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Recent observations of cosmic ray (CR) electrons from several instruments have revealed various degrees of deviation in the measured electron energy distribution from a simple power law, in the form of an excess around 0.1-1 TeV energies. An even more prominent deviation and excess has been observed in the fraction of CR positrons around 10 and 100 GeV energies. These observations have received considerable attention and many theoretical models have been proposed to explain them. The models rely on either dark matter annihilation/decay or specific nearby astrophysical sources, and involve several additional assumptions regarding dark matter distribution or particle acceleration. In this paper, we show that the observed excesses in the electron spectrum may be easily re-produced without invoking any unusual sources other than the general diffuse Galactic components of CRs. The model presented here assumes a power-law injection of electrons (and protons) by supernova remnants (SNRs), and evaluates their expected energy spectrum based on a simple kinetic equation describing the propagation of charged particles in the interstellar medium (ISM). The primary physical effect involved is the Klein-Nishina suppression of the electron cooling rate around TeV energies. With a very reasonable choice of the model parameters characterizing the local ISM, we can reproduce the most recent observations by the Fermi and HESS experiments. Interestingly, in our model the injection spectral index of CR electrons becomes comparable to, or even equal to that of CR protons. The Klein-Nishina effect may also affect the propagation of the secondary e +- pairs, and therefore modify the CR positron-to-electron ratio. We have explored this possibility by considering two mechanisms for production of e +- pairs within the Galaxy. The first is due to the decay of p+-'s produced by interaction of CR nuclei with ambient protons. The second source discussed here is due to the annihilation of the diffuse Galactic g-rays on the stellar photon field. We find that high positron fraction increasing with energy, as claimed by the PAMELA experiment, cannot be explained in our model with the conservative set of the model parameters. We are able, however, to reproduce the PAMELA (as well as the Fermi and HESS) results assuming high values of the starlight and interstellar gas densities, which would be more appropriate for vicinities of SNRs. A possible solution to this problem may be that CRs undergo most of their interactions near their sources due to the efficient trapping in the far upstream of supernova shocks by self-generated, CR-driven turbulence.

Acceleration and transport of high-energy particles and fluid dynamics of atmospheric plasma are interrelated aspects of solar flares, but for convenience and simplicity they were artificially separated in the past. We present here self-consistently combined Fokker-Planck modeling of particles and hydrodynamic simulation of flare plasma. Energetic electrons are modeled with the Stanford unified code of acceleration, transport, and radiation, while plasma is modeled with the Naval Research Laboratory flux tube code. We calculated the collisional heating rate directly from the particle transport code, which is more accurate than those in previous studies based on approximate analytical solutions. We repeated the simulation of Mariska et al. with an injection of power law, downward-beamed electrons using the new heating rate. For this case, a [?]10% difference was found from their old result. We also used a more realistic spectrum of injected electrons provided by the stochastic acceleration model, which has a smooth transition from a quasi-thermal background at low energies to a nonthermal tail at high energies. The inclusion of low-energy electrons results in relatively more heating in the corona (versus chromosphere) and thus a larger downward heat conduction flux. The interplay of electron heating, conduction, and radiative loss leads to stronger chromospheric evaporation than obtained in previous studies, which had a deficit in low-energy electrons due to an arbitrarily assumed low-energy cutoff. The energy and spatial distributions of energetic electrons and bremsstrahlung photons bear signatures of the changing density distribution caused by chromospheric evaporation. In particular, the density jump at the evaporation front gives rise to enhanced emission, which, in principle, can be imaged by X-ray telescopes. This model can be applied to investigate a variety of high-energy processes in solar, space, and astrophysical plasmas.

Solar energetic particles show a rich variety of spectra and relative abundances of many ionic species and their isotopes. A long-standing puzzle has been the extreme enrichments of 3He ions. The most extreme enrichments are observed in low-fluence, the so-called impulsive, events which are believed to be produced at the flare site in the solar corona with little scattering and acceleration during transport to the Earth. In such events, 3He ions show a characteristic concave curved spectra in a log-log plot. In two earlier papers of Liu et al., we showed how such extreme enrichments and spectra can result in the model developed by Petrosian and Liu, where ions are accelerated stochastically by plasma waves or turbulence. In this paper, we address the relative distributions of the fluences of 3He and 4He ions presented by Ho et al., which show that while the distribution of 4He fluence (which we believe is a good measure of the flare strength) like many other extensive characteristics of solar flare is fairly broad, the 3He fluence is limited to a narrow range. These characteristics introduce a strong anticorrelation between the ratio of the fluences and the 4He fluence. One of the predictions of our model presented in the 2006 paper was the presence of steep variation of the fluence ratio with the level of turbulence or the rate of acceleration. We show here that this feature of the model can reproduce the observed distribution of the fluences with very few free parameters. The primary reason for the success of the model in both fronts is because fully ionized 3He ion, with its unique charge-to-mass ratio, can resonantly interact with plasma modes not accessible to 4He and be accelerated more readily than 4He. Essentially in most flares, all background 3He ions are accelerated to few MeV/nucleon range, while this happens for 4He ions only in very strong events. A much smaller fraction of 4He ions reach such energies in weaker events.

