Power-law Electron Energy Research Articles

Particle-in-cell simulations of low-β magnetic reconnection driven by laser interaction with a capacitor–coil target

The dynamics of low-β magnetic reconnection (MR) driven by laser interaction with a capacitor–coil target are reexamined by simulations in this paper. We compare two cases MR and non-MR (also referred as AP-case and P-case standing for the anti-parallel and parallel magnetic field lines, respectively) to distinguish the different characteristics between them. We find that only in the AP-case the reconnection electric field shows up around the X line and the electron jet is directed toward the X line. The quadruple magnetic fields exist in both cases, however, they distribute in the current sheet area in the AP-case, and out of the squeezing area in the P-case, because electrons are demagnetized in the electron diffusion region in the MR process, which is absent in the P-case. The electron acceleration is dominant by the Fermi-like mechanism before the MR process, and by the reconnection electric field when the MR occurs. A power-law electron energy spectrum with an index of 1.8 is found in the AP-case. This work proves the significant potential of this experimental platform to be applied in the studies of low-β astronomy phenomena.

Multiwavelength study of the quiescent states of six brightest flat-spectrum radio quasars detected by Fermi-LAT

ABSTRACT The regular monitoring of flat-spectrum radio quasars (FSRQs) in γ-rays by Fermi-LAT (Large Area Telescope) since past 12 yr indicated six sources who exhibited extreme γ-ray outbursts crossing daily flux of 10−5 photons cm−2 s−1. We obtained nearly simultaneous multiwavelength data of these sources in radio to γ-ray waveband from OVRO (Owens Valley Radio Observatory), Steward Observatory, SMARTS (Small and Moderate Aperture Research Telescope System), Swift-UVOT (UV/Optical Telescope), Swift-XRT (X-ray Telescope), and Fermi-LAT. The time-averaged broad-band spectral energy distributions (SEDs) of these sources in quiescent states were studied to get an idea about the underlying baseline radiation processes. We modelled the SEDs using one-zone leptonic synchrotron and inverse Compton emission scenario from broken power-law electron energy distribution inside a spherical plasma blob, relativistically moving down a conical jet. The model takes into account inverse Compton scattering of externally and locally originated seed photons in the jet. The big blue bumps visible in quiescent state SEDs helped to estimate the accretion disc luminosities and central black hole masses. We found a correlation between the magnetic field inside the emission region and the ratio of emission region distance to disc luminosity, which implies that the magnetic field decreases with an increase in emission region distance and decrease in disc luminosity, suggesting a disc–jet connection. The high-energy index of the electron distribution was also found to be correlated with observed γ-ray luminosity as γ-rays are produced by high-energy particles. In most cases, kinetic power carried by electrons can account for jet radiation power as jets become radiatively inefficient during quiescent states.

Electron Energy Spectra and e–e Bremsstrahlung from Anisotropic Electron Distributions in Extreme Solar Flares

We study the electron energy spectra of two powerful solar flares SOL2003-10-28T 11:06:16 (GOES class X17.2) and SOL2002-07-23T00:18:16 (X4.8) on the basis of HXR and gamma-ray spectra obtained from RHESSI data. Electron-electron (e-e) bremsstrahlung makes a significant contribution to the X-ray flux at energies above 500 keV. In X-ray flux calculations different electron pitch-angle distributions were considered: quasi-transverse and quasi-longitudinal. It was shown that breaks in hard X-ray spectra occur on energies $\epsilon\approx100$ keV with photon spectral-index difference $\Delta\gamma\ge 1$ in the case of quasi-longitudinal anisotropy and hard power-law electron energy spectra. We deduce the parameters of non-thermal electrons energy spectra from RHESSI data for the extreme solar flares of 2003 October 28 and 2002 July 23. After including e-e bremsstrahlung, the non-thermal electrons energy spectra obtained in the thick-target model can be fitted using power-law with spectral index $\delta\approx 5$. For the 2002 July 23 flare, there is a pronounced asymmetry towards the southern footpoint, starting from energies above 100 keV. The separation of HXR sources at energies above 100 keV may be related to a feature of relativistic electron transport in flaring loops.

