Nonthermal Electron Spectrum Research Articles

Sunyaev-Zeldovich signatures from non-thermal, relativistic electrons using CMB maps

Relativistically energetic, non-thermal population of electrons can give rise to unique CMB spectral distortion signatures which can be significantly different from thermal Sunyaev-Zeldovich signal or y-distortion. These signatures depend upon the spectrum of non-thermal electrons, therefore, a detection can inform us about the existence and abundance of non-thermal electrons in our universe. Using public CMB maps and data, we derive upper limits on non-thermal y-parameter for a relativistic, power-law electron distribution. With future CMB experiments, we may be in a position to detect or put significantly tighter constraints on these signals which can affect our understanding of non-thermal electron distributions in our universe.

Solar Flare Ribbon Fronts. II. Evolution of Heating Rates in Individual Flare Footpoints

Solar flare ribbon fronts appear ahead of the bright structures that normally characterize solar flares, and can persist for an extended period of time in spatially localized patches before transitioning to “regular” bright ribbons. They likely represent the initial onset of flare energy deposition into the chromosphere. Chromospheric spectra (e.g., He i 10830 Å and the Mg ii near-UV lines) from ribbon fronts exhibit properties rather different to typical flare behavior. In prior numerical modeling efforts we were unable to reproduce the long lifetime of ribbon fronts. Here we present a series of numerical experiments that are rather simple but which have important implications. We inject a very low flux of nonthermal electrons (F = 5 × 108 erg s−1 cm−2) into the chromosphere for 100 s before ramping up to standard flare energy fluxes (F = 1010−11 erg s−1 cm−2). Synthetic spectra not only sustained their ribbon-front-like properties for significantly longer: in the case of harder nonthermal electron spectra, the ribbon front behavior persisted for the entirety of this weak-heating phase. Lengthening or shortening the duration of the weak-heating phase commensurately lengthened or shortened the ribbon front lifetimes. Ribbon fronts transitioned to regular bright ribbons when the upper chromosphere became sufficiently hot and dense, which happened faster for softer nonthermal electron spectra. Thus, the lifetime of flare ribbon fronts are a direct measure of the duration over which a relatively low flux of high-energy electrons precipitates to the chromosphere prior to the bombardment of a much larger energy flux.

The Evolution of Ion Charge States in Coronal Mass Ejections

We model the observed charge states of the elements C, O, Mg, Si, and Fe in the ejecta of coronal mass ejections (CMEs). We concentrate on “halo” CMEs observed in situ by the Advanced Composition Explorer/Solar Wind Ion Composition Spectrometer to measure ion charge states, and also remotely by the Solar Terrestrial Relations Observatory when in near quadrature with the Earth, so that the CME expansion can be accurately specified. Within this observed expansion, we integrate equations for the CME ejecta ionization balance, including electron heating parameterized as a fraction of the kinetic and gravitational energy gain of the CME. We also include the effects of non-Maxwellian electron distributions, characterized as a κ function. Focusing first on the 2010 April 3 CME, we find a somewhat better match to the observed charge states with κ close to the theoretical minimum value of κ = 3/2, implying a hard spectrum of nonthermal electrons. Similar but more significant results come from the 2011 February 15 event, although it is quite different in terms of its evolution. We discuss the implications of these values, and of the heating required, in terms of the magnetic reconnection Lundquist number and anomalous resistivity associated with CME evolution close to the Sun.

What aspects of solar flares can be clarified with mm/submm observations?

This paper identifies several unsolved questions about solar flares, which can potentially be answered or at least clarified with mm/submm observations with ALMA. We focus on such questions as preflare phases and the initiation of solar flares and the efficiency of particle acceleration during flares. To investigate the preflare phase we propose to use the extraordinary sensitivity and high spatial resolution of ALMA, which promises to identify very early enhancements of preflare emission with high spatial resolution and link them to the underlying photospheric magnetic structure and chromospheric flare ribbons. In addition to revealing the flare onsets, these preflare measurements will aid in the investigation of particle acceleration in multiple ways. High-frequency imaging spectroscopy data in combination with the microwave data will permit the quantification of the high-energy cutoff in the nonthermal electron spectra, thus helping to constrain the acceleration efficiency. Detection and quantification of secondary relativistic positron (produced due to nonthermal accelerated ions) contribution using the imaging polarimetry data will help constrain acceleration efficiency of nonthermal nuclei in flares. Detection of a “mysterious” rising spectral component with high spatial resolution will help determine the emission mechanism responsible for this component, and will then help in quantifying this either nonthermal or thermal component of the flaring plasma. We discuss what ALMA observing mode(s) would be the most suitable for addressing these objectives.

