOL2010-08-14T10:05 C4.1 event (studied previously by Battaglia and Kontar, 2013) were fitted with a κ-distribution yielding κ = 4.1 ±0.1, and also with a ξ κ (T ), yielding κ = 3.6 ±0.1.…”

Electron Distribution and Energy Release in Magnetic Reconnection Outflow Regions during the Pre-impulsive Phase of a Solar Flare

“…With this method, the data from the two instruments are treated as one data set and forward fitted with one model distribution. As shown by Battaglia et al (2015), this approach leads to a better constraint of the low-energy electrons, resulting in up to a factor of ∼ 30 lower total energy content of the electron distribution compared with traditional X-ray spectroscopy. Using these combined X-ray-EUV diagnostics, we can characterise the electron distribution function in the coronal regions of magnetic reconnection outflow during solar flares.…”

Shock-drift accelerated electrons andn-distribution

“…When compared to the Maxwellian distribution, the n-and kappa distributions represent two antipodes, the n-distribution function has a steeper (softer) energy tail than the Maxwellian distribution, while the kappa distribution has a harder energy tail. Both distributions are used to explain soft X-ray observations of solar flares, but in different cases (Kulinová et al 2011;Battaglia et al 2015). Leroy & Mangeney (1984) and Wu (1984) pointed out that nearly perpendicular collisionless shock waves are capable of accelerating electrons.…”