Formation of Power-law Electron Energy Spectra in Three-dimensional Low-β Magnetic Reconnection

Abstract While observations have suggested that power-law electron energy spectra are a common outcome of strong energy release during magnetic reconnection, e.g., in solar flares, kinetic simulations have not been able to provide definite evidence of power-laws in energy spectra of nonrelativistic reconnection. By means of 3D large-scale fully kinetic simulations, we study the formation of power-law electron energy spectra in nonrelativistic low-β reconnection. We find that both the global spectrum integrated over the entire domain and local spectra within individual regions of the reconnection layer have power-law tails with a spectral index p ∼ 4 in the 3D simulation, which persist throughout the nonlinear reconnection phase until saturation. In contrast, the spectrum in the 2D simulation rapidly evolves and quickly becomes soft. We show that 3D effects such as self-generated turbulence and chaotic magnetic field lines enable the transport of high-energy electrons across the reconnection layer and allow them to access several main acceleration regions. This leads to a sustained and nearly constant acceleration rate for electrons at different energies. We construct a model that explains the observed power-law spectral index in terms of the dynamical balance between particle acceleration and escape from main acceleration regions, which are defined based upon a threshold for the curvature drift acceleration term. This result could be important for explaining the formation of power-law energy spectrum in solar flares.

Inverse Compton Scattering of the Central Source Photons as an X-Ray Emission Mechanism on Kiloparsec Scales in PKS 1127–145

Abstract The beamed inverse Compton/cosmic microwave background model has generally been used for the interpretation of X-ray radiation from kiloparsec-scale jets of core-dominated quasars. Recent Fermi-LAT and HST observations have brought this model into question. We examine the assumption that X-rays from the kiloparsec-scale jet of the quasar PKS 1127−145 are produced by inverse Compton scattering of the central source emission. In this context, we show that both similarity and distinction between the observed radio and X-ray spectral indices for some of the jet knots can be explained under a single power-law electron energy distribution. We derive that the viewing angle of the kiloparsec-scale jet is about 35° and the jet has a moderate relativistic speed of ≈0.8c. The predicted gamma-ray flux of the jet is found to be a few orders of magnitude lower than the minimum flux level measured by Fermi-LAT, further supporting our scenario.

Modeling the Multiband Afterglows of GRB 060614 and GRB 060908: Further Evidence for a Double Power-law Hard Electron Energy Spectrum

Abstract Electrons accelerated in relativistic collisionless shocks are usually assumed to follow a power-law energy distribution with an index of p. Observationally, although most gamma-ray bursts (GRBs) have afterglows that are consistent with p > 2, there are still a few GRBs suggestive of a hard (p < 2) electron energy spectrum. Our previous work showed that GRB 091127 gave strong evidence for a double power-law hard electron energy (DPLH) spectrum with 1 < p 1 < 2, p 2 > 2 and an “injection break” assumed as γ b ∝ γ q in the highly relativistic regime, where γ is the bulk Lorentz factor of the jet. In this paper, we show that GRB 060614 and GRB 060908 provide further evidence for such a DPLH spectrum. We interpret the multiband afterglow of GRB 060614 with the DPLH model in a homogeneous interstellar medium by taking into account a continuous energy injection process, while, for GRB 060908, a wind-like circumburst density profile is used. The two bursts, along with GRB 091127, suggest a similar behavior in the evolution of the injection break, with q ∼ 0.5. Whether this represents a universal law of the injection break remains uncertain and more afterglow observations such as these are needed to test this conjecture.

On the Origin of the Hard X-Ray Excess of High-Synchrotron-Peaked BL Lac Object Mrk 421

Abstract For the first time, Kataoka & Stawarz reported a clear detection of a hard X-ray excess, above , in the high-synchrotron-peaked BL Lac object Mrk 421. We find that this feature may not be produced by the low-energy part of the same electron population that produced the Fermi/LAT γ-ray. Because of that, it is required that the power-law electron energy go down to , which predicts a very strong radio emission (radio flux larger than the observed), even considering the synchrotron self-absorption effect. We investigate the possibility of this excess being produced from the spine/layer jet structure, which has been clearly detected in Mrk 421. We find that (1) similar to one-zone modeling, the spine emissions provide good modeling of the broadband spectral energy distribution, except for the hard X-ray excess; and (2) the hard X-ray excess can be well represented by the synchrotron photons (from the layer) being inverse Compton scattered by the spine electrons.

