Probing solar flare electron acceleration with prospective X-ray polarimetry missions

Solar flare electron acceleration is an extremely efficient process, but the method of acceleration is not well constrained. Two of the essential diagnostics: electron anisotropy (velocity angle to the guiding magnetic field) and the high energy cutoff (highest energy electrons produced by the acceleration conditions: mechanism, spatial extent, time), are important quantities that can help to constrain electron acceleration at the Sun but both are poorly determined. Here, using electron and X-ray transport simulations that account for both collisional and non-collisional transport processes such as turbulent scattering, and X-ray albedo, we show that X-ray polarization can be used to constrain the anisotropy of the accelerated electron distribution and the most energetic accelerated electrons together. Moreover, we show that prospective missions, e.g. CubeSat missions without imaging information, can be used alongside such simulations to determine these parameters. We conclude that a fuller understanding of flare acceleration processes will come from missions capable of both X-ray flux and polarization spectral measurements together. Although imaging polarimetry is highly desired, we demonstrate that spectro-polarimeters without imaging can also provide strong constraints on electron anisotropy and the high energy cutoff

Size dependence of solar X-ray flare properties

Non-thermal and thermal parameters of 85 solar flares of GOES class B1 to M6 (background subtracted classes A1 to M6) have been compared to each other. The hard X-ray flux has been measured by RHESSI and a spectral fitting provided flux and spectral index of the non-thermal emission, as well as temperature and emission measure of the thermal emission. The soft X-ray flux was taken from GOES measurements. We find a linear correlation in a double logarithmic plot between the non-thermal flux and the spectral index. The higher the acceleration rate of a flare, the harder the non-thermal electron distribution. The relation is similar to the one found by a comparison of the same parameters from several sub-peaks of a single flare. Thus small flares behave like small subpeaks of large flares. Thermal flare properties such as temperature, emission measure and the soft X-ray flux also correlate with peak non-thermal flux. A large non-thermal peak flux entails an enhancement in both thermal parameters. The relation between spectral index and the non-thermal flux is an intrinsic feature of the particle acceleration process, depending on flare size. This property affects the reported frequency distribution of flare energies.Comment: Astronomy and Astrophysics, in pres

Solar flare electron acceleration: comparing theories and observations

A popular scenario for electron acceleration in solar flares is transit-time damping of low-frequency MHD waves excited by reconnection and its outflows. The scenario requires several processes in sequence to yield energetic electrons of the observed large number. Until now there was very little evidence for this scenario, as it is even not clear where the flare energy is released. RHESSI measurements of bremsstrahlung by non-thermal flare electrons yield energy estimates as well as the position where the energy is deposited. Thus quantitative measurements can be put into the frame of the global magnetic field configuration as seen in coronal EUV line observations. We present RHESSI observations combined with TRACE data that suggest primary energy inputs mostly into electron acceleration and to a minor fraction into coronal heating and primary motion. The more sensitive and lower energy X-ray observations by RHESSI have found also small events (C class) at the time of the acceleration of electron beams exciting meter wave Type III bursts. However, not all RHESSI flares involve Type III radio emissions. The association of other decimeter radio emissions, such as narrowband spikes and pulsations, with X-rays is summarized in view of electron accelerationComment: COSPAR meeting Houston 2002, PASP proceedings, in pres

Numerical simulations of chromospheric hard X-ray source sizes in solar flares

X-ray observations are a powerful diagnostic tool for transport, acceleration, and heating of electrons in solar flares. Height and size measurements of X-ray 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.Comment: 19 pages, 9 figures, accepted for publication in Ap

The influence of albedo on the size of hard X-ray flare sources

Context: Hard X-rays from solar flares are an important diagnostic of particle acceleration and transport in the solar atmosphere. Any observed X-ray flux from on-disc sources is composed of direct emission plus Compton backscattered photons (albedo). This affects both the observed spectra and images as well as the physical quantities derived from them such as the spatial and spectral distributions of accelerated electrons or characteristics of the solar atmosphere. Aims: We propose a new indirect method to measure albedo and to infer the directivity of X-rays in imaging using RHESSI data. Methods: Visibility forward fitting is used to determine the size of a disc event observed by RHESSI as a function of energy. This is compared to the sizes of simulated sources from a Monte Carlo simulation code of photon transport in the chromosphere for different degrees of downward directivity and true source sizes to find limits on the true source size and the directivity. Results: The observed full width half maximum of the source varies in size between 7.4 arcsec and 9.1 arcsec with the maximum between 30 and 40 keV. Such behaviour is expected in the presence of albedo and is found in the simulations. A source size smaller than 6 arcsec is improbable for modest directivities and the true source size is likely to be around 7 arcsec for small directivities. Conclusions: While it is difficult to image the albedo patch directly, the effect of backscattered photons on the observed source size can be estimated. The increase in source size caused by albedo has to be accounted for when computing physical quantities that include the size as a parameter such as flare energetics. At the same time, the study of the albedo signature provides vital information about the directivity of X-rays and related electrons.Comment: 8 pages, 6 figures, A&A (accepted

The spectral evolution of impulsive solar X-ray flares

The time evolution of the spectral index and the non-thermal flux in 24 impulsive solar hard X-ray flares of GOES class M was studied in RHESSI observations. The high spectral resolution allows for a clean separation of thermal and non-thermal components in the 10-30 keV range, where most of the non-thermal photons are emitted. Spectral index and flux can thus be determined with much better accuracy than before. The spectral soft-hard-soft behavior in rise-peak-decay phases is discovered not only in the general flare development, but even more pronounced in subpeaks. An empirically found power-law dependence between the spectral index and the normalization of the non-thermal flux holds during the rise and decay phases of the emission peaks. It is still present in the combined set of all flares. We find an asymmetry in this dependence between rise and decay phases of the non-thermal emission. There is no delay between flux peak and spectral index minimum. The soft-hard-soft behavior appears to be an intrinsic signature of the elementary electron acceleration process.Comment: 10 pages, 7 figures. Accepted for publication by A&

Hard X-ray footpoint sizes and positions as diagnostics of flare accelerated energetic electrons in the low solar atmosphere

The hard X-ray (HXR) emission in solar flares comes almost exclusively from a very small part of the flaring region, the footpoints of magnetic loops. Using RHESSI observations of solar flare footpoints, we determine the radial positions and sizes of footpoints as a function of energy in six near-limb events to investigate the transport of flare accelerated electrons and the properties of the chromosphere. HXR visibility forward fitting allows to find the positions/heights and the sizes of HXR footpoints along and perpendicular to the magnetic field of the flaring loop at different energies in the HXR range. We show that in half of the analyzed events, a clear trend of decreasing height of the sources with energy is found. Assuming collisional thick-target transport, HXR sources are located between 600 and 1200 km above the photosphere for photon energies between 120 and 25 keV respectively. In the other events, the position as a function of energy is constant within the uncertainties. The vertical sizes (along the path of electron propagation) range from 1.3 to 8 arcseconds which is up to a factor 4 larger than predicted by the thick-target model even in events where the positions/heights of HXR sources are consistent with the collisional thick-target model. Magnetic mirroring, collisional pitch angle scattering and X-ray albedo are discussed as potential explanations of the findings.Comment: 10 pages, 8 figures, accepted for publication in Ap