It is well recognized that the presence of magnetic fields will lead to anisotropic energy cascade and dissipation of astrophysical turbulence. With the diffusion approximation and linear dissipation rates, we study the cascade and damping of Alfven-cyclotron fluctuations in solar plasmas numerically for two diagonal diffusion tensors, one (isotropic) with identical components for the parallel and perpendicular directions (with respect to the magnetic field) and one with different components (nonisotropic). It is found that for the isotropic case the steady-state turbulence spectra are nearly isotropic in the inertial range and can be fitted by a single power-law function with a spectral index of -3/2, similar to the Iroshnikov-Kraichnan phenomenology, while for the nonisotropic case the spectra vary greatly with the direction of propagation. The energy fluxes in both cases are much higher in the perpendicular direction than in the parallel direction due to the angular dependence (or inhomogeneity) of the components. In addition, beyond the MHD regime the kinetic effects make the spectrum softer at higher wavenumbers. In the dissipation range the turbulence spectrum cuts off at the wavenumber, where the damping rate becomes comparable to the cascade rate, and the cutoff wavenumber changes with the wave propagation direction. The angle-averaged turbulence spectrum of the isotropic model resembles a broken power law, which cuts off at the maximum of the cutoff wavenumbers or the 4He cyclotron frequency. Taking into account the Doppler effects, the model naturally reproduces the broken power-law turbulence spectra observed in the solar wind and predicts that a higher break frequency always comes along with a softer dissipation range spectrum that may be caused by the increase of the turbulence intensity, the reciprocal of the plasma bp, and/or the angle between the solar wind velocity and the mean magnetic field. These predictions can be tested by detailed comparisons with more accurate observations.

We present a detailed imaging and spectroscopic study of the conjugate hard X-ray (HXR) footpoints (FPs) observed with the Ramaty High Energy Solar Spectroscopic Imager (RHESSI) in the 2003 October 29 X10 flare. The double FPs first move toward and then away from each other, mainly parallel and perpendicular to the magnetic neutral line, respectively. The transition of these two phases of FP unshearing motions coincides with the direction reversal of the motion of the loop-top (LT) source, and with the minima of the estimated loop length and LT height. We find temporal correlations between the HXR flux, spectral index, and magnetic field strength of each FP. The HXR flux exponentially correlates with the magnetic field strength, which also anticorrelates with the spectral index before the second HXR peak's maximum, suggesting that particle acceleration sensitively depends on the magnetic field strength and/or reconnection rate. Asymmetries are observed between the FPs: on average, the eastern FP is 2.2 times brighter in HXR flux and 1.8 times weaker in magnetic field strength, and moves 2.8 times faster away from the neutral line than the western FP; the estimated coronal column density to the eastern FP from the LT source is 1.7 times smaller. The two FPs have marginally different spectral indices. The eastern-to-western FP HXR flux ratio and magnetic field strength ratio are anticorrelated only before the second HXR peak's maximum. Neither magnetic mirroring nor column density alone can explain the totality of these observations, but their combination, together with other transport effects, might provide a full explanation. We have also developed novel techniques to remove particle contamination from HXR counts and to estimate effects of pulse pileup in imaging spectroscopy, which can be applied to other RHESSI flares in similar circumstances.

We address the problem of particle acceleration in solar flares by fast modes which may be excited during the reconnection and undergo cascade and are subjected to damping. We extend the calculations beyond the quasi-linear approximation and compare the acceleration and scattering by transit time damping and gyroresonance interactions. We find that the acceleration is dominated by the so-called transit time damping mechanism. We estimate the total energy transferred into particles and show that our approach provides sufficiently accurate results. We compare this rate with the energy-loss rate. Scattering by fast modes appears to be sufficient to prevent the protons from escaping the system during the acceleration. Confinement of electrons, on the other hand, requires the existence of plasma waves. Electrons can be accelerated to GeV energies through the process described here for solar flare conditions.

We investigate the feasibility of bremsstrahlung radiation from "nonthermal" electrons as a source of hard X-rays from the intracluster medium of clusters of galaxies. With an exact treatment of the Coulomb collisions in a Fokker-Planck analysis of the electron distribution, we find that the severe difficulties with lifetimes of nonthermal particles found earlier by Petrosian in 2001 using a cold-target model remain problematic. We then address the possible acceleration of background electrons into a nonthermal tail. We assume a simplified but generic acceleration rate and determine the expected evolution of an initially Maxwellian distribution of electrons. We find that strong nonthermal components arise only for a rapid rate of acceleration, which also heats up the entire plasma. These results confirm the conclusion that if the observed nonthermal excesses are due to some process accelerating the background thermal electrons, then this process must be short lived.

