Study of hard X-ray characteristics of solar flares - support for non-thermal processes

The spatial and angular distributions and also the energy spectrum of hard X-rays from solar flares have been studied in terms of the energy and angular distributions of the accelerated electron beam. The incident electron distributions as functions of column density have been computed by combining the analytical treatment of small-angle scattering with the Monte-Carlo calculations for large angle scattering. To start with monoenergetic electrons at 0°, 30°, and 60° incidence angles have been taken. Using the Bethe-Heitler total cross section and the Sauter differential cross section along with the calculated electron distributions, the bremsstrahlung flux and its angular distribution for different photon energies > 10 keV have been studied as function of column density. The shape of the calculated curves agrees with the observations of PVO/ISEE-3 lending support to the beamed thick-target model for X-ray generation with continuous injection.Physics Department, Vishwa Bharti Institution, Rainawari, Srinagar, India.     

Calculation of anisotropy ratio of hard X-rays from solar flares — evidence for continuous electron injections/accelerations

Variation of electron energy and angular distributions has been studied as a function of column density by combining small-angle analytical treatment with large-angle Monte Carlo calculations. The distributions have been calculated for initial electron energy 300 keV and various incidence directions. Using these distributions and Sauter bremsstrahlung cross-section differential in photon energy and emission angle, we have calculated the X-ray energy and angular distributions for photon energies 10, 20, 50, 100, 150 and 200 keV. By taking the ratio of X-ray flux at 90 and 180°, we have computed the anisotropy ratio A as function of column density. Calculated anisotropy ratio compares well with ISEE-3 and PVO observations.     

Hard X-rays from solar flares — time characteristics in correlation with energy and angular distributions of electrons

Fine time variation of hard X-rays has been explained in terms of a spread in the angle of incidence of the source electrons in non-thermal thick-target model for bremsstrahlung generation. The electron energy and angular distributions have been calculated by combining small angle scatterings using analytical treatment with a large angle collision using Monte Carlo calculations as a function of column density. The incidence angles of electrons are taken as 0, 30, and 60°. Using the Bethe-Heitler cross section and the above calculated electron distributions, the bremsstrahlung flux for different photon energies as a function of column density has been studied. The computed X-ray pulse as a function of column density has been converted into time profile. It corresponds well with the observed fine time structure. The calculated spectra of X-rays at the peak and valley are also consistent with the observations. The variation of photon flux with time has also been computed for photon energies 20, 50, and 100 keV for 90 and 180° observation angles together with the changes in spectral shapes of photon energy spectrum at different times for 90 and 180° observation angles.     

Role of non-thermal electrons on the generation of X-ray and EUV lines in solar flares

The energy and angular distributions of electrons have been studied by combining small angle scatterings using analytical treatment with large angle collisions using Monte Caroo calculations as a function of column density for initially power-law electron distributions and incidence angles of 0, 30, and 60°. Using these distributions the X-ray and EUV line flux as a function of column density has been computed. The flux increases with increase in column density. At the initial column densities the contribution of non-thermal electrons for the production of line flux is negligible. However, it becomes significant at intermediate column densities at which the electron energy and angular distributions have non-Maxwellian nature. X-ray and EUV flux have also been calculated as a function of electron spectral index at a fixed column density. It falls steeply with increase in spectral index. The calculated flux is compared with the observations.     

Microwave emission from solar flares and comparison with observations

We have studied the evolution of electron energy and angular distributions using Monte Carlo technique for electron beams directed vertically downwards towards chromosphere for incident energies 30 keV, and 300 keV at different incidence angles. Using these distributions we have calculated microwave flux for different frequencies at a fixed column density as well as for a fixed frequency at different column densities. We have also calculated the total microwave flux coming out of solar atmosphere and have compared it with observations. Our results agree well with observational results and produce the observed nature of flux.     

on the role of nonthermal electrons in EUV and X-ray line emissions from solar flares

The energy and angular distribution of electrons as a function of column densities initially for monoenergetic and monodirectional electron beams and incidence angles of 0‡, 30‡ and 60‡ have been studied by combining small angle scattering using analytical treatment with large angle collisions using Monte Carlo calculations. Using these distributions, X-ray and EUV-line flux have been studied as a function of column density. It is observed that the line flux increases with the increase in column density, becoming significant at intermediate column densities where the electron energies and angular distributions have a non-Maxwellian nature.     

A three-dimensional code for muon propagation through the rock: MUSIC

We present a new three-dimensional Monte-Carlo code MUSIC (MUon SImulation Code) for muon propagation through the rock. All processes of muon interaction with matter with high energy loss (including the knock-on electron production) are treated as stochastic processes. The angular deviation and lateral displacement of muons due to multiple scattering, as well as bremsstrahlung, pair production and inelastic scattering are taken into account. The code has been applied to obtain the energy distribution and angular and lateral deviations of single muons at different depths underground. The muon multiplicity distributions obtained with MUSIC and CORSIKA (Extensive Air Shower simulation code) are also presented. We discuss the systematic uncertainties of the results due to different muon bremsstrahlung cross-sections.     