Probing the low-energy spectrum of non-thermal electrons in galaxy clusters with soft gamma ray observations

In this paper we study the possibility of probing the low-energy part of the spectrum of non-thermal electrons in galaxy clusters by detecting their non-thermal bremsstrahlung (NTB) emission in the soft gamma ray band, using instruments like e-ASTROGAM. Using the Coma cluster as a reference case, we find that, for very low values of the minimum energy of the electrons, in principle the NTB is detectable, but this situation is possible only for conditions that can be maintained only for a short time compared to the cluster lifetime. The possibility of constraining the low energy spectrum of non-thermal electrons through NTB is therefore hard to achieve in next years.

Solar flares with similar soft but different hard X-ray emissions: case and statistical studies

From the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) catalog we select events which have approximately the same GOES class (high C - low M or 500–1200 counts s−1 within the RHESSI 6–12 keV energy band), but with different maximal energies of detected hard X-rays. The selected events are subdivided into two groups: (1) flares with X-ray emissions observed by RHESSI up to only 50 keV and (2) flares with hard X-ray emission observed also above 50 keV. The main task is to understand observational peculiarities of these two flare groups. We use RHESSI X-ray data to obtain spectral and spatial information in order to find differences between selected groups. Spectra and images are analyzed in detail for six events (case study). For a larger number of samples (85 and 28 flares in the low-energy and high-energy groups respectively) we only make some generalizations. In spectral analysis we use the thick-target model for hard X-ray emission and one temperature assumption for thermal soft X-ray emission. RHESSI X-ray images are used for determination of flare region sizes. Although thermal and spatial properties of these two groups of flares are not easily distinguishable, power law indices of hard X-rays show significant differences. Events from the high-energy group generally have a harder spectrum. Therefore, the efficiency of chromospheric evaporation is not sensitive to the hardness of nonthermal electron spectra but rather depends on the total energy flux of nonthermal electrons.

Synchrotron X-ray diagnostics of cutoff shape of nonthermal electron spectrum at young supernova remnants

Synchrotron X-rays can be a useful tool to investigate electron acceleration at young supernova remnants (SNRs). At present, since the magnetic field configuration around the shocks of SNRs is uncertain, it is not clear whether electron acceleration is limited by SNR age, synchrotron cooling, or even escape from the acceleration region. We study whether the acceleration mechanism can be constrained by the cutoff shape of the electron spectrum around the maximum energy. We derive analytical formulae of the cutoff shape in each case where the maximum electron energy is determined by SNR age, synchrotron cooling and escape from the shock. They are related to the energy dependence of the electron diffusion coefficient. Next, we discuss whether information on the cutoff shape can be provided by observations in the near future which will simply give the photon indices and the flux ratios in the soft and hard X-ray bands. We find that if the power-law index of the electron spectrum is independently determined by other observations, then we can constrain the cutoff shape by comparing theoretical predictions of the photon indices and/or the flux ratios with observed data which will be measured by NuSTAR and/or ASTRO-H. Such study is helpful in understanding the acceleration mechanism. In particular, it will supply another independent constraint on the magnetic field strength around the shocks of SNRs.

PARTICLE DENSITIES WITHIN THE ACCELERATION REGION OF A SOLAR FLARE

The limb flare SOL2012-07-19T05:58 (M7.7) provides the best example of a non-thermal above-the-loop-top hard X-ray source with simultaneous observations by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) and the Atmospheric Imaging Assembly on board the Solar Dynamic Observatory. By combining the two sets of observations, we present the first direct measurement of the thermal proton density and non-thermal electron density within the above-the-loop-top source where particle acceleration occurs. We find that both densities are of the same order of magnitude of a few times 109 cm–3, about 30 times lower than the density in the underlying thermal flare loops. The equal densities indicate that the entire electron population within the above-the-loop-top source is energized. While the derived densities depend on the unknown source depth and filling factor, the ratio of these two densities does not. Within the uncertainties, the ratio is one for a low energy cutoff of the non-thermal electron spectrum between 10 and 15 keV. RHESSI observations only constrain the cutoff energy to below ~15 keV, leaving the spectral shape of the electrons within the above-the-loop-top source at lower energies unknown. Nevertheless, these robust results strongly corroborate earlier findings that the above-the-loop-top source is the acceleration region where a bulk energization process acts on all electrons.