Here we investigate some aspects of stochastic acceleration of ultrarelativistic electrons by magnetic turbulence. In particular, we discuss the steady state energy spectra of particles undergoing momentum diffusion due to resonant interactions with turbulent MHD modes, taking rigorously into account direct energy losses connected with different radiative cooling processes. For the magnetic turbulence we assume a given power spectrum of the type W(k) [?] k[?]q $&mathstrut;{&cal; W} (k) ∝ k^−q$ . In contrast to the previous approaches, however, we assume a finite range of turbulent wavevectors k, consider a variety of turbulence spectral indices 1 [?] q[?] 2, and concentrate on the case of a very inefficient particle escape from the acceleration site. We find that for different cooling and injection conditions, stochastic acceleration processes tend to establish a modified ultrarelativistic Maxwellian distribution of radiating particles, with the high-energy exponential cutoff shaped by the interplay between cooling and acceleration rates. For example, if the timescale for the dominant radiative process scales with the electron momentum as [?] pr, the resulting electron energy distribution is of the form ne(p) [?] p2exp [ [?] (1/a)(p/peq)a] , where a = 2 [?] q [?] r and peq is the equilibrium momentum defined by the balance between the stochastic acceleration and energy loss timescales. We also discuss in more detail the synchrotron and inverse-Compton emission spectra produced by such an electron energy distribution, taking into account Klein-Nishina effects. We point out that the curvature of the high-frequency segments of these spectra, even though they are produced by the same population of electrons, may be substantially different between the synchrotron and inverse-Compton components.

We present data analysis and interpretation of an M1.4 class flare observed with the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) on 2002 April 30. This event, with its footpoints occulted by the solar limb, exhibits a rarely observed, but theoretically expected, double-source structure in the corona. The two coronal sources, observed over the 6-30 keV range, appear at different altitudes and show energy-dependent structures with the higher energy emission being closer together. Spectral analysis implies that the emission at higher energies in the inner region between the two sources is mainly nonthermal, while the emission at lower energies in the outer region is primarily thermal. The two sources are both visible for about 12 minutes and have similar light curves and power-law spectra above about 20 keV. These observations suggest that the magnetic reconnection site lies between the two sources. Bidirectional outflows of the released energy in the form of turbulence and/or particles from the reconnection site could be the source of the observed radiation. The spatially resolved thermal emission below about 15 keV, on the other hand, indicates that the lower source has a larger emission measure but a lower temperature than the upper source. This is likely the result of the differences in the magnetic field and plasma density of the two sources.

Flares in Sagittarius A* are produced by hot plasmas within a few Schwarzschild radii of the supermassive black hole at the Galactic center. The recent detection of a correlation between the spectral index and flux during a near-infrared (NIR) flare provides a means to conduct detailed investigations of the plasma heating and radiation processes. We study the evolution of the electron distribution function under the influence of a turbulent magnetic field in a hot collisionless plasma. The magnetic field, presumably generated through instabilities in the accretion flow, can both heat the plasma through resonant wave-particle coupling and cool the electrons by radiation. The electron distribution can generally be approximated as relativistic Maxwellian. To account for the observed correlation, we find that the magnetic field needs to be anticorrelated with the electron "temperature." NIR and X-ray light curves are produced for a cooling and a heating phase. The model predicts simultaneous flare activity in the NIR and X-ray bands, which can be compared with observations. These results can be applied to MHD simulations to study the radiative characteristics of collisionless plasmas, especially accretion flows in low-luminosity active galactic nuclei.

Evidence for nonthermal activity in clusters of galaxies is well established from radio observations of synchrotron emission by relativistic electrons. New windows in the extreme-ultraviolet and hard X-ray ranges have provided more powerful tools for the investigation of this phenomenon. Detections of hard X-rays in the 20-100 keV range have been reported for several clusters of galaxies, notably from Coma and others. Based on these earlier observations we identified the relatively high-redshift cluster 1ES 0657-558 (also known as RX J0658-5557) as a good candidate for hard X-ray observations. This cluster, also known as the Bullet Cluster, has many other interesting and unusual features, most notably that it is undergoing a merger, clearly visible in the X-ray images. Here we present results from successful RXTE observations of this cluster. We summarize past observations and their theoretical interpretation that guided us in the selection process. We describe the new observations and present the constraints we can set on the flux and spectrum of the hard X-rays. Finally, we discuss the constraints one can set on the characteristics of accelerated electrons that produce the hard X-rays and the radio radiation.

We present analyses of the spatial and spectral evolution of hard X-ray emission observed by RHESSI during the impulsive phase of an M1.7 flare on 2003 November 13. In general, as expected, the loop top (LT) source dominates at low energies, while the footpoint (FP) sources dominate the high-energy emission. At intermediate energies, both the LT and FPs may be seen, but during certain intervals emission from the legs of the loop dominates, in contrast to the commonly observed LT and FP emission. The hard X-ray emission tends to rise above the FPs and eventually merge into a single LT source. This evolution starts at low energies and proceeds to higher energies. The spectrum of the resultant LT source becomes more and more dominated by a thermal component with an increasing emission measure as the flare proceeds. The soft and hard X-rays show a Neupert-type behavior. With a nonthermal bremsstrahlung model, the brightness profile along the loop is used to determine the density profile and its evolution, which reveals a gradual increase of the gas density in the loop. These results are evidence for chromospheric evaporation and are consistent with the qualitative features of hydrodynamic simulations of this phenomenon. However, some observed source morphologies and their evolution cannot be accounted for by previous simulations. Therefore, simulations with more realistic physical conditions are required to explain the results and the particle acceleration and plasma heating processes.