Applying Relativistic Reconnection to Blazar Jets

Rapid and luminous flares of non-thermal radiation observed in blazars require an efficient mechanism of energy dissipation and particle acceleration in relativistic active galactic nuclei (AGN) jets. Particle acceleration in relativistic magnetic reconnection is being actively studied by kinetic numerical simulations. Relativistic reconnection produces hard power-law electron energy distributions N ( γ ) ∝ γ − p exp ( − γ / γ max ) with index p → 1 and exponential cut-off Lorentz factor γ max ∼ σ in the limit of magnetization σ = B 2 / ( 4 π w ) ≫ 1 (where w is the relativistic enthalpy density). Reconnection in electron-proton plasma can additionally boost γ max by the mass ratio m p / m e . Hence, in order to accelerate particles to γ max ∼ 10 6 in the case of BL Lacs, reconnection should proceed in plasma of very high magnetization σ max ≳ 10 3 . On the other hand, moderate mean jet magnetization values are required for magnetic bulk acceleration of relativistic jets, σ mean ∼ Γ j ≲ 20 (where Γ j is the jet bulk Lorentz factor). I propose that the systematic dependence of γ max on blazar luminosity class—the blazar sequence—may result from a systematic trend in σ max due to homogeneous loading of leptons by pair creation regulated by the energy density of high-energy external radiation fields. At the same time, relativistic AGN jets should be highly inhomogeneous due to filamentary loading of protons, which should determine the value of σ mean roughly independently of the blazar class.

THE HARD X-RAY VIEW OF THE YOUNG SUPERNOVA REMNANT G1.9+0.3

NuSTAR observed G1.9+0.3, the youngest known supernova remnant in the Milky Way, for 350 ks and detected emission up to $\sim$30 keV. The remnant's X-ray morphology does not change significantly across the energy range from 3 to 20 keV. A combined fit between NuSTAR and CHANDRA shows that the spectrum steepens with energy. The spectral shape can be well fitted with synchrotron emission from a power-law electron energy distribution with an exponential cutoff with no additional features. It can also be described by a purely phenomenological model such as a broken power-law or a power-law with an exponential cutoff, though these descriptions lack physical motivation. Using a fixed radio flux at 1 GHz of 1.17 Jy for the synchrotron model, we get a column density of N$_{\rm H}$ = $(7.23\pm0.07) \times 10^{22}$ cm$^{-2}$, a spectral index of $\alpha=0.633\pm0.003$, and a roll-off frequency of $\nu_{\rm rolloff}=(3.07\pm0.18) \times 10^{17}$ Hz. This can be explained by particle acceleration, to a maximum energy set by the finite remnant age, in a magnetic field of about 10 $\mu$G, for which our roll-off implies a maximum energy of about 100 TeV for both electrons and ions. Much higher magnetic-field strengths would produce an electron spectrum that was cut off by radiative losses, giving a much higher roll-off frequency that is independent of magnetic-field strength. In this case, ions could be accelerated to much higher energies. A search for $^{44}$Ti emission in the 67.9 keV line results in an upper limit of $1.5 \times 10^{-5}$ $\,\mathrm{ph}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}$ assuming a line width of 4.0 keV (1 sigma).

Electron acceleration observed by the FAST satellite within the IAR during a 3 Hz modulated EISCAT heater experiment

Abstract. A quantitative analysis is presented of the FAST satellite electric field and particle flux data during an EISCAT heating experiment run on 8 October 1998. Radio frequency heating, modulated at 3 Hz, launched ULF waves from the ionosphere into the lower magnetosphere. The ULF waves were observed in FAST data and constituted the first satellite detection of artificially excited Alfvénic ULF waves. The downward electron flux data for this event contain the first observations of electrons undergoing acceleration within the Ionospheric Alfvén Resonator (IAR) due to parallel electric fields associated with an artificially stimulated Alfvén wave. The time history and spectral content of the observed down-ward electron fluxes is investigated by considering the effects of a localised parallel electric field. Furthermore, it is demonstrated that a power law electron energy distribution describes the time-variable observed fluxes better than a Maxwellian distribution.Key words. Ionosphere (active experiments; particle acceleration) – Magnetospheric physics (electric fields)

Synchrotron emission from anisotropic disordered magnetic fields

We derive expressions for the total and linearly-polarized synchrotron emissivity of an element of plasma containing relativistic particles and disordered magnetic field which has been sheared or compressed along three independent directions. Our treatment follows that given by Matthews & Scheuer (1990) in the special case of a power-law electron energy spectrum. We show that the emissivity integrals depend on a single parameter, making it straightforward to generate one-dimensional look-up tables. We also demonstrate that our formulae give identical results to those in the literature in special cases.

