Electron Spectral Index Research Articles

Effect of orbital angular momentum on electron acoustic waves in double‐Kappa plasma

AbstractKinetic theory of electron acoustic waves (EAWs) in the presence of wave angular momentum has been derived to study the effect of wave angular momentum on the propagation of EAWs in a non‐Maxwellian plasma. Both types of electrons (hot and cool) are modeled as Kappa‐distributed velocity distribution functions. The theory is also applied to Saturn's magnetosphere where these kinds of distribution functions are commonly found. It is seen that the presence of wave angular momentum in the model has a significant effect on the existence of the regions where EAWs are weakly damped. The effect of wave angular momentum on EAWs is studied by defining a parameter η = k/(lqθ), which is the ratio of the planar wave number to the azimuthal wave number. The wave is purely planar if . The weakly damped region of EAWs depends strongly on this parameter in addition to other parameters such as hot electron spectral index κh, cool electron spectral index κc, the fraction of hot electrons, and hot to cool electrons temperature ratio. The results also show the effect of η on the propagation of EAWs in various regions of Saturn's magnetosphere.

PRE-FLARE CORONAL JET AND EVOLUTIONARY PHASES OF A SOLAR ERUPTIVE PROMINENCE ASSOCIATED WITH THE M1.8 FLARE: SDO AND RHESSI OBSERVATIONS

ABSTRACT We investigate the triggering, activation, and ejection of a solar eruptive prominence that occurred in a multi-polar flux system of active region NOAA 11548 on 2012 August 18 by analyzing data from the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory, the Reuven Ramaty High Energy Solar Spectroscopic Imager, and the Extreme Ultraviolet Imager/Sun Earth Connection Coronal and Heliospheric Investigation on board the Solar Terrestrial Relation Observatory. Prior to the prominence activation, we observed striking coronal activities in the form of a blowout jet, which is associated with the rapid eruption of a cool flux rope. Furthermore, the jet-associated flux rope eruption underwent splitting and rotation during its outward expansion. These coronal activities are followed by the prominence activation during which it slowly rises with a speed of ∼12 km s−1 while the region below the prominence emits gradually varying EUV and thermal X-ray emissions. From these observations, we propose that the prominence eruption is a complex, multi-step phenomenon in which a combination of internal (tether-cutting reconnection) and external (i.e., pre-eruption coronal activities) processes are involved. The prominence underwent catastrophic loss of equilibrium with the onset of the impulsive phase of an M1.8 flare, suggesting large-scale energy release by coronal magnetic reconnection. We obtained signatures of particle acceleration in the form of power-law spectra with hard electron spectral index (δ ∼ 3) and strong HXR footpoint sources. During the impulsive phase, a hot EUV plasmoid was observed below the apex of the erupting prominence that ejected in the direction of the prominence with a speed of ∼177 km s−1. The temporal, spatial, and kinematic correlations between the erupting prominence and the plasmoid imply that the magnetic reconnection supported the fast ejection of prominence in the lower corona.

Turnover Frequency in Solar Microwave Bursts with an Extremely Flat Optically Thin Spectrum

Four microwave bursts have been selected from the Nobeyama Radio Polarimeter (NoRP) observations with an extremely flat spectrum in the optically thin part and a very hard spectral index between 0 and −1 in the maximum phase of all bursts. It is found that the time evolution of the turnover frequency is inversely proportional to the time profiles of the radio flux in all bursts. Based on the nonthermal gyrosynchrotron theory of Ramaty (Astrophys. J. 158, 753, 1969), the local magnetic field strength and the electron spectral index are calculated uniquely from the observed radio spectral index and the turnover frequency. We found that the electron energy spectrum is very hard (spectral index 1 – 2), and the time variation of the magnetic field strength is also inversely proportional to the radio flux as a function of time in all bursts. Hence, the time evolution of the turnover frequency can be explained directly by its dependence on the local magnetic field strength. The high turnover frequency (several tens of GHz) is mainly caused by a strong magnetic field of up to several hundred gauss, and probably by the Razin effect under a high plasma density over $10^{10}~\mbox{cm}^{-3}$ in the maximum phase of these bursts. Therefore, the extremely flat microwave spectrum can be well understood by the observed high turnover frequency and the calculated hard electron spectral index.