The near-IR and X-ray flares in Sagittarius A* are believed to be produced by relativistic electrons via synchrotron and synchrotron self-Comptonization, respectively. These electrons are likely energized by turbulent plasma waves through second-order Fermi acceleration that, in combination with the radiative cooling processes, produces a relativistic Maxwellian distribution in the steady state. This model has four principal parameters, namely the magnetic field B, the electron density n and temperature gcmec2, and the size of the flare region R. In the context of stochastic acceleration, the quantities Rn1/2B and gcRn should remain nearly constant in time. Therefore, simultaneous spectroscopic observations in the NIR and X-ray bands can readily test the model, which, if proven to be valid, may be used to determine the evolution of the plasma properties during an eruptive event with spectroscopic observations in either band or simultaneous flux density measurements in both bands. The formulae can be applied to other isolated or confined systems, where electrons are accelerated to relativistic energies by plasma wave turbulence and produce most of the emission via synchrotron processes.

Stochastic acceleration of electrons interacting resonantly with a turbulent magnetic field in a small accretion torus appears to be the likely mechanism responsible for much of Sagittarius A*'s millimeter and shorter wavelength spectrum. The longer wavelength radiation is produced at larger radii by electrons either diffusing from smaller scales or accelerated in situ. An important prediction of this model is the ejection of a significant flux of relativistic protons from a magnetic-field-dominated acceleration site into the wind-shocked medium surrounding the black hole. Recently, several air Cerenkov telescopes, notably HESS, have detected TeV emission from the Galactic center, with characteristics hinting at a p-p-induced pion decay process for the g-ray emission. Given (1) the size of this acceleration region measured in the radio band and (2) the wind-injected ISM mapped with Chandra using the diffuse X-rays, it is feasible to test the idea that protons accelerated within ~20 Schwarzschild radii of the black hole produce the TeV emission farther out. We show a fraction of TeV protons scattering about once within ~3 pc of Sagittarius A* and the proton power (~1037 ergs s-1) produced in concert with the 7 mm radio emission matches the TeV luminosity well. This model explains why the TeV source does not vary on a timescale of a year or less. The particle cascade generated by the p-p scatterings also produces bremsstrahlung, inverse Compton, and synchrotron emission at longer wavelengths from secondary particles. We compare these with current measurements and demonstrate that GLAST will detect this source during its one-year all-sky survey.

We describe the cascade of plasma waves or turbulence injected, presumably by reconnection, at scales comparable to the size of a solar flare loop, L ~ 109 cm, to scales comparable to elementary particle gyroradii and evaluate their damping at small scales by various mechanisms. We show that the classical viscous damping valid on scales larger than the collision mean free path (~108 cm) is unimportant for magnetically dominated or low-b plasmas and the primary damping mechanism is the collisionless damping by the background particles. We show that the damping rate is proportional to the total random momentum density of the particles. For solar flare conditions this means that in most flares, except the very large ones in which essentially all background electrons are accelerated into a nonthermal distribution, the damping is dominated by thermal background electrons. In general, damping by protons is negligible compared to that of electrons except for rare proton-dominated flares with strong nuclear gamma-ray line emission and for quasi-perpendicular propagating waves. We also determine the critical scale below which the damping becomes important and the spectrum of the turbulence steepens. We show that this scale has a strong dependence on the propagation angle of the waves with respect to the background magnetic field, resulting in a highly anisotropic spectral distribution, with quasi-parallel and quasi-perpendicular waves cascading undamped to small scales.

We present a study of the spatial and spectral evolution of the loop-top (LT) sources in a sample of six flares near the solar limb observed by RHESSI. A distinct coronal source, which we identify as the LT source, was seen in each of these flares from the early "preheating" phase through the late decay phase. Spectral analyses reveal an evident steep power-law component in the preheating and impulsive phases, suggesting that the particle acceleration starts upon the onset of the flares. In the late decay phase the LT source has a thermal spectrum and appears to be confined within a small region near the top of the flare loop and does not spread throughout the loop, as is observed at lower energies. The total energy of this source decreases usually faster than expected from the radiative cooling but much slower than that due to the classical Spitzer conductive cooling along the flare loop. These results indicate the presence of a distinct LT region, where the thermal conductivity is suppressed significantly and/or there is a continuous energy input. We suggest that plasma wave turbulence could play important roles in both heating the plasma and suppressing the conduction during the decay phase of solar flares. With a simple quasi-steady loop model we show that the energy input in the gradual phase can be comparable to that in the impulsive phase and demonstrate how the observed cooling and confinement of the LT source can be used to constrain the wave-particle interaction.

