The effect of wave generation on HXR bremsstrahlung spectra from flare thick-target beams

Fast electrons in the solar atmosphere are detected by their hard X-ray bremsstrahlung and by type III radio bursts caused by ‘bump-on-tail’ plasma wave generation. This paper investigates empirically the effect of wave generation on the HXR spectrum. Purely collisional propagation of an electron beam generates a bump in the distribution function, due to stopping of low-velocity electrons. The consequent positive gradient means there is a possibility of wave generation, production of type III radio bursts, and energy redistribution of the electron beam. We have represented this relaxation parametrically and calculated the global bremsstrahlung HXR emission spectrum. We show that for a range of relaxed forms, with different local electron spectral shapes, the bremsstrahlung spectrum integrated over the whole target is identical in shape to the purely collisionally evolved beam. Our results show that spatially integrated HXR spectral measurements would be unable to distinguish between the presence or absence of relaxation effects. Only spatially resolved hard X-ray spectra, such as anticipated from the HESSI mission, will be able to remove this ambiguity in HXR diagnostics of beam relaxation.     

Low-Energy Cutoffs in Electron Spectra of Solar Flares: Statistical Survey

The Reuven Ramaty High Energy Spectroscopic Imager (RHESSI) X-ray data base (February 2002 – May 2006) has been searched to find solar flares with weak thermal components and flat photon spectra. Using a regularized inversion technique, we determine the mean electron flux distribution from count spectra for a selection of events with flat photon spectra in the 15 – 20 keV energy range. Such spectral behavior is expected for photon spectra either affected by photospheric albedo or produced by electron spectra with an absence of electrons in a given energy range (e.g., a low-energy cutoff in the mean electron spectra of nonthemal particles). We have found 18 cases that exhibit a statistically significant local minimum (a dip) in the range of 13 – 19 keV. The positions and spectral indices of events with low-energy cutoff indicate that such features are likely to be the result of photospheric albedo. It is shown that if the isotropic albedo correction is applied, all low-energy cutoffs in the mean electron spectrum are removed, and hence the low-energy cutoffs in the mean electron spectrum of solar flares above ∼ 12 keV cannot be viewed as real features. If low-energy cutoffs exist in the mean electron spectra, their energies should be less than ∼ 12 keV.     

Inversion of synchrotron spectra

The problem of synchrotron radiation spectra is treated from the viewpoint of deconvolving the spectrum of ultrarelativistic source electrons from the observed photon spectrum. It is shown that for homogeneous sources the problem amounts to inversion of a Meijer transform with a modified Bessel finction kernel. A precise analytic inversion is only possible in the complex plane but Meijer transform tables are available for a wide range of functions. More convenient inversion formulae prove possible by use of a Laplace transform approximation or by analysing the spectra in terms of their integral moments. The filtering property of the transform is also established showing that the contribution to the synchrotron spectrum of high frequency components in the electron spectrum declines exponentially with their frequency. Thus, as with other Laplace-like transforms, only a few terms in an electron spectrum expansion can be deconvolved for any plausible noise level in the synchrotron spectrum.     

Broadening of the thermal component of the prompt GRB emission due to rapid temperature evolution

The observations of the prompt emission of gamma ray bursts (GRB) by GLAST Burst Monitor (GBM), on board Fermi Gamma-ray Space Telescope, suggest the presence of a significant thermal spectral component, whose origin is not well understood. Recently, it has been shown that for long duration GRBs, the spectral width as defined as the logarithm of the ratio of the energies at which the spectrum falls to half its peak value, lie in the range of 0.84–1.3 with a median value of 1.07. Thus, while most of the GRB spectra are found to be too narrow to be explained by synchrotron emission from an electron distribution, they are also significantly broader than a blackbody spectrum whose width should be 0.54. Here, we consider the possibility that an intrinsic thermal spectrum from a fire-ball like model, may be observed to be broadened if the system undergoes a rapid temperature evolution. We construct a toy-model to show that for bursts with durations in the range 5–70 s, the widths of their 1 second time-averaged spectra can be at the most ≲ 0.557. Thus, while rapid temperature variation can broaden the detected spectral shape, the observed median value of ∼ 1.07 requires that there must be significant sub-photospheric emission and/or an anisotropic explosion to explain the broadening for most GRB spectra.     

