Numerical Simulations of Chromospheric Hard X-Ray Source Sizes in Solar Flares

Abstract

X-ray observations are a powerful diagnostic tool for transport, acceleration, and heating of electrons in solar flares. Height and size measurements of Xray footpoints sources can be used to determine the chromospheric density and constrain the parameters of magnetic field convergence and electron pitch-angle evolution. We investigate the influence of the chromospheric density, magnetic mirroring and collisional pitch-angle scattering on the size of X-ray sources. The time-independent Fokker-Planck equation for electron transport is solved numerically and analytically to find the electron distribution as a function of height above the photosphere. From this distribution, the expected X-ray flux as a function of height, its peak height and full width at half maximum are calculated and compared with RHESSI observations. A purely instrumental explanation for the observed source size was ruled out by using simulated RHESSI images. We find that magnetic mirroring and collisional pitch-angle scattering tend to change the electron flux such that electrons are stopped higher in the atmosphere compared with the simple case with collisional energy loss only. However, the resulting X-ray flux is dominated by the density structure in the chromosphere and only marginal increases in source width are found. Very high loop densities (> 10 11 cm −3 ) could explain the observed sizes at higher energies, but are unrealistic and would result in no footpoint emission below about 40 keV, contrary to observations. We conclude that within a monolithic density model the vertical sizes are given mostly by the density scale-height and are predicted smaller than the RHESSI results show.

Hybrid simulations of chromospheric HXR flare sources

“…5. All studied models give much smaller HXR sources than observed ones, this is in agreement with previous parametric study of (Battaglia et al 2012). The largest HXR source, 1.2 arcsec, is found for δ = 3 and pancake distribution, but its location is higher than those from observations .…”

“…To describe the characteristics of HXR emission in the modelled loop, we follow the approach of Battaglia et al (2012) and define the position of the source as the first moment of the height profile of HXR emission and the FWHM as the second moment of that profile. Similarly, only emission above 10% of the maximum HXR is considered in orwww.an-journal.org der to emulate the limited dynamic range of RHESSI images.…”

“…Battaglia et al (2012) modelled the vertical sizes of the HXR sources for several prescribed density distributions along the loop, for various pitch-angle distributions in a singular (compact) flare loop with converging magnetic field (i.e. including magnetic mirroring).…”

Implications for electron acceleration and transport from non-thermal electron rates at looptop and footpoint sources in solar flares

“…The observations show that the HXR source height in the chromosphere decreases with increasing X-ray energy (Matsushita et al 1992;Aschwanden et al 2002;Kontar et al 2008;Saint-Hilaire et al 2010;Battaglia & Kontar 2011a) as anticipated from downward propagating electron beams. In addition, the characteristic sizes of HXR sources decrease with increasing energy, which is consistent with collisional electron transport along converging magnetic flux tubes (Kontar et al 2008;Battaglia & Kontar 2011a;Fedun et al 2011;Battaglia et al 2012;Xu et al 2012). Coronal X-ray sources are prominently visible at and below ∼10−30 keV and are usually due to thermal and non-thermal bremsstrahlung, which indicates plasma heating and the presence of non-thermal electron populations (e.g.…”

RESIK and RHESSI observations of the 20 September 2002 flare

“…The parameters of the NTE beams, such as the energy distribution, total energy, and precipitation depths, vary rapidly on timescales of seconds. The time variations of the HXR emis-sion are also a function of the temporal and spatial variations of the plasma properties along the flaring loop: mostly the density and the temperature of the plasma near the loop footpoints (Battaglia et al 2012). In particular, both HXR and SXR emissions are related to a flux of the NTEs; while the HXR emission is directly excited in a bremsstrahlung process by the NTEs, the SXR emission, thermal in origin, is related to the energy deposited by NTEs in the plasma.…”