Recent near-IR (NIR) and X-ray observations of Sagittarius A*'s spectrum have yielded several strong constraints on the transient energizing mechanism, justifying a reexamination of the stochastic acceleration model proposed previously for these events. We here demonstrate that the new results are fully consistent with the acceleration of electrons via the transit-time damping process. But more importantly, these new NIR and X-ray flares now can constrain the source size, the gas density, the magnetic field, and the wave energy density in the turbulent plasma. Future simultaneous multiwavelength observations with good spectral information will, in addition, allow us to study their temporal evolution, which will eventually lead to an accurate determination of the behavior of the plasma just minutes prior to its absorption by the black hole.

We study the acceleration in solar flares of 3He and 4He from a thermal background by parallel-propagating plasma waves with a general broken power-law spectrum. The exact dispersion relation for a cold plasma is used to describe the relevant wave modes, and the Coulomb collision loss and escape processes are included. Under the quasi-linear approximation, the pitch-angle-averaged acceleration time of a-particles is at least 1 order of magnitude longer than that of 3He ions at low energies and starts to approach that of 3He beyond a few tens of keV nucleon-1. Because their loss and escape times are comparable, the acceleration of 4He is suppressed significantly at low energies, and the spectrum of the accelerated a-particles is always softer than that of 3He. Quantitative results depend primarily on the wave generation and damping length scales, the electron plasma to gyrofrequency ratio, and the intensity of turbulence. The model gives a reasonable account of the observed low-energy 3He and 4He fluxes and spectra in the impulsive solar energetic particle events observed with the Advanced Composition Explorer. Other acceleration processes and/or stochastic acceleration by other wave modes seem to be required to explain the occasionally observed decrease of 3He to 4He ratio at energies beyond a few MeV nucleon-1.

Stochastic acceleration of electrons and protons by waves propagating parallel to the large-scale magnetic fields of magnetized plasmas is studied with emphasis on the feasibility of accelerating particles from a thermal background to relativistic energies and with the aim of determining the relative acceleration of the two species in one source. In general, the stochastic acceleration by these waves results in two distinct components in the particle distributions, a quasi-thermal and a hard nonthermal, with the nonthermal one being more prominent in hotter plasmas and/or with higher level turbulence. This can explain many of the observed features of solar flares. Regarding the proton-to-electron ratio, we find that in a pure hydrogen plasma the dominance of the wave-proton interaction by the resonant Alfven mode reduces the acceleration rate of protons in the intermediate energy range significantly, while the electron-cyclotron and Whistler waves are very efficient in accelerating electrons from a few keV to MeV energies. The presence of such an acceleration barrier prohibits the proton acceleration under solar flare conditions. This difficulty is alleviated when we include the effects of 4He in the dispersion relation and the damping of the turbulent waves by the thermal background plasma. The additional 4He cyclotron branch of the turbulent plasma waves suppresses the proton acceleration barrier significantly, and the steep turbulence spectrum in the dissipation range makes the nonthermal component have a near power-law shape. The relative acceleration of protons and electrons is very sensitive to a plasma parameter a = ope/Oe, where ope and Oe are the electron plasma frequency and gyrofrequency, respectively. Protons are preferentially accelerated in weakly magnetized plasmas (large a). The formalism developed here is applicable to the acceleration of other ion species and to other astrophysical systems.

Temporal and spectral characteristics of prompt emission of gamma-ray burst (GRB) pulses are the primary observations for constraining the energizing and emission mechanisms. In spite of very complex temporal behavior of the GRBs, several patterns have been discovered in how some spectral characteristics change during the decaying phase of individual, well-defined long (greater than a few seconds) pulses. In this paper we compare these observed signatures with those expected from a relativistically expanding, shock-heated, and radiation-emitting plasma shell. Within the internal shock model and assuming a short cooling time, we show that the angular dependence in arrival time from a spherical expanding shell can explain the general characteristics of some well-defined long GRB pulses. This includes the pulse shape, with a fast rise and a slower decay, [?](1 + t/t)2, where t is a time constant, and the spectral evolution, which can be described by the hardness-intensity correlation (HIC), with the intensity being proportional to the square of the hardness measured by the value of the peak, e.g., Ep of the nFn spectrum. A variation of the relevant timescales involved (the angular spreading and the dynamic) can explain the broad, observed dispersion of the HIC index. Reasonable estimates of physical parameters lead to situations where the HIC relation deviates from a pure power law, features that are indeed present in the observations. Depending on the relative values of the rise and decay times of the intrinsic light curve, the spectral/temporal behavior, as seen by an observer, will produce the hard-to-soft evolution and the so-called tracking pulses. In our model the observed spectrum is a superposition of many intrinsic spectra arriving from different parts of the fireball shell with varying spectral shifts. Therefore, it will be broader than the emitted spectrum and its spectral parameters could have complex relations with the intrinsic ones. Furthermore, we show that the softening of the low-energy power-law index, that has been observed in some pulses, can be explained by geometric effects and does not need to be an intrinsic behavior.