Radio to optical spectral index variations along the M87 jet

CCD photometry and MERLIN observations of M87 (Virgo A) have been used to study the variations of the radio to optical spectral index along the jet. In general, the radio spectrum is flatter than the optical one and both become steeper with distance from the nucleus. The optical fluxes of the bright knots lie at or below the extrapolation of the radio spectrum. These properties can be explained by power-law spectra at low frequencies that turn down gradually beyond a cut-off frequency. The location of the local cut-off frequency is estimated by fitting the measured fluxes to the theoretical spectrum of a truncated power-law electron energy distribution. The results are interpreted in terms of models of synchrotron emission from shock waves in extragalactic jets.     

The derivation of parent electron spectra from bremsstrahlung hard X-ray spectra

We formulate a numerical method to derive the spectrum of the parent electrons from the hard X-ray spectrum produced in optically thin bremsstrahlung. The method can utilize any form for the bremsstrahlung cross sections, and it provides accurate estimates of uncertainties in the derived electron spectrum based on uncertainties in the photon measurements. This method is applied to test photon spectra, as well as to hard X-ray spectra of the 27 June, 1980 solar flare which was observed by high spectral resolution detectors. Future measurements with much more sensitive detectors will enable this method to be used to derive detailed, accurate flare electron spectra.     

Solar Microwave Bursts from Electron Populations with a 'Broken’ Energy Spectrum

Usually the gyrosynchrotron emission of microwave bursts from electron populations with a power-law (PL) energy distribution has been considered under the assumption that the spectral index of the distribution is constant over a wide range of energies. Meanwhile, there is strong evidence, in particular from hard X-ray and -ray, but also from cm/mm wavelength radio observations, that in many solar flare events the spectrum of the emitting electrons is characterized by a significant hardening at energies above 100–500 keV. We present some examples of calculated microwave burst spectra at cm/mm wavelengths taking into account the above evidence. It is shown that a break in the energy spectrum of the PL electrons can indeed result in a spectral hardening sometimes observed in microwave bursts at frequencies above 10–30 GHz.     

Inversion of Thick-Target Bremsstrahlung Spectra from Nonuniformly Ionised Plasmas

The effects of non-uniform plasma target ionisation on the spectrum of thick-target HXR bremsstrahlung from a non-thermal electron beam are analysed. In particular the effect of the target ionisation structure on beam collisional energy losses, and hence on inversion of an observed photon spectrum to yield the electron injection spectrum, is considered and results compared with those obtained under the usual assumption of a fully ionised target.The problem is formulated and solved in principle for a general target ionisation structure, then discussed in detail for the case of a step function distribution of ionisation with column depth as an approximation to the sharp coronal–chromospheric step structure in solar flare plasmas. It is found that such ionisation structure has very dramatic effects on derivation of the thick-target electron injection spectrum F₀(E₀) as compared with the result F*₀(E ₀) obtained under the usual assumption of a fully ionised target: (a) Inferred F*₀ contain more electrons than F ₀ and in some cases include electrons at energies where none are actually present. Although the total (energy-integrated) beam fluxes in the two cases do not differ by a factor of more than A_ee/A_eH, the spectral shapes can differ greatly over finite energy intervals resulting in the danger of misleading results for total fluxes obtained by extrapolation. (b) The unconstrained mathematical solution for F₀ for any photon spectrum is never unique, while that for F*₀ is unique. When the physical constraint F₀ 0 is added, for some photon spectra solutions for F₀ may not exist or may not be unique. (This is not an effect of noise but of real analytic ambiguity.) (c) For data corresponding to F*₀ with a low-energy cut-off, or a cut-off or rapid enough exponential decline at high energies, a unique solution F₀ does exist and we obtain a recursive summation for its evaluation.Consequently, in future work on the inversion of HXR bremsstrahlung spectra it will be vital for algorithms to include the effects of target ionisation if spurious results on thick-target electron spectra are not to be inferred. Finally it is pointed out that the depth of the transition zone, and its evaporative evolution during flares may be derivable from its effect on the HXR spectrum.     

A Hybrid Algorithm for Spectral Analysis

In this paper we present a method that combines evolution strategies (ES) and standard optimization algorithms to solve the problem of fitting line profiles of stellar spectra. This method provides a reliable decomposition and a reduction in computing time over conventional algorithms. Using a stellar spectrum as input, we implemented an evolution strategy to find an approximation of the continuum spectrum and spectral lines. After a few generations, the parameters found by ES are given as starting search point to a standard optimization algorithm, which then finds the correct spectral decomposition. We used Gaussian functions to fit spectral lines and the Planck function to represent the continuum spectrum. Our experimental results present the application of this method to real spectra, showing that they can be approximated very accurately. This revised version was published online in July 2006 with corrections to the Cover Date.     