Wave-particle interactions in non-uniform plasma and the interpretation of hard X-ray spectra in solar flares

Context. High energy electrons accelerated during solar flare are abundant in the solar corona and in the interplanetary space. Commonly, the number and the energy of non-thermal electrons at the Sun is estimated using hard X-ray (HXR) spectral observations (e.g. RHESSI) and a single-particle collisional approximation. Aims. To investigate the role of the spectrally evolving Langmuir turbulence on the population of energetic electrons in the solar corona. Methods. We numerically simulate the relaxation of a power-law non-thermal electron population in a collisional inhomogeneous plasma including wave-particle, and wave-wave interactions. Results. The numerical simulations show that the long-time evolution of electron population above 20 keV deviates substantially from the collisional approximation when wave-particle interactions in non-uniform plasma are taken into account. The evolution of Langmuir wave spectrum towards smaller wavenumbers, due to large-scale density fluctuations and wave-wave interactions, leads to an effective acceleration of electrons. Furthermore, the time-integrated spectrum of non-thermal electrons, which is normally observed with HXR above 20 keV, is noticeably increased due to acceleration of non-thermal electrons by Langmuir waves. Conclusions. The results show that the observed HXR spectrum, when interpreted in terms of collisional relaxation, can lead to an overestimated number and energy of energetic electrons accelerated in the corona.

Relationship between non-thermal electron energy spectra and GOES classes

We investigate the influence of the variations of energy spectrum of non-thermal electrons on the resulting GOES classes of solar flares. Twelve observed flares with various soft to hard X-ray emission ratios were modelled using different non-thermal electron energy distributions. Initial values of the flare physical parameters including geometrical properties were estimated using observations. We found that, for a fixed total energy of non-thermal electrons in a flare, the resulting GOES class of the flare can be changed significantly by varying the spectral index and low energy cut-off of the non-thermal electron distribution. Thus, the GOES class of a flare depends not only on the total non-thermal electrons energy but also on the electron beam parameters. For example, we were able to convert a M2.7 class solar flare into a merely C1.4 class one and a B8.1 class event into a C2.6 class flare. The results of our work also suggest that the level of correlation between the cumulative time integral of HXR and SXR fluxes can depend on the considered HXR energy range.

Evidence of a Curved Synchrotron Spectrum in the Supernova Remnant SN 1006

A joint spectral analysis of some Chandra ACIS X-ray data and Molonglo Observatory Synthesis Telescope radio data was performed for 13 small regions along the bright northeastern rim of the supernova remnant SN 1006. These data were fitted with a synchrotron radiation model. The nonthermal electron spectrum used to compute the photon emission spectra is the traditional exponentially cut off power law, with one notable difference: The power-law index is not a constant. It is a linear function of the logarithm of the momentum. This functional form enables us to show, for the first time, that the synchrotron spectrum of SN 1006 seems to flatten with increasing energy. The effective power-law index of the electron spectrum is 2.2 at 1 GeV (i.e., radio synchrotron-emitting momenta) and 2.0 at about 10 TeV (i.e., X-ray synchrotron-emitting momenta). This amount of change in the index is qualitatively consistent with theoretical models of the amount of curvature in the proton spectrum of the remnant. The evidence of spectral curvature implies that cosmic rays are dynamically important instead of being test particles. The spectral analysis also provides a means of determining the critical frequency of the synchrotron spectrum associated with the highest-energy electrons. The critical frequency seems to vary along the northeastern rim, with a maximum value of 1.1+1.0−0.5 × 1017 Hz. This value implies that the electron diffusion coefficient can be no larger than a factor of ~4.5-21 times the Bohm diffusion coefficient if the velocity of the forward shock is in the range 2300-5000 km s−1. Since the coefficient is close to the Bohm limit, electrons are accelerated nearly as fast as possible in the regions where the critical frequency is about 1017 Hz.

Nonthermal Radiation Mechanisms

In this paper we review the possible radiation mechanisms for the observed non-thermal emission in clusters of galaxies, with a primary focus on the radio and hard X-ray emission. We show that the difficulty with the non-thermal, non-relativistic Bremsstrahlung model for the hard X-ray emission, first pointed out by Petrosian (Astrophys. J. 557, 560, 2001) using a cold target approximation, is somewhat alleviated when one treats the problem more exactly by including the fact that the background plasma particle energies are on average a factor of 10 below the energy of the non-thermal particles. This increases the lifetime of the non-thermal particles, and as a result decreases the extreme energy requirement, but at most by a factor of three. We then review the synchrotron and so-called inverse Compton emission by relativistic electrons, which when compared with observations can constrain the value of the magnetic field and energy of relativistic electrons. This model requires a low value of the magnetic field which is far from the equipartition value. We briefly review the possibilities of gamma-ray emission and prospects for GLAST observations. We also present a toy model of the non-thermal electron spectra that are produced by the acceleration mechanisms discussed in an accompanying paper Petrosian and Bykov (Space Sci. Rev., 2008, this issue, Chap. 11).