AMS-02 measurement of cosmic ray positrons and electrons

Precision measurements by AMS of the primary cosmic-ray positron fraction and the positron flux in the energy range 0.5 to 500 GeV, and the electron flux in the range 0.5 to 700 GeV are presented. The results show that above 200 GeV the positron fraction no longer exhibits an increase with energy. The positron flux and the electron flux are significantly different in their magnitude and energy dependence. They each require a description beyond a single power-law spectrum. Between 20 and 200 GeV the positron spectral index is significantly harder than the electron spectral index. The incoming direction of primary CR positrons and electrons are found to be consistent with isotropy within the current accuracy.

The extended jet of AP Librae: Origin of the very high-energyγ-ray emission?

The low-frequency peaked BL Lac object (LBL) AP Librae exhibits very-high-energy (VHE, $E>100$GeV) $\gamma$-ray emission and hosts an extended jet, which has been detected in radio and X-rays. The jet X-ray spectral index implies an inverse Compton origin. These observations are unusual for LBLs calling for a consistent explanation of this extraordinary source. The observationally constrained parameters necessary to describe the core emission within the standard one-zone model are unable to explain the broad-band spectrum, even if observationally unconstrained external photon fields are taken into account. We demonstrate that the addition of the extended jet emission successfully reproduces the total spectral energy distribution. In particular, the VHE radiation is produced in the $>100\,$kpc long extended jet via inverse Compton scattering of cosmic microwave background photons by highly relativistic electrons. We present several ways to test this theory. The extended jet is weakly magnetized ($B_0 = 2.5\,\mu$G), while its minimum and maximum electron Lorentz factors are $\gamma_{min}=60$ and $\gamma_{max}=5\times 10^6$, respectively. The electron spectral index is $s=2.6$. These parameters are comparable to parameters of other blazars with extended X-ray jets dominated by inverse Compton scattering.

Kinetic theory of dust ion acoustic waves in a kappa-distributed plasma

Using a kinetic theory approach, dust ion acoustic (DIA) waves are investigated in an unmagnetized collisionless plasma with kappa-distributed electrons and ions, and Maxwellian dust grains of constant charge. Both analytical and numerical results, the latter following from the full solution of the associated dispersion relation, are presented, and a comparison is made. The effects of the ion and electron spectral indices, as well as the species' density (ne/ni) and temperature (Te/Ti) ratios, on the dispersion and damping of the waves are considered. In the long wavelength regime, increases in both the electron spectral index (κe) and the dust density fraction (reduced f=ne/ni) lead to an increase in phase velocity. The range in wavelength over which modes are weakly damped increases with an increase in Te/Ti. However, the ion spectral index, κi, does not have a significant effect on the dispersion or damping of DIA waves.

Modified Zakharov–Kuznetsov equation for a non-uniform electron–positron–ion magnetoplasma with kappa-distributed electrons

We investigate the low-frequency (by comparison with the ion Larmor frequency) electrostatic solitary structures in a spatially non-uniform electron–positron–ion (e–p–i) magnetoplasma with non-Maxwellian electrons. A linear dispersion relation for the obliquely propagating ion acoustic drift wave is derived and it is shown that the non-Maxwellian electron population modifies the dispersion characteristics of the wave under consideration. We also carry out a nonlinear analysis and derive the modified Zakharov–Kuznetsov (MZK) equation for the coupled drift acoustic wave in a non-uniform magnetized plasma. We highlight the differences between the MZK equation and its homogeneous counterpart. We also find the solution of the MZK equation using the tangent hyperbolic method. It is observed that the electron spectral index ${\it\kappa}$, positron concentration, and propagation angle ${\it\alpha}$ alter the structure of the ion acoustic drift solitary waves. The results obtained in this paper may be beneficial to understanding the propagation characteristics of electrostatic drift solitary structures in the interstellar medium and in laboratory experiments where electron–positron plasmas have recently been created by impinging ultra-intense laser pulses on a solid density target at the Lawrence Livermore National Laboratory (LLNL).

LARGE-SCALE CONTRACTION AND SUBSEQUENT DISRUPTION OF CORONAL LOOPS DURING VARIOUS PHASES OF THE M6.2 FLARE ASSOCIATED WITH THE CONFINED FLUX ROPE ERUPTION