Spectral variability in Cygnus X-3

We model the broad-band X-ray spectrum of Cyg X-3 in all states displayed by this source as observed by the Rossi X-ray Timing Explorer . From our models, we derive for the first time unabsorbed spectral shapes and luminosities for the full range of spectral states. We interpret the unabsorbed spectra in terms of Comptonization by a hybrid electron distribution and strong Compton reflection. We study the spectral evolution and compare with other black hole as well as neutron star sources. We show that a neutron star accretor is not consistent with the spectral evolution as a function of L _E and especially not with the transition to a hard state. Our results point to the compact object in Cyg X-3 being a massive,  ∼30 M_⊙  black hole.     

Generalized Regularization Techniques with Constraints for the Analysis of Solar Bremsstrahlung X-ray Spectra

Hard X-ray spectra in solar flares provide knowledge of the electron spectrum that results from acceleration and propagation in the solar atmosphere. However, the inference of the electron spectra from solar X-ray spectra is an ill-posed inverse problem. Here, we develop and apply an enhanced regularization algorithm for this process making use of physical constraints on the form of the electron spectrum. The algorithm incorporates various features not heretofore employed in the solar flare context: Generalized Singular Value Decomposition (GSVD) to deal with different orders of constraints; rectangular form of the cross-section matrix to extend the solution energy range; regularization with various forms of the smoothing operator; and preconditioning of the problem. We show by simulations that this technique yields electron spectra with considerably more information and higher quality than previous algorithms.     

Influence of the Return Current on the EUV and X-Ray Flare Line Emissions

Electron beams accelerated during solar flares carry electric currents which should be neutralized by so-called return currents. Both the electron beam and return current modify the electron distribution function in the solar transition region and low corona. Thus, they influence the intensities of the spectral lines formed in these layers. Synthetic spectra for the solar flare atmosphere are computed from model conditions and the possibilities of diagnostics of the return current from the EUV and X-ray line spectra are discussed.     

STARE doppler spectral studies of westward electrojet radar aurora

This paper presents crossed-beam Doppler spectral measurements of radar aurora during westward electrojet conditions made with the STARE system in northern Scandinavia. The averaged spectral characteristics (e.g. spectral shape, relative power, spectrum width, spectrum asymmetry) are examined relative to the electron drift velocity estimated by combining the mean Doppler shifts from both radars. The type of spectrum was found to depend on the flow angle θ defined as the angle between drift velocity and radar wavevector. Typically, narrow spectra, similar to equatorial type I spectra, are observed for angles θ up to 60° while for larger angles the spectra become much broader and less stable in space and time. The observed spectral types are closely identified with primary and secondary irregularities. On average, a power law relationship was found to exist between the relative backscatter power and the drift velocity magnitude. A weak trend was found for the narrow spectra to become narrower for larger drifts contrary to broad spectrum width which increases linearly with drift magnitude. The spectra are often asymmetric with elongated tails toward zero Doppler shifts but this asymmetry is of a different nature for the narrow and broad spectra. The averaged spectral properties presented in this paper are similar to those reported by Nielsen et al. (1984) for eastward electrojet radar aurora.     

Joint Effects of Compton Backscattering and Low-Energy Cutoff on the Flattening of Solar Hard X-Ray Spectra at Lower Energies

Theoretical calculation has shown that the spectrum of the Compton backscattering component in solar hard X-ray flares has a peak around 30 keV for a primary power-law source. Thus the superposition of the Compton backscattering component could cause a photon spectrum received at the Earth to be flattened below the peak energy and steeper above the peak energy. On the other hand, because a thick-target bremsstrahlung photon with a given energy E only could be produced by a nonthermal electron with an energy larger than E, thus if a power-law electron spectrum is cutoff below an energy E _c, then the produced photon spectrum will become flattened below E _c. In this work we present a calculation of the joint effects of the Compton backscattering and the low-energy cutoff on the spectral characteristics of the received solar hard X-ray in the energy range 10–100 keV. The results show that the flattening caused purely by the Compton backscattering could be comparable with that by the low-energy cutoff for hard spectra. So, it is obvious that the joint effects of the low-energy cutoff and the Compton backscattering could result in the received photon spectra to be much more flattened at lower energies. On the other hand, compared to the primary photon spectrum, the received photon spectral index will increase about 0.15 due to the Compton backscattering at higher energy, which seems independent of the primary spectral index.     