Photoelectron flux in the earth''s ionosphere

We present calculations of the photoelectron flux in the ionosphere which have been obtained by solving the Boltzmann equation. The method is flexible enough to allow for a wide range of energy and angular dependences for both external and internal electron sources. This work represents the first attempt to incorporate anisotropic electron-neutral cross sections for elastic collisions in a multi-stream photoelectron flux calculation. Detailed comparisons of calculated and measured photoelectron fluxes show excellent agreement.     

The penetration of soft electrons into the ionosphere

Calculations are presented of energy spectra and angular and spatial distributions of electron fluxes in the ionosphere resulting from precipitation ofmonoenergetic (E = 25, 50 and 100 eV) electrons. The incident electrons are assumed to be isotropic over the downward direction. It is found that the resulting steady-state electron fluxes above ca. 300 km are highly anisotropic, and that the pitch angle distribution is energy dependent. About 15 per cent of the incident electrons are backscattered elastically to the protonosphere. A much larger number of electrons escape after they have deposited a part of their energy in the atmosphere. The mean energy of the escaping electrons is about half that of the incident electrons. About 50% of the incident energy is absorbed in the atmosphere, the remainder being returned to the protonosphere. The rate of absorption of energy is a maximum at heights between 300 and 400 km. Most of the energy is absorbed in ionization and excitation of atomic oxygen. An appreciable amount of energy is, however, absorbed as heat by the ambient electron gas. Altitude profiles are presented of the rates of ionization, excitation, and electron heating caused by soft electron precipitation.     

Thermal structure of the equatorialE-region over Thumba

Photoionization and absorbed energy rates have been computed by making use of the latest available semi-empirical solar XUV fluxes and cross-sections for two rocket flights for electron density measurements on 3 March, 1973 and 7 April, 1972 corresponding to low and medium solar active conditions over Thumba. Various heating and cooling rate profiles have been computed by making use of the latest available information. Various efficiency parameters such as photoelectron heating efficiency, photoionization efficiency, and ultraviolet heating efficiency, that are extremely important in understanding the thermal structure of the ionosphere, are clearly defined and distinguished.     

On the polarization and anisotropy of solar X-radiation during flares

Starting from the idea that the electrons accelerated during a solar flare have originally a preferred direction, the angular distribution and the polarization of bremsstrahlung below 10 Å is calculated taking into account the influence of the magnetic field. The energy distribution of the nonthermal electrons is based on X-ray spectra measured by the Leicester group during flares in 1962 and 1967. In addition to the case of a fixed angle between the electron velocity and the magnetic field, an angular distribution of the form sin ⁿ is considered. The results may be used to test flare models. Recent measurements of the polarization of solar X-radiation yield the expected order of magnitude.Paper presented to the Int. Symp. on Solar-Terr. Phys., Leningrad, May 1970.     

Electron distribution function and ion concentrations in the earth's lower ionosphere from Boltzmann-Fokker-Planck theory

Using the Boltzmann-Fokker-Planck method and the local approximation we derive coupled non-linear equations for the electron and ion concentrations and the energy-dependent electron distribution function in the Earth's lower ionosphere. These equations are new and give the appropriate generalization of the standard electron-ion continuity equations in the local approximation when electron-neutral particle impact ionization is treated rigorously. We report stable, numerical solutions to these equations and compare our calculated electron concentration to the experimentally determined result for a rocket experiment where the electron concentration and solar EUV spectral flux were measured simultaneously.     

Boltzmann-Fokker-Planck model for the electron distribution function in the Earth's ionosphere

Using Boltzmann-Fokker-Planck methods and the diffusion approximation, we derive coupled non-linear equations for the first two angular moments of the electron distribution function in the Earth's ionosphere. The theory includes a phenomenological treatment of photionization of the neutral species by an externally produced photon flux; electron-ion recombination; electronneutral particle attachment; elastic, excitation, deexcitation, and ionizing electron-neutral particle collisions; and elastic electron-electron and electron-ion collisions. At high and low energies, we obtain approximate analytic solutions for the steady-state electron distribution function. Under certain conditions we also obtain the standard continuous slowing-down formulae for the steady-state electron distribution function in the diffusion approximation.     

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.     

