Emission, absorption and polarization of gyrosynchrotron radiation of mildly relativistic paricles

Approximate analytic expressions for the emissivity and absorption coefficient of synchrotron radiation of mildly relativistic particles with an arbitrary energy spectrum and pitch angle distribution are given. From these, an expression for the degree of polarization is derived. To accomplish this, previously developed methods of integration are used. The analytic results are compared with numerical results for both thermal and non-thermal (power law) distributions of particles

Emission, absorption and polarization of gyrosynchrotron radiation of mildly relativistic particles

Approximate analytic expressions are presented for the emissivity and absorption coefficient of synchrotron radiation of mildly relativistic particles with an arbitrary energy spectrum and pitch angle distribution. From these, an expression for the degree of polarization is derived. The analytic results are compared with numerical results for both thermal and non-thermal (power law) distributions of particles

The behavior of beams of relativistic non-thermal electrons under the influence of collisions and synchrotron losses

For many astrophysical situations, such as in solar flares or cosmic gamma-ray bursts, continuum gamma rays with energies up to hundreds of MeV were observed, and can be interpreted to be due to bremsstrahlung radiation by relativistic electrons. The region of acceleration for these particles is not necessarily the same as the region in which the radiation is produced, and the effects of the transport of the electrons must be included in the general problem. Hence it is necessary to solve the kinetic equation for relativistic electrons, including all the interactions and loss mechanisms relevant at such energies. The resulting kinetic equation for non-thermal electrons, including the effects of Coulomb collisions and losses due to synchrotron emission, was solved analytically in some simple limiting cases, and numerically for the general cases including constant and varying background plasma density and magnetic field. New approximate analytic solutions are presented for collision dominated cases, for small pitch angles and all energies, synchrotron dominated cases, both steady-state and time dependent, for all pitch angles and energies, and for cases when both synchrotron and collisional energy losses are important, but for relativistic electrons. These analytic solutions are compared to the full numerical results in the proper limits. These results will be useful for calculation of spectra and angular distribution of the radiation (x rays, gamma-rays, and microwaves) emitted via synchrotron or bremsstrahlung processes by the electrons. These properties and their relevance to observations will be observed in subsequent papers

The Hard X-rays and Gamma-rays from Solar Flares

Radiation of energies from 10 KeV to greater than 10 MeV has been observed during solar flares, and is interpreted to be due to bremsstrahlung by relativistic electrons. A complete treatment of this problem requires solution of the kinetic equation for relativistic electrons and inclusion of synchrotron energy losses. Using the electron distributions obtained from numerical solutions of this equation the bremsstrahlung spectra in the impulsive x ray and gamma-ray regimes are calculated, and the variation of these spectral indices and directivities with energy and observation angle are described. The dependences of these characteristics of the radiation of changes in the solar atmospheric model, including the convergence of the magnetic field, the injected electron spectral index, and most importantly, in the anisotropy of the injected electrons and of the convergence of the magnetic field are also described. The model results are compared with stereoscopic observations of individual flares and the constraints that this data sets on the models are discussed

Plasma heating in the very early and decay phases of solar flares

In this paper we analyze the energy budgets of two single-loop solar flares under the assumption that non-thermal electrons are the only source of plasma heating during all phases of both events. The flares were observed by the Ramaty High Energy Solar Spectroscopic Imager (RHESSI) and Geostationary Operational Environmental Satellite (GOES) on September 20, 2002 and March 17, 2002, respectively. For both investigated flares we derived the energy fluxes contained in non-thermal electron beams from the RHESSI observational data constrained by observed GOES light-curves. We showed that energy delivered by non-thermal electrons was fully sufficient to fulfil the energy budgets of the plasma during the pre-heating and impulsive phases of both flares as well as during the decay phase of one of them. We concluded that in the case of the investigated flares there was no need to use any additional ad-hoc heating mechanisms other than heating by non-thermal electrons.Comment: 22 pages, 10 figures, The Astrophysical Journal (accepted, March 2011

Stereoscopic observations of hard x ray sources in solar flares made with GRO and other spacecraft

Since the launch of the Gamma Ray Observatory (GRO) in Apr. 1991, the Burst and Transient Source Experiment (BATSE) instrument on GRO has recorded a large number of solar flares. Some of these flares have also been observed by the Gamma-Ray Burst Detector on the Pioneer Venus Orbiter (PVO) and/or by the Solar X-Ray/Cosmic Gamma-Ray Burst Experiment on the Ulysses spacecraft. A preliminary list of common flares observed during the period May-Jun. 1991 is presented and the possible joint studies are indicated