The discovery of hard X-ray sources near the top of a flaring loop by the Hard X-Ray Telescope on board the Yohkoh satellite represents a significant progress toward the understanding of the basic processes driving solar flares. In this paper we extend the previous study of limb flares by Masuda by including all Yohkoh observations up through 1998 August. We report that from 1991 October to 1998 August, 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 eight previously unanalyzed flares. Of these 18 events, 15 show detectable impulsive loop top emission. Considering that the finite dynamic range (about a decade) of the detection introduces a strong bias against observing comparatively weak loop top sources, we conclude that loop top emission is a common feature of all flares. We summarize the observations of the footpoint-to-loop top flux ratio and the spectral indexes. 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 indexes of the loop top 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.

In this paper, we explore time-resolved gamma-ray burst (GRB) spectra in the context of the synchrotron emission model presented by Lloyd & Petrosian in 2000. First, we show that our model--which involves three distinct emission regimes--can provide excellent fits to the time-resolved spectra of GRBs, and we present these results for a few bursts. We then describe how the phenomenological Band spectrum can be interpreted in the context of our models based on the value of the low-energy photon index a. We discuss the types of correlations one would expect to observe among the Band parameters if these models are correct. We then compare these predictions to the existing data, combining a sample of 2026 time-resolved spectra (from approximately 80 bursts). We show that the correlations found in the data are consistent with the models and discuss the constraints they place on the emission physics. In particular, we find a (~4 s) negative correlation between the peak of the nFn spectrum Ep and the low-energy photon index a for bursts with - img1.gif < a < 0, in contrast to what is predicted by the instrumental effect discussed in Lloyd & Petrosian. We suggest that this correlation is simply due to the mechanism responsible for producing values of a above the value of - img1.gif--namely, a decreasing mean pitch angle of the electrons. We also show that Ep is correlated with the photon flux and interpret this as a result of changing magnetic field or characteristic electron energy between emission episodes. Finally, we discuss the implications that our results have on particle acceleration in GRBs and prospects for further testing these models with the anticipated data from the High Energy Transient Explorer 2, Swift, and the Gamma-Ray Large Area Space Telescope.

Some clusters of galaxies, in addition to thermal bremsstrahlung (TB), emit detectable diffuse radiation from the intracluster medium (ICM) at radio, EUV, and hard X-ray (HXR) ranges. The radio radiation must be due to synchrotron by relativistic electrons, and the inverse Compton scattering by the cosmic microwave background radiation of the same electrons is the most natural source for the HXR and perhaps the EUV emissions. However, simple estimates give a weaker magnetic field than that suggested by Faraday rotation measurements. Consequently, nonthermal bremsstrahlung (NTB) and TB have also been suggested as sources of these emissions. We show that NTB cannot be the source of the HXRs (except for a short period) and that the difficulty with the low magnetic field in the IC model is alleviated if the effects of observational selection bias, nonisotropic pitch angle distribution, and spectral breaks in the energy distribution of the relativistic electrons are taken into account. From these considerations and the strength of the EUV emission, we derive a spectrum for the radiating electrons and discuss possible acceleration scenarios for its production. We show that continuous and in situ acceleration in the ICM of the background thermal electrons is difficult and requires unreasonably high energy input. Similarly, acceleration of injected relativistic electrons, say, by galaxies, seems unreasonable because it will give rise to a much flatter spectrum of electrons than required, unless a large fraction of energy input is carried away by electrons escaping the ICM, in which case one obtains EUV and HXR emissions extending well beyond the boundaries of the diffuse radio source. A continuous emission by a cooling spectrum resulting from interaction with ICM of electrons accelerated elsewhere also suffers from similar shortcomings. The most likely scenario appears to be an episodic injection acceleration model, whereby one obtains a time-dependent spectrum that for certain phases of its evolution satisfies all the requirements.

We investigate synchrotron emission models as the source of gamma-ray burst (GRB) spectra. We show that including the possibility for synchrotron self-absorption, a "smooth cutoff" to the electron energy distribution, and an anisotropic distribution for the electron pitch angles produces a whole range of low-energy spectral behavior. In addition, we show that the procedure of spectral fitting to GRB data over a finite bandwidth can introduce a spurious correlation between spectral parameters--in particular, the value of the peak of the nFn spectrum, Ep, and the low-energy photon spectral index a (the lower Ep is, the lower [softer] the fitted value of a will be). From this correlation and knowledge of the Ep distribution, we show how to derive the expected distribution of a. We show that optically thin synchrotron models with an isotropic electron pitch angle distribution can explain the distribution of a below a = - img1.gif. This agreement is achieved if we relax the unrealistic assumption of the presence of a sharp low-energy cutoff in the spectrum of accelerated electrons and allow for a more gradual break. We show that this low-energy portion of the electron spectrum can be at most flat. We also show that optically thin synchrotron models with an anisotropic electron pitch angle distribution can explain all bursts with - img1.gif [?] a [?] 0. The very few bursts with low-energy spectral indices that fall above a = 0 may be due to the presence of a synchrotron self-absorption frequency entering the lower end of the BATSE window. Our results also predict a particular relationship between a and Ep during the temporal evolution of a GRB. We give examples of spectral evolution in GRBs and discuss how its behavior is consistent with the above models.