We present a detailed multi-wavelength study of the M6.2 flare which was associated with a confined eruption of a prominence using TRACE, RHESSI, and NoRH observations. The pre-flare phase of this event is characterized by spectacular large-scale contraction of overlying extreme ultraviolet (EUV) coronal loops during which the loop system was subjected to an altitude decrease of ~20 Mm for an extended span of ~30 min. This contraction phase is accompanied by sequential EUV brightenings associated with hard X-ray (HXR) (up to 25 keV) and microwave (MW) sources from low-lying loops in the core of the flaring region which together with X-ray spectra indicate strong localized heating in the source region before the filament activation and associated M-class flare. With the onset of the impulsive phase of the M6.2 flare, we detect HXR and MW sources that exhibit intricate temporal and spatial evolution in relation with the fast rise of the prominence. Following the flare maximum, the filament eruption slowed down and subsequently confined within the large overlying active region loops; the event did not lead to a coronal mass ejection (CME). During the confinement process of the erupting prominence, we detect MW emission from the extended coronal region with multiple emission centroids which likely represent emission from hot blobs of plasma formed after the collapse of the expanding flux rope and entailing prominence material. RHESSI observations reveal high plasma temperature (~30 MK) and substantial non-thermal characteristics with electron spectral index (~5) during the impulsive phase of the flare. The time-evolution of thermal energy exhibits a good correspondence with the variations in cumulative non-thermal energy which suggest that the energy of accelerated particles efficiently converted to hot flare plasma implying an effective validation of the Neupert effect.

Recent results of the AMS-02 experiment on the ISS

The Alpha Magnetic Spectrometer has recently released a first set of precise measurements of cosmic rays detected on the International Space Station in the GeV to TeV energy range. The fluxes of positrons, electrons and protons are presented. Neither of the fluxes is compatible with a single power law. Both the electron flux and the positron flux change their behavior at ∼30 GeV but the fluxes are significantly different in their magnitude and energy dependence. Between 20 and 200 GeV the positron spectral index is significantly harder than the electron spectral index. Above ∼200 GeV the positron fraction no longer exhibits an increase with energy. The proton flux is progressively hardening above rigidity ∼100 GV. The detailed variation with rigidity of the proton flux spectral index is presented.

GAMMA-RAY BURSTS ARE OBSERVED OFF-AXIS

We use the ScaleFit package to perform Markov chain Monte Carlo light curve fitting on a large sample of Swift-XRT gamma-ray burst afterglows. The ScaleFit model uses scaling relations in the hydrodynamic and radiation equations to compute synthetic light curves directly from a set of high resolution two-dimensional relativistic blast wave simulations. The data sample consists of all Swift-XRT afterglows from 2005 to 2012 with sufficient coverage and a known redshift, 188 bursts in total. We find the jet half opening angle varies widely but is commonly less than 0.1 radians. The distribution of the electron spectral index is also broad, with a median at 2.23. This approach allows, for the first time, for the off-axis observer angle to be inferred directly from the light curve. We find the observer angle to have a median value of 0.57 of the jet opening angle over our sample, which has profound consequences for the predicted rate of observed jet breaks and effects the beaming corrected total energies of gamma-ray bursts.

Electron and positron fluxes in primary cosmic rays measured with the alpha magnetic spectrometer on the international space station.

Precision measurements by the Alpha Magnetic Spectrometer on the International Space Station of the primary cosmic-ray electron flux in the range 0.5 to 700GeV and the positron flux in the range 0.5 to 500GeV are presented. The electron flux and the positron flux each require a description beyond a single power-law spectrum. Both the electron flux and the positron flux change their behavior at ∼30 GeV but the fluxes are significantly different in their magnitude and energy dependence. Between 20 and 200GeV the positron spectral index is significantly harder than the electron spectral index. The determination of the differing behavior of the spectral indices versus energy is a new observation and provides important information on the origins of cosmic-ray electrons and positrons.

The low-high-low trend of type III radio burst starting frequencies and solar flare hard X-rays

Using simultaneous X-ray and radio observations from solar flares, we investigate the link between the type III radio burst starting frequency and hard X-ray spectral index. For a proportion of events the relation derived between the starting height (frequency) of type III radio bursts and the electron beam velocity spectral index (deduced from X-rays) is used to infer the spatial properties (height and size) of the electron beam acceleration region. Both quantities can be related to the distance travelled before an electron beam becomes unstable to Langmuir waves. To obtain a list of suitable events we considered the RHESSI catalogue of X-ray flares and the Phoenix 2 catalogue of type III radio bursts. From the 200 events that showed both type III and X-ray signatures, we selected 30 events which had simultaneous emission in both wavelengths, good signal to noise in the X-ray domain and > 20 seconds duration. We find that > 50 % of the selected events show a good correlation between the starting frequencies of the groups of type III bursts and the hard X-ray spectral indices. A low-high-low trend for the starting frequency of type III bursts is frequently observed. Assuming a background electron density model and the thick target approximation for X-ray observations, this leads to a correlation between starting heights of the type III emission and the beam electron spectral index. Using this correlation we infer the altitude and vertical extents of the flare acceleration regions. We find heights from 183 Mm down to 25 Mm while the sizes range from 13 Mm to 2 Mm. These values agree with previous work that places an extended flare acceleration region high in the corona. We analyse the assumptions required and explore possible extensions to our assumed model. We discuss these results with respect to the acceleration heights and sizes derived from X-ray observations alone.