Plasma heating in the very early phase of solar flares

In this paper we analyze soft and hard X-ray emission of the 2002 September 20 M1.8 GOES class solar flare observed by RHESSI and GOES satellites. In this flare event, soft X-ray emission precedes the onset of the main bulk hard X-ray emission by ~5 min. This suggests that an additional heating mechanism may be at work at the early beginning of the flare. However RHESSI spectra indicate presence of the non-thermal electrons also before impulsive phase. So, we assumed that a dominant energy transport mechanism during rise phase of solar flares is electron beam-driven evaporation. We used non-thermal electron beams derived from RHESSI spectra as the heating source in a hydrodynamic model of the analyzed flare. We showed that energy delivered by non-thermal electron beams is sufficient to heat the flare loop to temperatures in which it emits soft X-ray closely following the GOES 1-8 A light-curve. We also analyze the number of non-thermal electrons, the low energy cut-off, electron spectral indices and the changes of these parameters with time.Comment: Comments: 17 pages, 5 figures, The Astrophysical Journal Letters (accepted, October 2009

Global Energetics of Solar Flares: III. Non thermal Energies

This study entails the third part of a global flare energetics project, in which Ramaty High-Energy Solar Spectroscopic Imager (RHESSI) data of 191 M and X-class flare events from the first 3.5 yrs of the Solar Dynamics Observatory (SDO) mission are analyzed. We fit a thermal and a nonthermal component to RHESSI spectra, yielding the temperature of the differential emission measure (DEM) tail, the nonthermal power law slope and flux, and the thermal/nonthermal cross-over energy $e_{\mathrm{co}}$. From these parameters we calculate the total nonthermal energy $E_{\mathrm{nt}}$ in electrons with two different methods: (i) using the observed cross-over energy $e_{\mathrm{co}}$ as low-energy cutoff, and (ii) using the low-energy cutoff $e_{\mathrm{wt}}$ predicted by the warm thick-target bremsstrahlung model of Kontar et al. {\bf Based on a mean temperature of $T_e=8.6$ MK in active regions we find low-energy cutoff energies of $e_{\mathrm{wt}} =6.2\pm 1.6$ keV for the warm-target model, which is significantly lower than the cross-over energies $e_{\mathrm{co}}=21 \pm 6$ keV. Comparing with the statistics of magnetically dissipated energies $E_{\mathrm{mag}}$ and thermal energies $E_{\mathrm{th}}$ from the two previous studies, we find the following mean (logarithmic) energy ratios with the warm-target model: $E_{\mathrm{nt}} = 0.41 \ E_{\mathrm{mag}}$, $E_{\mathrm{th}} = 0.08 \ E_{\mathrm{mag}}$, and $E_{\mathrm{th}} = 0.15 \ E_{\mathrm{nt}}$. The total dissipated magnetic energy exceeds the thermal energy in 95% and the nonthermal energy in 71% of the flare events, which confirms that magnetic reconnection processes are sufficient to explain flare energies. The nonthermal energy exceeds the thermal energy in 85\% of the events, which largely confirms the warm thick-target model.Comment: 34p, 9 Figs., 1 Tabl

Looptop Hard X-Ray Emission in Solar Flares: Images and Statistics

The discovery of hard X-ray sources near the top of a flaring loop by the HXT instrument on board the YOHKOH satellite represents a significant progress towards the understanding of the basic processes driving solar flares. In this paper we extend the previous study of limb flares by Masuda (1994) by including all YOHKOH observations up through August 1998. We report that from October 1991 to August 1998, YOHKOH observed 20 X-ray bright limb flares (where we use the same selection criteria as Masuda), of which we have sufficient data to analyze 18 events, including 8 previously unanalyzed flares. Of these 18 events, 15 show detectable impulsive looptop emission. Considering that the finite dynamic range (about a decade) of the detection introduces a strong bias against observing comparatively weak looptop sources, we conclude that looptop emission is a common feature of all flares. We summarize the observations of the footpoint to looptop flux ratio and the spectral indices. We present light curves and images of all the important newly analyzed limb flares. Whenever possible we present results for individual pulses in multipeak flares and for different loops for multiloop flares. We then discuss the statistics of the fluxes and spectral indices of the looptop and footpoint sources taking into account observational selection biases. The importance of these observations (and those expected from the scheduled HESSI satellite with its superior angular spectral and temporal resolution) in constraining acceleration models and parameters is discussed briefly.Comment: 27 pages (13 embedded figures). Accepted for publication in Ap