Solar impulsive EUV and UV brightenings in flare footpoints and their connection with X-ray emission

Context. The thick-target model of the impulsive phase of solar flares describes the propagation of non-thermal electron beams into the chromosphere. The stopping depth of the electron is related to its energy. Thus, the thermal reaction at different levels should be connected to the parameters of the electron spectrum. Aims. We investigate the impulsive thermal reaction produced by non-thermal electron beams at different heights of the solar atmosphere observed in solar flare footpoints. Methods. We used methods developed for the investigation of the impulsive SXR brightenings. The EUV and UV images obtained by TRACE in the 171 A and 1600 A filter were used as the basic data set for this analysis. For the first time, EUV images have been desaturated using diffraction pattern properties. Results. We find that the thermal impulsive reaction observed in solar flare footpoints is different for UV and EUV brightenings. Results are compared to those obtained for the impulsive SXR brightenings. We find that observed dissimilarities are connected to the properties of the non-thermal electron spectrum and to the depth of their penetration into the chromosphere. Moreover, we show that the lower levels of the chromosphere are excited by more energetic electrons.

Electron kinetics in collisionless shock waves

We study the kinetic model of the formation of the energy spectrum of nonthermal electrons near the front of a quasilongitudinal, supercritical, collisionless shock wave. Nonresonant interactions of the electrons and the fluctuations generated by kinetic instabilities of the ions in the transition region inside the shock front play the main role in the heating and preacceleration of electrons. We calculate the electron energy spectrum in the vicinity of the shock wave and show that the heating and preacceleration of electrons occur on a scale of the order of several hundred ion inertial lengths in the vicinity of the viscous discontinuity. Although the electron distribution function is significantly nonequilibrium near the shock front, its low-energy part can be approximated by a Maxwellian distribution. The effective electron temperature T eff 2 behind the front, obtained in this manner, increases with the Mach number of the shock wave slower than it would if it followed the Hugoniot adiabat. We determine the condition under which the electron heating is ineffective but the electrons are effectively accelerated to high energies. The high-energy asymptotic behavior of the distribution function is that of a power law, with the exponent determined by the total compression ratio of the plasma, as in the case of acceleration by the first-order Fermi mechanism. The model is used to describe the case (important for applications) of acceleration of electrons by shock waves with large total Mach numbers, with the structure of these waves modified by the nonlinear interaction of nonthermal ions and consisting of an extended prefront with a smooth variation of the macroscopic parameters and a viscous discontinuity in speed with a moderate value of the Mach number.

The energetic spectrum of non-thermal electrons in an acceleration region calculated from a solar microwave type III burst with both positive and negative frequency drifts

A typical event of solar microwave type III burst with both positive and negative frequency drifts was observed by the 1-2 GHz spectrograph at Beijing Observatory on January 5, 1994. The separatrix frequency (1.3 GHz) may correspond to an acceleration region. The energy of the electron beam responsible for the burst is calculated from the drift rate and the height of the source above the photosphere. Moreover, if the solar microwave type III burst is explained by the beam-plasma instability as suggested by Huang (1998), the energy density as well as the particle density of the electron beam may be estimated from the burst flux, the growth rates and the modularity (Huang et al., 1996). So that, a very good power-law distribution is simulated for the energetic spectrum of the electron beam in this event with a spectrum index 4.5. The electron beam may be accelerated by an electric field with a length of 10(7) m and a strength of 10(-4) V m(-1). These results are necessary for understanding the acceleration process in solar flares.

Distinguishing Solar Flare Types by Differences in Reconnection Regions

Observations show that magnetic reconnection and its slow shocks occur in solar flares. The basic magnetic structures are similar for long duration event (LDE) flares and faster compact impulsive (CI) flares, but the former require fewer nonthermal electrons than the latter. Slow shocks can produce the required nonthermal electron spectrum for CI flares by Fermi acceleration if electrons are injected with large enough energies to allow them to resonate with scattering waves. The dissipation region may provide the injection electrons, so the overall number of nonthermal electrons reaching the footpoints would depend on the size of the dissipation region and its distance from the chromosphere. In this picture, the LDE flares have converging inflows toward a dissipation region that spans a smaller overall length fraction than for CI flares. Bright loop-top X-ray spots in some CI flares can be attributed to particle trapping at fast shocks in the downstream flow, the presence of which is determined by the angle of the inflow field and velocity to the slow shocks.