We investigate the cosmological evolution of gamma-ray bursts (GRBs) using the total gamma-ray fluence as a measure of the burst strength. This involves an understanding of the distributions of the spectral parameters of GRBs, as well as the total fluence distribution--both of which are subject to detector selection effects. We present new nonparametric statistical techniques to account for these effects, and we use these methods to estimate the true distribution of the peak of the nFn spectrum--Ep--from the raw distribution. The distributions are obtained from four-channel data, and therefore are rough estimates; hence we emphasize the methods and present qualitative results. Given its spectral parameters, we then calculate the total fluence for each burst and compute its cumulative and differential distributions. We use these distributions to estimate the cosmological rate evolution of GRBs for three cosmological models. Our two main conclusions are the following: (1) given our estimates of the spectral parameters, we find that there may exist a significant number of high-Ep bursts that are not detected by BATSE; and (2) we find a GRB comoving rate density quite different from that of other extragalactic objects--in particular, it is different from the recently determined star formation rate.

We describe classical cosmological tests, such as the log N-log S, redshift-magnitude, and angular diameter tests, and propose some new tests of the evolution of galaxies and the universe. Most analyses of these tests treat the problem in terms of a luminosity function and its evolution. The main thrust of this paper is to show that this is inadequate and can lead to incorrect conclusions when dealing with high-redshift sources. We develop a proper treatment in three parts. First, we describe these tests based on the isophotal values of quantities such as flux, size, or surface brightness. We show the shortcomings of the simple point-source approximation based solely on the luminosity function and consideration of the flux limit. We emphasize the multivariate nature of the problem and quantify the effects of other selection biases arising from the surface brightness and angular size limitations. In these considerations, the surface brightness profile and the distribution of the basic parameters describing it play a critical role in modeling the problem. In general, in the isophotal scheme the data analysis and comparison with the model predictions is complicated. Next, we show that considerable simplification is achieved if these test are carried out in some sort of metric scheme, for example that suggested by Petrosian. This scheme, however, is limited to well-resolved sources. Finally, we describe the new tests and compare them to the traditional tests, demonstrating the observational and modeling ease that they provide. These new procedures, which can use the data to a fuller extent than the isophotal or metric-based tests, amount to simply counting the pixels or adding their intensities as a function of the surface brightness of all galaxies instead of dealing with surface brightness, size, and flux (or magnitude) of individual galaxies. We also show that a comparison of the data with the theoretical models of the distributions and evolution of galaxies has the simplicity of the metric test and utilizes the data as fully as the isophotal test.

In this paper we consider the interaction of particles with turbulent plasma waves propagating perpendicular to the ordered magnetic field. Our investigation of the dispersion relation for waves propagating at an arbitrary angle th with respect to the magnetic field lines indicates that the qualitative behavior of the acceleration characteristics at all angles th[?]0 are similar to that of the th=p/2 case. We use the perpendicular case as a representative example because it leads to a much simpler analysis. Therefore, the results presented here and the results of our earlier papers dealing with the th=0 case will give a somewhat complete picture of stochastic acceleration for all waves. Unlike the th=0 case, where only the fundamental mode of each wave contributes, for general value of th, and in particular for the perpendicular case, many harmonics enter into the equation, making the analysis more complicated. We develop a recipe for evaluation of the contributions of all harmonics and derive an analytic expression for the asymptotic behavior at nonrelativistic energies. We use the formalism of our previous papers and find that all Fokker-Planck coefficients for the perpendicular waves are of the same order of magnitude, so the ratio of the pitch angle to momentum (or energy) diffusion rates is of order unity at all energies and pitch angles. This is unlike the parallel case, where this ratio varies from being much less than 1 at low energies to much greater than 1 at relativistic energies. As a result, the simplifications of the transport equation arising from these inequalities are no longer applicable. On the other hand, we find that when the transport equation for the th=p/2 case is expressed in terms of diffusion in the parallel and perpendicular components of the momentum, only diffusion in the perpendicular component is present. This again yields a one-dimensional diffusion equation and implies that the parallel momentum does not change. Consequently, we expect a rapid anisotropization of the pitch angle distribution (into a pancake-like distribution) for particles accelerated by perpendicular waves. From comparison of the acceleration rate of the thermal particles with the decay rate of the waves in hot plasmas, we find that a substantial fraction of the background plasma electrons can be accelerated through this process for reasonable values of the energy density and spectrum of turbulence.

