Measurements of Electron Anisotropy in Solar Flares Using Albedo with RHESSI X-Ray Data

The angular distribution of electrons accelerated in solar flares is a key parameter in the understanding of the acceleration and propagation mechanisms that occur there. However, the anisotropy of energetic electrons is still a poorly known quantity, with observational studies producing evidence for an isotropic distribution and theoretical models mainly considering the strongly beamed case. We use the effect of photospheric albedo to infer the pitch-angle distribution of X-ray emitting electrons using Hard X-ray data from RHESSI. A bi-directional approximation is applied and a regularised inversion is performed for eight large flare events to deduce the electron spectra in both downward (towards the photosphere) and upward (away from the photosphere) directions. The electron spectra and the electron anisotropy ratios are calculated for a broad energy range, from about ten up to ～?300 keV, near the peak of the flares. The variation of electron anisotropy over short periods of time lasting 4, 8 and 16 seconds near the impulsive peak has been examined. The results show little evidence for strong anisotropy and the mean electron flux spectra are consistent with the isotropic electron distribution. The 3σ level uncertainties, although energy and event dependent, are found to suggest that anisotropic distribution with anisotropy larger than ～?three are not consistent with the hard X-ray data. At energies above 150?–?200 keV, the uncertainties are larger and thus the possible electron anisotropies could be larger.     

Chromospheric Height and Density Measurements in a Solar Flare Observed with RHESSI – II. Data Analysis

We present an analysis of hard X-ray imaging observations from one of the first solar flares observed with the Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI) spacecraft, launched on 5 February 2002. The data were obtained from the 22 February 2002, 11:06 UT flare, which occurred close to the northwest limb. Thanks to the high energy resolution of the germanium-cooled hard X-ray detectors on RHESSI we can measure the flare source positions with a high accuracy as a function of energy. Using a forward-fitting algorithm for image reconstruction, we find a systematic decrease in the altitudes of the source centroids z(ε) as a function of increasing hard X-ray energy ε, as expected in the thick-target bremsstrahlung model of Brown. The altitude of hard X-ray emission as a function of photon energy ε can be characterized by a power-law function in the ε=15–50 keV energy range, viz., z(ε)≈2.3(ε/20 keV)^−1.3 Mm. Based on a purely collisional 1-D thick-target model, this height dependence can be inverted into a chromospheric density model n(z), as derived in Paper I, which follows the power-law function n _e(z)=1.25×10¹³(z/1 Mm)^−2.5 cm⁻³. This density is comparable with models based on optical/UV spectrometry in the chromospheric height range of h≲1000 km, suggesting that the collisional thick-target model is a reasonable first approximation to hard X-ray footpoint sources. At h≈1000–2500 km, the hard X-ray based density model, however, is more consistent with the `spicular extended-chromosphere model' inferred from radio sub-mm observations, than with standard models based on hydrostatic equilibrium. At coronal heights, h≈2.5–12.4 Mm, the average flare loop density inferred from RHESSI is comparable with values from hydrodynamic simulations of flare chromospheric evaporation, soft X-ray, and radio-based measurements, but below the upper limits set by filling-factor insensitive iron line pairs.     

Regularized Energy-Dependent Solar Flare Hard X-Ray Spectral Index

The deduction from solar flare X-ray photon spectroscopic data of the energy-dependent model-independent spectral index is considered as an inverse problem. Using the well-developed regularization approach we analyze the energy dependency of spectral index for a high-resolution energy spectrum provided by Ramaty High Energy Solar Spectroscopic Imager (RHESSI). The regularization technique produces much smoother derivatives while avoiding additional errors typical of finite differences. It is shown that observations imply a spectral index varying significantly with energy, in a way that also varies with time as the flare progresses. The implications of these findings are discussed in the solar flare context.     

Effect of Collisions and Magnetic Convergence on Electron Acceleration and Transport in Reconnecting Twisted Solar Flare Loops

We study a model of particle acceleration coupled with an MHD model of magnetic reconnection in unstable twisted coronal loops. The kink instability leads to the formation of helical currents with strong parallel electric fields resulting in electron acceleration. The motion of electrons in the electric and magnetic fields of the reconnecting loop is investigated using a test-particle approach taking into account collisional scattering. We discuss the effects of Coulomb collisions and magnetic convergence near loop footpoints on the spatial distribution and energy spectra of high-energy electron populations and possible implications on the hard X-ray emission in solar flares.     

Direct measurements of submarine groundwater discharge (SGD) over a fractured rock aquifer in Flamengo Bay Brazil

Measurements of submarine groundwater discharge (SGD) along the South American coast and over fractured rock aquifers are rare. The rate and distribution of SGD was measured using three types of vented benthic chambers on the floor of Flamengo Bay located at the southeast coast of Brazil. Discharge rates were found up to almost 400 cm day⁻¹, although typically less than 100 cm d⁻¹. Large variations in SGD rates were seen over distances of a few meters which are attributed to the geomorphologic features of the fracture rock aquifer underlying a thin blanket of coastal sediments; clustering of fractures and the topography of the rock–sediment interface might be focusing or dispersing the discharge of groundwater. SGD was modulated by the tides with the highest values occurring at times of low tide, but the interaction was non-linear and, the correlation was weak at tidal ranges less than 1 m. The effect was masked by devices that integrated the SGD, but detected on continuously recording devices.     

Evolution of the Solar Flare Energetic Electrons in the Inhomogeneous Inner Heliosphere

Solar flare accelerated electrons escaping into the interplanetary space and seen as type III solar radio bursts are often detected near the Earth. Using numerical simulations we consider the evolution of energetic electron spectrum in the inner heliosphere and near the Earth. The role of Langmuir wave generation, heliospheric plasma density fluctuations, and expansion of magnetic field lines on the electron peak flux and fluence spectra is studied to predict the electron properties as could be observed by Solar Orbiter and Solar Probe Plus. Considering various energy loss mechanisms we show that the substantial part of the initial energetic electron energy is lost via wave–plasma processes due to plasma inhomogeneity. For the parameters adopted, the results show that the electron spectrum changes mostly at the distances before ～?20 R _⊙. Further into the heliosphere, the electron flux spectrum of electrons forms a broken power law relatively similar to what is observed at 1 AU.     

Nonuniform Target Ionization and Fitting Thick Target Electron Injection Spectra to RHESSI Data

Past analyses of flare hard X-ray (HXR) spectra have largely ignored the effect of nonuniform ionization along the electron paths in the thick-target model, though it is very significant for well-resolved spectra. The inverse problem (photon spectrum to electron injection spectrum F ₀(E ₀)) is disturbingly non-unique. However, we show that it is relatively simple to allow for the effect in forward fitting of parametric models of F ₀(E ₀)) and provide an expression to evaluate it for the usual single power-law form of F ₀(E ₀)).The expression involves the column depth N _* of the transition region in the flare loop as one of the parameters so data fitting can enable derivation of N _* (and its evaporative evolution) as part of the fitting procedure. The fit to RHESSI data on four flares for a single power law F ₀(E ₀)) is much improved when ionization structure is included compared to when the usual fully ionized approximation is used. This removes the need, in these events at least, to invoke broken power laws, or other forms, of the acceleration spectrum F ₀(E ₀)) to explain the observed photon spectrum