Propagation and confinement of energetic electrons in solar flares

The propagation, cofinement and total energy of energetic (>25 keV) electrons in solar flares are examined through a brief review of the following hard X-ray measurements: (1) spatially resolved observations obtained by imaging instruments; (2) stereoscopic observations of partially occulted sources providing radial (vertical) spatial resolution; and (3) directivity of the emission measured through stereoscopic observations and the center-to-limb variation of the occurrence frequency of hard X-ray flares. The characteristics of the energetic electrons are found to be quite distinct in impulsive and gradual hard X-ray flares. In impulsive flares the non-thermal electron spectrum seems to extend down to ∼2 keV indicating that the total energy of non-thermal electrons is much larger than that assumed in the past.

A qualitative interpretation of 7 August 1972 impulsive phase flare H? line profiles

Tanaka's (1977) unique Hα profiles of the kernels of the 7 August 1972 flare were quantitatively interpreted by Brown et al. (1978; henceforth BCR) in terms of a thick target electron beam model. They found that this interpretation required beam inhomogeneity and/or partial precipation and large (60–100 km s−1) macroturbulence. The latter requirement is somewhat suspect, since the only independent evidence also comes from efforts to understand the profiles of optically thick chromospheric lines. Relationships between model atmosphere parameters and line profile parameters calculated by Dinh (1980) show that these requirements could be considerably reduced, if not totally eliminated, if the actual chromospheric flare heating mechanism were simultaneously capable of pushing the flare transition region to greater column density and causing less heating of the residual chromosphere than the BCR models. This then implies that the chromosphere is heated primarily by a mechanism through which the heating effects do not penetrate as far below the flare transition region as is the case for a power-law spectrum of non-thermal electrons whose parameters are chosen appropriate to the nonthermal thick target interpretation of hard X-rays. Thermal conduction and optically thick radiation are examples of such a mechanism.

Compton scattering on the diffuse UV and X-ray background. A reappraisal

On the basis of a Monte Carlo calculation BuI-VAx and HURLEY (1) suggested tha t the double inverse Compton scattering of a suitable electron spectrum on the universal b lack-body radiat ion could explain the excess at MeV energies. To do so they had to postulate tha t the nonthermal electron spectrum originally introduced by BR]~CI~ER and MOI~I~ISON (2) could be ext rapola ted down to a Lorentz factor T = E/m~c ~ ~_ 20. Such a view has been s t rongly opposed by F~LT]~N and GOVLD (8), who, on the basis of an approximate but accurate analyt ical calculation, proved tha t the electron spectrum adopted by BvI-VAN and HURLa~ could not produce in a second scattering more than about 1% of the in tensi ty due to the first scattering, near about 3 MeV. In fact, in no region of the spectrum the second-scattering photons could add a subs tant ia l contribution. Although these conclusions cannot be disputed in themselves, we feel tha t they do not make full justice to the main idea of BuI-VAN and HunL~Y. In addit ion, some of the conclusions by FV, LT~N and GOULD are expressed in a form which is unfavourable to a fur ther s tudy of the question. In the present le t ter we want to show that scattering of electrons on the low-energy X-ray spectrum may give a high enough flux in some energy range as to deform in a substantial way the previous shape. This is t rue in part icular for the electron spectrum adopted in both ref. (~,8). We only need to l if t the requirement tha t the low-energy ( < 0.3 keV) X-rays are produced by the first inverse Compton scattering. Our work, which involves essentially numerical calculations, has been divided into two steps. F i rs t of all we have checked the fact that , by using the complete formula for the inverse Compton effect (which has been given by BLU~NTI~AL and GOVLI) (4), eq. {2.75), and needs some refinements in the l imi t s of integrat ion over the parameter q), one essentially reaches the same conclusions as F~LTEI~ and GOI;LD.

The Observation of Nonthermal Solar X-Radiation in the Energy Range 3 &lt; E &lt; 10 KeV

view Abstract Citations (43) References (21) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Observation of Nonthermal Solar X-Radiation in the Energy Range 3 < E < 10 KeV Kahler, S. W. ; Kreplin, R. W. Abstract The low-energy (3-10 keV) X-ray spectra observed during solar impulsive bursts of E> 10 keV X-rays reported by Kane and Anderson are analyzed. In two of these bursts we can separate the total low-energy X-ray emission into thermal and nonthermal components. Tlie inferred nonthermal electron spectrum is discussed in relation to acceleration by electric fields. The electron spectrum allows a determination of the minimum value of Ef/fl , the ratio of electric field strength to electron density. Publication: The Astrophysical Journal Pub Date: September 1971 DOI: 10.1086/151107 Bibcode: 1971ApJ...168..531K full text sources ADS |