The ~10 hour modulation of the relativistic electron spectrum as a result of the periodic motion of the Jovian outer magnetosphere layer: Ulysses observations

We analyze relativistic (E>3MeV) electron observations during the dayside inbound trajectory of Ulysses (day 33 to day 38, 1992) in the Jovian magnetosphere and we demonstrate that the continuous presence of a relativistic electron layer at higher north latitudes (Ulysses reached ~40° lat. during closest approach the planet). In particular, we evaluated the cross-B field anisotropy of relativistic (E>3MeV) electrons intensity by the COSPIN/HET detector onboard Ulysses, and we found that between the times of plasma sheet crossings/approaches, when Ulysses was found far from the magnetodisc, at higher north latitudes, local increases in the relativistic electron intensity and intensity gradient in the northward direction were persistently observed. We also found that (1) the well known ~10h separated relativistic electron spectral index peaks (spectral softening) and (2) the detection of relativistic electron intensity gradient in the northward direction are related phenomena. We infer that phenomenon 1 and 2 are explained by the ~10h periodic upward-downward motion of the Jovian magnetosphere, and consequently of the outer magnetosphere relativistic electron layer. Τhe above results extends earlier results for low energy electrons and energetic protons (Anagnostopoulos et al., 1998, 2001b) to relativistic electron phenomena, and provide strong evidence, for the first time, that the well known ~10h rocking of the relativistic electron spectrum in the outer magnetosphere (the so called “clock phenomenon”) is a spatial and not a temporal effect, as was earlier hypothesized (Simpson et al.,1992).

Arbitrary amplitude dust-acoustic double-layers in a warm dusty plasma with suprathermal electrons, two-temperature thermal ions, and drifting dust grains

Arbitrary amplitude dust-acoustic double-layers (DA-DLs) in a plasma with suprathermal electrons, two-temperature thermal ions, and warm drifting dust grains are investigated. Our results reveal that the spatial patterns of the DA-DLs are affected by the degree of the electron suprathermality. The electron thermalization involves a decrease of the cold ion component density, for the existence of localized DA-DLs. An increase of the dust drift velocity requires a decrease of κ (the electron spectral index), for the onset of dust-acoustic double-layers. An increase of the Mach number M leads to an increase of the DL amplitude as well as the corresponding electron spectral index for which the DL occurs.

Second-order Fermi acceleration as the origin of the Fermi bubbles

Gamma-ray data from Fermi-LAT show a bi-lobular structure extending up to 50° above and below the Galactic centre, coincident with a possibly related structure in the ROSAT X-ray map which presumably originated in some energy release close to the centre a few million years ago. It has been argued that the gamma-rays arise due to inverse Compton scattering of relativistic electrons accelerated at plasma shocks present in the bubbles. We explore the alternative possibility that the relativistic electrons undergo stochastic second-order Fermi acceleration in the entire volume of the bubbles by plasma wave turbulence. This turbulence is generated behind the outer shock and propagates into the bubble volume, leading to a non-trivial spatial variation of the electron spectral index. Rather than a constant volume emissivity as predicted in other models we find an almost constant surface brightness in gamma-rays and also reproduce the observed sharp edges of the bubbles. We comment on possible cross-checks in other channels.

Characteristics of the flare acceleration region derived from simultaneous hard X-ray and radio observations

We investigate the type III radio bursts and X-ray signatures of accelerated electrons in a well observed solar flare in order to find the spatial properties of the acceleration region. Combining simultaneous RHESSI hard X-ray flare data and radio data from Phoenix-2 and the Nan\c{c}ay radioheliograph, the outward transport of flare accelerated electrons is analyzed. The observations show that the starting frequencies of type III bursts are anti-correlated with the HXR spectral index of solar flare accelerated electrons. We demonstrate both analytically and numerically that the type III burst starting location is dependent upon the accelerated electron spectral index and the spatial acceleration region size, but weakly dependent on the density of energetic electrons for relatively intense electron beams. Using this relationship and the observed anti-correlation, we estimate the height and vertical extent of the acceleration region, giving values of around 50 Mm and 10 Mm respectively. The inferred acceleration height and size suggests that electrons are accelerated well above the soft X-ray loop-top, which could be consistent with the electron acceleration between 40 Mm and 60 Mm above the flaring loop.