A study of RATAN-600 observations of solar S-component sources

A sample of 36 S-component sources observed by the radio telescope RATAN-600 was compared with calculations of gyromagnetic emission and bremsstrahlung based on recent sunspot models. The diagnostic possibilities of the spectral distributions in the radio flux, the degree of polarization, and the source sizes for the estimation of magnetic scale heights and other source parameters were checked by different methods.Depending on the magnetic field structure, the observations show different types of polarization spectra. Most regular spectra and highest values of the degree of polarization were observed from sources above the leading part of the associated spot group. Magnetic scale heights were found to be intrinsically associated with the source size of the gyromagnetic emission.The flare production rate of active regions appears to be related to their S-component flux and magnetic scale heights.     

Rocket observation of conjugate photoelectrons in the predawn ionosphere

Photoelectron flux in the energy range 6–70 eV coming from the sunlight conjugate ionosphere has been measured directly by the rocket borne low energy electron spectrometer in the altitude region of 210–350 km. Pitch angle distribution of the measured flux is nearly isotropic, the flux decreasing slightly with pitch angle. The photoelectron fluxes measured at 350 km at the energies of 15 and 30 eV are 3 × 10⁶ and 1 × 10⁶ (cm² s str eV)^?1 respectively which decrease to 1 × 10⁶ and 1 × 10⁵ at 250 km at the same energies. These values are consistent with the vertical profile of the 630 nm airglow intensity measured simultaneously. The fluxes obtained near apogee show peaks in the range 20–30 eV which also appear in the daytime photoelectron flux, indicating reduced loss of electrons during the passage from the conjugate ionosphere through the plasmasphere at the low geomagnetic latitude where observation was made. Photoelectron fluxes observed below the apogee height are compared to the calculated fluxes to investigate the interaction of electrons with the atmospheric species during the passage in the ionosphere. Calculated fluxes obtained by using continuous slowing-down approximation and neglecting pitch angle scattering are in good agreement with the observations although there still remain disagreements in detailed comparison which may be ascribed to the assumptions inherent in the calculation and/or to the uncertainties of the input data for the calculation.     

On the role of reverse current on the hard X-ray production in solar flares and time-lags between high- and low-energy photons

The evolution of energy and angular distributions of electrons has been studied accounting for the reverse current effect by combining analytically treated small angle multiple scatterings with large angle Monte-Carlo calculations. Reverse current and potential variations as function of column density have been computed. It is found that the reverse current decreases steeply with increase in electron energy. However, it becomes significant for low-energy electrons. By use of these distributions and bremsstrahlung crosssection, the X-ray energy spectrum has been calculated. The nature of the resulting X-ray spectrum integrated over all column depths is similar to the one without reverse current. The time-lag between high-and low-energy photon production has been calculated. It is found that there is a small difference between time-lags as function of observation angles. This fact can be used to test the validity of the beamed thick target model.     

Altitude profiles of the photoelectron induced OD(λ6300Å) predawn enhancement by observation and theory

Emission profiles of the 6300Åline are determined from OGO 4 data in the dark ionosphere during conjugate sunrise. From Saint-Santin electron density profile measurements, it is shown that, for the two cases studied in December 1967, the recombination cannot account for the measured O¹D emission profiles. However, direct photoelectron-oxygen excitation can reproduce the data: if the photoelectron escape flux in the sunlit ionosphere, computed from standard photoelectron production, is transmitted through the field tube with an additional attenuation of 0.6 due to angular diffusion through photoelectron-electron and photoelectron-ion Coulomb collisions, the Hinteregger (1965) solar flux data must be increased by a factor 2, which agrees with previous results.     

On the Dynamics of the Jovian Ionosphere and Thermosphere: III. The Modelling of Auroral Conductivity

Recent work has been concerned with calculating the three-dimensional ion concentrations and Pedersen and Hall conductivities within the auroral region of Jupiter for varying conditions of incident electron precipitation. Using the jovian ionospheric model, we present results that show the auroral ionospheric response to changing the incoming flux of precipitating electrons (for constant initial energy) and also the response to changing the initial energy (for both constant flux and constant energy flux). The results show that, for expected energy fluxes of precipitating particles, the average auroral integrated Pedersen conductivity attains values in excess of 1 mho. In addition, it is shown that electrons with an initial energy of around 60 keV are particularly effective at generating auroral conductivity: Particles of this energy penetrate most effectively to the layer of the jovian ionosphere at which the auroral conductivity is at a maximum.     

A model of the solar radio slowly varying component

Our model uses the latest EUV data on the chromosphere-corona transition region. We take the three physical parameters (electron temperature and density and magnetic field) to be functions both of the height above the photosphere and the distance from the axis of our unipolar model. We consider both the gyroresonance radiation and the bremsstrahlung. Our calculated flux and polarization spectra peak at λ = 6 cm and 3 cm respectively, in general agreement with observations. Some features in the spatial distribution of the flux and polarization were obtained, which may be compared with future high-resolution data. We found that in the SVC radiation, the gyroresonance emission is all-important, while the contribution from the reflection of the extraordinary wave is almost nil. These results are directly opposite to the conclusions by Shimabuburo et al./1/.