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Photospheric albedo and the measurement of energy and angular electron distributions in solar flares

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Publication Date
Keywords
  • Qb Astronomy
  • Qc Physics
Disciplines
  • Logic
  • Mathematics
  • Physics

Abstract

In this thesis I examine the role of Compton back-scatter of solar flare Hard X-rays, also known as albedo, in the inference of the parent electron spectrum. I consider how albedo affects measurements of the energy and angular distributions when the mean electron flux spectrum in a solar flare is inferred using regularised inversion techniques. The angular distribution of the accelerated electron spectrum is a key parameter in the understanding of the acceleration and propagation mechanisms that occur in solar flares. 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. First we investigate the effect of albedo on the observed spectrum for a variety of commonly considered analytic forms of the pitch angle distribution. As albedo is the result of the scattering of X-ray photons emitted downwards towards the photosphere different angular distributions are likely to exhibit a varying amount of albedo reflection, in particular, downward directed beams of electrons are likely to produce spectra which are strongly influenced by albedo. The low-energy cut-off of the non-thermal electron spectrum is another significant parameter which it is important to understand, as its value can have strong implications for the total energy contained in the flare. However, both albedo and a low energy cut-off will cause a flattening of the observed X-ray spectrum at low energies. The Ramaty High Energy Solar Spectroscopic Imager (RHESSI) X-ray data base has been searched to find solar flares with weak thermal components and flat photon spectra in the 15 - 20 keV energy range. Using the method of Tikhonov Regularisation, we determine the mean electron flux distribution from count spectra of a selection of these events. We have found 18 cases which exhibit a statistically significant local minimum (a dip) in the range of 10 - 20 keV. The positions and spectral indices of events with low-energy cut-off indicate that such features are likely to be the result of photospheric albedo. It is shown that if the isotropic albedo correction was applied, all low-energy cut-offs in the mean electron spectrum were removed. The effect of photospheric albedo on the observed X-ray spectrum suggest RHESSI observations can be used to infer the anisotropy in the angular distribution of X-ray emitting electrons. A bi-directional approximation is applied and regularized inversion is performed for eight large flare events viewed by RHESSI to deduce the electron spectra in both downward (towards the photosphere) and upward (away form the photosphere) directions. The electron spectra and the electron anisotropy ratios are calculated for broad energy range from about 10 and up to ~ 300 keV near the peak of the flares. The variation of electron anisotropy over short periods of time intervals 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 inferred X-ray emitting electron spectrum is likely to have been modified from the accelerated or injected distribution by transport effects thus models of electron transport are necessary to connect the observations. We use the method of stochastic simulations to investigate the effect of Coulomb collisions on an electron beam propagating through a coronal loop. These simulations suggest that the effect of Coulomb collisions on a uniformly downward directed beam as envisaged in the collisional thick target model is not strong enough to sufficiently scatter the pitch angle distribution to be consistent with the measurements made in the previous chapter. Furthermore these simulations suggest that for the conditions studied the constraints inferred in Chapter 4 are only consistent with a low level of anisotropy in the injected electron distribution.

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