We use several quasar samples (Large Bright QSO Survey, Homogeneous Bright QSO Survey, Durham/AAT, and Edinburgh QSO Survey) to determine the density functions and the luminosity evolution of quasars. Combining these different samples and accounting for varying selection criteria require tests of correlation and the determination of density functions for multiply truncated data. We describe new nonparametric techniques for accomplishing these tasks, which have been developed recently by Efron & Petrosian. With these methods, the luminosity evolution can be found through an investigation of the correlation of the bivariate distribution of luminosities and redshifts. Here, one assumes a cosmological model to convert the observed fluxes into luminosities. We use matter-dominated models with either zero cosmological constant or zero spatial curvature. Of the two most commonly used models for luminosity evolution, L[?]ekt(z) and L[?](1+z)k', we find that the second functional form is a better description of the data at all luminosities; we find k'=2.58 ([2.14, 2.91] 1 s region) for the Einstein-de Sitter cosmological model. Using this form of luminosity evolution, we determine a global luminosity function and the evolution of the comoving density for the two types of cosmological models. For the Einstein-de Sitter cosmological model we find a relatively strong increase in comoving density up to z[?]2, at which point the density peaks and begins to decrease rapidly. This is in agreement with results from high-redshift surveys. However, we find that pure luminosity evolution, i.e., constant comoving density, is possible for some cosmological models for 3[?]2. We find that the local luminosity function Ph(L0) exhibits the usual double power-law behavior. The luminosity density (z)=[?]LPs(L, z) dL, where Ps(L, z) is the luminosity function, is found to increase rapidly at low redshift and to reach a peak at around z[?]2. Our results for (z) are compared to results from high-redshift surveys and to the variation of the star formation rate with redshift.

The aim of this paper is to investigate the spatial structure of the impulsive phase hard X-ray emission from solar flares. This work is motivated by the Yohkoh and the forthcoming High-Energy Solar Spectroscopic Imager (HESSI) observations. Summarizing past results, it is shown that the transport effects can account for the observations in inhomogeneous loop models where there is a strong field convergence and/or density enhancement at the top of the flaring loop. Scattering by plasma turbulence at the acceleration site or a pancake-type pitch-angle distribution of the accelerated electrons can also give rise to enhanced emission at the looptops. These could be a natural consequence of acceleration by plasma waves. This paper considers a general case of stochastic scattering and acceleration that leads to an isotropic pitch-angle distribution and an enhanced emission from the looptops or the acceleration site. Following the formalism developed in earlier papers, the strength and the spectrum of the radiation expected from the acceleration site and the footpoints are evaluated and their dependence on the parameters describing the acceleration process and the flare plasma are determined. The theoretical ratio of these two intensities and relative values of their spectral indices are compared with Yohkoh observations, demonstrating that the above-mentioned parameters can be constrained with such observations. It is shown that future high spatial and spectral resolution observations, for example those expected from HESSI, will be able to begin to distinguish between different models and constrain their parameters.

We investigate the possibility of stochastic acceleration of background low-energy electrons by turbulent plasma waves. We consider the resonant interaction of the charged particles with all branches of the transverse plasma waves propagating parallel to a uniform magnetic field. Numerical results and asymptotic analytic solutions valid at nonrelativistic and ultrarelativistic energies are obtained for the acceleration and scattering times of electrons. These times have a strong dependence on plasma parameter a = ope/Oe (the ratio of electron plasma frequency to electron gyrofrequency) and on the spectral index of plasma turbulence. It is shown that particles with energies above a certain critical value may interact with higher frequency electromagnetic plasma waves, and this interaction is allowed only in plasmas with a < 1. We show that for nonrelativistic and semirelativistic electrons in low-a plasmas, the ratio of the acceleration time to the scattering time can be less than unity for a wide range of energies. From this we conclude that the transport equation derived for cosmic rays that requires this ratio to be much larger than unity is not applicable at these energies. An approximate "critical" value of particle energy above which the dynamics of charged particles may be described by this transport equation is determined as a function of plasma parameters. We propose new transport equation for the opposite limit (energies less than this critical value) when the acceleration rate is much faster than the pitch angle scattering rate. This equation is needed to describe the electron dynamics in plasmas with a [?] 0.1.

We examine four electron-dominated flares, two from the GRS instrument on 1989 March 6, and two from the EGRET and BATSE instruments on 1991 June 30 and 1991 July 2. Their photon spectra, which are almost all caused by electron bremsstrahlung radiation, show significant deviations from a simple power-law form. These are attributed to the deviations in the spectra of the accelerated electrons. We develop three stochastic acceleration models to explain the shape of the photon spectra: the hard sphere model, the whistler wave model, and a more general, but still simplified, stochastic acceleration model. For photon emissions, we use a simple sum of the thin target emission from the trapped electrons at the acceleration site near the loop top and the thick target emission from the escaping electrons which travel along the magnetic field lines and radiate in the denser chromosphere at the footpoints. We find that the hard sphere model does not fit any of the flares and can be ruled out. The other two models show that the high-energy cutoff in the two GRS flares can be attributed to synchrotron radiation losses in the presence of a 500 G magnetic field at the acceleration site. The observed break in the photon spectra of all four flares around 1 MeV is attributed to a combination of the energy dependence of the escape time of particles out of the acceleration region and the change in the energy dependence of the bremsstrahlung cross section between the nonrelativistic and relativistic regimes. Further steepening of the spectrum at even lower energies is caused by Coulomb losses at the acceleration site. We find that acceleration timescales as low as ~1 s are possible with a ratio of turbulent to the magnetic field energy densities of ~10-4. We also set limits on the plasma density, the size of the acceleration region, and the spectrum of the plasma turbulence.