PROBING THE TRANSITION BETWEEN THE SYNCHROTRON AND INVERSE-COMPTON SPECTRAL COMPONENTS OF 1ES 1959+650

1ES 1959+650 is one of the most remarkable high-peaked BL Lacertae objects (HBL). In 2002, it exhibited a TeV gamma-ray flare without a similar brightening of the synchrotron component at lower energies. We present the results of a multifrequency campaign, triggered by the INTEGRAL IBIS detection of 1ES 1959+650. Our data range from the optical to hard X-ray energies, thus covering the synchrotron and inverse-Compton components simultaneously. We observed the source with INTEGRAL, the Swift X-Ray Telescope, and the UV-Optical Telescope, and nearly simultaneously with a ground-based optical telescope. The steep spectral component at X-ray energies is most likely due to synchrotron emission, while at soft gamma-ray energies the hard spectral index may be interpreted as the onset of the high-energy component of the blazar spectral energy distribution (SED). This is the first clear measurement of a concave X-ray-soft gamma-ray spectrum for an HBL. The SED can be well modeled with a leptonic synchrotron self-Compton model. When the SED is fitted this model requires a very hard electron spectral index of q ~ 1.85, possibly indicating the relevance of second-order Fermi acceleration.

Nonlinear dust acoustic waves in a charge varying dusty plasma with suprathermal electrons

Arbitrary amplitude dust acoustic waves in a dusty plasma with a high-energy-tail electron distribution are investigated. The effects of charge variation and electron deviation from the Boltzmann distribution on the dust acoustic soliton are then considered. The dust charge variation makes the dust acoustic soliton more spiky. The dust grain surface collects less electrons as the latter evolves far away from their thermodynamic equilibrium. The dust accumulation caused by a balance of the electrostatic forces acting on the dust grains is more effective for lower values of the electron spectral index. Under certain conditions, the dust charge fluctuation may provide an alternate physical mechanism causing anomalous dissipation, the strength of which becomes important and may prevail over that of dispersion as the suprathermal character of the plasma becomes important. Our results may explain the strong spiky waveforms observed in auroral plasmas.

Probing magnetic turbulence by synchrotron polarimetry: statistics and structure of magnetic fields from Stokes correlators

We describe a technique for probing the statistical properties of cosmic magnetic fields based on radio polarimetry data. Second-order magnetic field statistics like the power spectrum cannot always distinguish between magnetic fields with essentially different spatial structure. Synchrotron polarimetry naturally allows certain 4th-order magnetic field statistics to be inferred from observational data, which lifts this degeneracy and can thereby help us gain a better picture of the structure of the cosmic fields and test theoretical scenarios describing magnetic turbulence. In this work we show that a 4th-order correlator of physical interest, the tension-force spectrum, can be recovered from the polarized synchrotron emission data. We develop an estimator for this quantity based on polarized-emission observations in the Faraday-rotation-free frequency regime. We consider two cases: a statistically isotropic field distribution, and a statistically isotropic field superimposed on a weak mean field. In both cases the tension force power spectrum is measurable; in the latter case, the magnetic power spectrum may also be obtainable. The method is exact in the idealized case of a homogeneous relativistic-electron distribution that has a power-law energy spectrum with a spectral index p=3, and assumes statistical isotropy of the turbulent field. We carry out tests of our method using synthetic data generated from numerically simulated magnetic fields. We show that the method is valid, that it is not prohibitively sensitive to the value of the electron spectral index, and that the observed tension-force spectrum allows one to distinguish between, e.g., a randomly tangled magnetic field (a default assumption in many studies) and a field organized in folded flux sheets or filaments.

Small amplitude ion-acoustic double layers in a plasma with superthermal electrons and thermal positrons

Small-amplitude ion-acoustic double layers (IA-DLs) in a plasma with superthermal electrons and thermal positrons are investigated. Due to the electron superthermality and the relative fraction of positrons, our plasma model can admit compressive as well as rarefactive IA-DLs. As the electrons evolve toward their thermodynamic equilibrium, the negative IA-DL shrinks and, beyond a certain critical value of the electron spectral index κc, develops into a positive structure allowing therefore the existence of compressive IA-DLs. This critical value is lowered as the number of positrons becomes important. As the superthermal character of the plasma increases, the threshold pc above which only compressive IA-DLs are admitted is shifted toward higher values. Our investigation may help to understand the DL structures observed in the ionosphere and the auroral acceleration regions.