Numerical modelling of the electron energy distribution functionin the electric field of a nanosecond pulsed discharge

A numerical code is developed and used to model an unsteady electronenergy distribution function (EEDF) in the electric field of ananosecond repetitive discharge propagating as a fast ionization wave(FIW) of negative polarity. The EEDF in a FIW is shown to form as aresult of the interaction between two oppositely directed electronfluxes along the energy axis. On the one hand, high-energy electronsoriginating in the breakdown front give rise to a decreasing power-lawelectron energy distribution: high-energy electrons loseenergy in inelastic collisions in the weak field region behind thefront, thereby producing the downward electron flux along the energyaxis. On the other hand, near the thresholds for inelastic processes,the formation of the EEDF is strongly affected by the electric field,which heats the electron component and thus increases the energy of thecold electrons. The time required for the EEDF to relax to a quasisteadyfunction is governed by the time scales of both the upward and downwardelectron fluxes along the energy axis. The spatially non-local processesthat increase the mean electron energy ahead of the front of the strongelectric fields are also found to have a significant effect on the shapeof the resulting EEDF.

Simultaneous Radio and X‐Ray Observations of the Wolf‐Rayet Star WR 147

We present results of simultaneous ASCA/Very Large Array (VLA) observations of the Wolf-Rayet star WR 147 (AS 431). This WN 8 star is an optical double and may be a WR+OB colliding wind binary system. The new observations place tight constraints on the origin of its X-ray and radio emission. The X-ray emission is due to a multitemperature, optically thin thermal plasma, with the dominant contribution coming from plasma at kT ≈ 1 keV. The absorption column density derived from the X-ray spectrum is NH = 2 × 1022 cm-2, which agrees well with estimates based on the visual extinction but is too large to explain by wind absorption alone. The X-ray temperature structure is consistent with colliding wind shock emission, but the unabsorbed X-ray luminosity Lx = 1032.55 ergs s-1 (0.5-10 keV) is several times smaller than that predicted from colliding wind shock models. The VLA data provide the most complete picture ever obtained of the radio spectral energy distribution of a WR star and consist of near-simultaneous observations at five different wavelengths (1.3, 2, 3.6, 6, and 21 cm). The radio emission consists of a thermal free-free component from the WR wind and a nonthermal component. If the nonthermal emission is due to relativistic particles accelerated by the Fermi mechanism in wind shocks, then the flux is expected to decline at high frequencies according to Sν ∝ ν-0.5. However, the observed falloff is much steeper and cannot be reproduced by a simple power law or by synchrotron models that assume power-law electron energy distributions. A surprising result is that the nonthermal emission can be accurately modeled as synchrotron radiation from relativistic electrons that are nearly monoergetic.

A coronal loop model for the production of X-ray and radio flares in the RS CVn binary HR 1099

The RS CVn binary stellar system HR 1099 is a source of both X-ray and radio flares. We present here a model of the system in which the two types of flare are produced by the same population of mildly-relativistic (γ ≲ 10) electrons, injected into a coronal loop. After reviewing possible radiation mechanisms we conclude that, given the probable conditions in the flaring region, the radio emission is gyrosynchrotron radiation and the X-ray emission is thermal bremsstrahlung. The thermal X-ray source must lie in the stellar chromosphere, but the apparent absence of plasma absorption at radio frequencies indicates that the radio source is located high in the coronal loop. Using the relationships given by Dulk and Marsh (1982) for the radio emission from a power-law electron energy spectrum,N(γ)α (γ - 1)−δ, we conclude that 3 ≲δ ≲ 7, with ≳ 30% of the electron population trapped in the radio source. Some implications of these results for one particular version of the model are discussed.

Radio observations of HR 1099 during the large flare of October 1988

Observations at five frequencies in the range 1.4–15 GHz were made using the US VLA on the chromospheric activity type binary HR1099. During the period of observation the source was in the course of a strong flare event, its radio luminosity reached l.8 × 10 18erg s −1 Hz −1. As the flux decreased, the spectrum steepened, the spectral inversion frequency decreased and the degree of circular polarization increased towards a medium strong polarization. The direction of circular polarization varied with the frequency. The emission mechanism during the strong flare is probably synchrotron accelerated emission. We found, for the time of the flare, and at optical depth τ ∼ 1, a magnetic field of about 10 G, a mean electron energy of about 4MeV, an electron density of 3–9 × 10 4 cm −3 and a spectral index of about 1.3 in the power-law electron energy spectrum.

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.

A radio burst with peculiar polarization behaviour in July 1974

Observing the total solar flux at 17 GHz a radio burst with unusual polarization characteristics (e.g. correlation of intensity maxima with maxima of polarization degree) has been recorded. The discussion shows that there is a possibility for a small optical depth of the source for at least one propagation mode during the burst maximum. Furthermore it could be found that the emission has been caused probably by synchroton radiation with a power law electron energy distribution (N(ɛ)∼ɛ−γ) with γ≈4.