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

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

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

Comparison of Hinode/XRT and RHESSI detection of hot plasma in the non-flaring solar corona

We compare observations of the non-flaring solar corona made simultaneously with Hinode/XRT and with RHESSI. The analyzed corona is dominated by a single active region on 12 November 2006. The comparison is made on emission measures. We derive emission measure distributions vs temperature of the entire active region from multifilter XRT data. We check the compatibility with the total emission measure values estimated from the flux measured with RHESSI if the emission come from isothermal plasma. We find that RHESSI and XRT data analyses consistently point to the presence of a minor emission measure component peaking at log T ~ 6.8-6.9. The discrepancy between XRT and RHESSI results is within a factor of a few and indicates an acceptable level of cross-consistency.Comment: 12 pages, 3 figures, Letter accepted for publicatio

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

Reconciliation of Waiting Time Statistics of Solar Flares Observed in Hard X-Rays

We study the waiting time distributions of solar flares observed in hard X-rays with ISEE-3/ICE, HXRBS/SMM, WATCH/GRANAT, BATSE/CGRO, and RHESSI. Although discordant results and interpretations have been published earlier, based on relatively small ranges ($< 2$ decades) of waiting times, we find that all observed distributions, spanning over 6 decades of waiting times ($\Delta t \approx 10^{-3}- 10^3$ hrs), can be reconciled with a single distribution function, $N(\Delta t) \propto \lambda_0 (1 + \lambda_0 \Delta t)^{-2}$, which has a powerlaw slope of $p \approx 2.0$ at large waiting times ($\Delta t \approx 1-1000$ hrs) and flattens out at short waiting times \Delta t \lapprox \Delta t_0 = 1/\lambda_0. We find a consistent breakpoint at $\Delta t_0 = 1/\lambda_0 = 0.80\pm0.14$ hours from the WATCH, HXRBS, BATSE, and RHESSI data. The distribution of waiting times is invariant for sampling with different flux thresholds, while the mean waiting time scales reciprocically with the number of detected events, $\Delta t_0 \propto 1/n_{det}$. This waiting time distribution can be modeled with a nonstationary Poisson process with a flare rate $\lambda=1/\Delta t$ that varies as $f(\lambda) \propto \lambda^{-1} \exp{-(\lambda/\lambda_0)}$. This flare rate distribution represents a highly intermittent flaring productivity in short clusters with high flare rates, separated by quiescent intervals with very low flare rates.Comment: Preprint also available at http://www.lmsal.com/~aschwand/eprints/2010_wait.pd