Spectrum,angular distribution and polarization of auroral hard X-rays

The angular variations of elastic and inelastic scattering cross-sections have been calculated accounting for Hartree-Fock atomic model. Using these cross-sections the evolution of electron energy and angular distributions at different heights in the ionosphere have been computed with the help of Monte Carlo technique. Mono-energetic, power law and exponential electron spectra with isotropic and mono-directional incidence starting at an altitude of 300 km have been taken to obtain the angular and energy distribution at certain height intervals. It is found that isotropic distribution incident at the top of the ionosphere becomes anisotropic due to collisions at lower heights. Using Sauter bremsstrahlung cross-section and the calculated electron flux we have computed the spectrum, angular distribution and polarization of bremsstrahlung X-rays at different heights.The emission is found to be peaked at lower angles at higher heights and becomes isotropic with depth of penetration. Polarization is considerable at higher altitudes for mono-directional beams and becomes significant at lower heights for isotropic incidence. It is argued that the study of angular distribution and polarization can yield information about the nature of precipitating electron flux and hence about the acceleration mechanism operating during electron precipitation.     

Spatial distribution of high energy cosmic ray electrons perpendicular to the galactic plane

With the help of empirical data concerning the latitudinal distribution of galactic gamma rays the contribution of inverse Compton scattered gamma rays is calculated using various models concerning the distribution of high energy cosmic ray electrons perpendicular to the galactic plane. It is shown that gamma ray astronomy from regions with vanishing stellar and interstellar matter densities at energies greater than 100 MeV provides instructive information on the cosmic ray electron density. We find evidence for the existence of a broad galactic electron disk with a total thickness of at least 6.4 kpc. The uncertainties of the cosmic ray electron spectrum measurements above 100 GeV imply an additional uncertainty in the inverse Compton source function of at least a factor 6.     

The optical spectral slope variability of 17 blazars

Many quasi-simultaneous optical observations of 17 blazars are obtained from previous papers published over the last 19 years in order to investigate the spectral slope variability and understand the radiation mechanism of blazars. The long-period dereddened optical spectral slopes are calculated. We analyse the average spectral slope distribution, which suggests that the spectra of flat spectrum radio quasars (FSRQs) and high energy peaked BL Lac objects (HBLs) are probably deformed by other emission components. The average spectral slopes of low energy peaked BL Lac objects(LBLs), which scatter around 1.5, show a good accordance with the synchrotron self-Compton (SSC) loss-dominated model. We present and discuss the variability between the spectral slope and optical luminosity. The spectra of all HBLs and LBLs get flatter when they turn brighter, while for FSRQs this trend does not exist or may even be reversed. This phenomenon may imply that there is a thermal contribution to the optical spectrum for FSRQs. For the FSRQ 1156+295, there is a hint that the slope gets flatter at both the brightest and faintest states. Our result shows that three subclasses locate in different regions in the pattern of slope variability indicator versus average spectral slope. The relativistic jet mechanism is supported by the significant correlation between the optical Doppler factor and the average spectral slope.     

A Special Radio Spectral Fine Structure Used for Plasma Diagnostics in Coronal Magnetic Traps

A specific combination of spectral fine structures in meter –  decimeter dynamic spectra of solar radio burst emission is reported in observations carried out at the Astrophysical Institute Potsdam. We describe and interpret the occurrence of zebra patterns in fast drifting (type III burst-like) envelopes of absorbed continuum emission. A possible mechanism of the origin of such an involved spectral pattern is put forward, leading to a necessarily multinonequlibrium component coronal plasma. The suggested mechanism is based on the fact that during the passage of a fast electron beam through the corona the loss cone instability (which is caused by electrons captured in a magnetic trap generating the continuum) is quenched. As result, a fast drift burst appears in absorption, and the zebra pattern becomes visible on the low background emission. This zebra pattern is generated by a group of electrons with a nonequilibrium distribution over transverse velocities. In the absence of the beam the pattern is invisible against the background of the stronger continuum. It is shown that the mechanism is sensitive to the distribution parameters of the different electron ensembles. Therefore the effect in dynamic radio spectra is comparatively rare but its proper existence underlines that the simultaneous presence of different ensembles of electrons in the flaring corona can be quite a frequent situation. This can explain some problems in deconvolving X-ray photon spectra to electron energy spectra.