Power-law Energy Distribution Research Articles

Analytical Afterglow Light Curves of Gamma-ray Bursts: the Case of a Flat Electron Spectrum

In the standard afterglow model, the swept electrons have a single power-law energy distribution dn/dγe ∝ γ−p e (p ∼ 2.3), owing to the first order Fermi acceleration process. However, in some events people find a lot of evidence for a flat electron spectrum (i.e., p < 2). In this work, the analytical afterglow light curves in the case of a flat electron energy distribution are presented respectively for a single power-law spectrum and a broken power-law spectrum, then the results are applied to the specific burst GRB 060908. Besides, we have also speculated a possible solution of the so-called low energy spectrum crisis of Gamma-ray Bursts

Time-dependent galactic winds

Cosmic rays are transported out of the galaxy by diffusion and advection due to streaming along magnetic field lines and resonant scattering off self-excited MHD waves. Thus momentum is transferred to the plasma via the frozen-in waves as a mediator assisting the thermal pressure in driving a galactic wind. The bulk of the Galactic CRs are accelerated by shock waves generated in SNRs, a significant fraction of which occur in OB associations on a timescale of several $10^7$ years. We examine the effect of changing boundary conditions at the base of the galactic wind due to sequential SN explosions on the outflow. Thus pressure waves will steepen into shock waves leading to in situ post-acceleration of GCRs. We performed simulations of galactic winds in flux tube geometry appropriate for disk galaxies, describing the CR diffusive-advective transport in a hydrodynamical fashion along with the energy exchange with self-generated MHD waves. Our time-dependent CR hydrodynamic simulations confirm the existence of time asymptotic outflow solutions (for constant boundary conditions). It is also found that high-energy particles escaping from the Galaxy and having a power-law distribution in energy ($\propto E^{-2.7}$) similar to the Milky Way with an upper energy cut-off at $\sim 10^{15}$ eV are subjected to efficient and rapid post-SNR acceleration in the lower galactic halo up to energies of $10^{17} - 10^{18}$ eV by multiple shock waves propagating through the halo. The particles can gain energy within less than $3\,$kpc from the galactic plane corresponding to flow times less than $5\cdot 10^6\,$years. The mechanism described here offers a natural solution to explain the power-law distribution of CRs between the "knee" and the "ankle". The mechanism described here offers a natural and elegant solution to explain the power-law distribution of CRs between the "knee" and the "ankle".

Prompt, early and afterglow optical observations of five γ-ray bursts: GRB 100901A, GRB 100902A, GRB 100905A, GRB 100906A and GRB 101020A

We present the results of the prompt, early and afterglow optical observations of five γ-ray bursts (GRBs): GRB 100901A, GRB 100902A, GRB 100905A, GRB 100906A and GRB 101020A. These observations were made with the Mobile Astronomical System of TElescope-Robots in Russia (MASTER-II Net), the 1.5-m telescope of the Sierra Nevada Observatory and the 2.56-m Nordic Optical Telescope. For two sources, GRB 100901A and GRB 100906A, we detected optical counterparts and obtained light curves starting before the cessation of γ-ray emission, at 113 and 48 s after the trigger, respectively. Observations of GRB 100906A were conducted in two polarizing filters. Observations of the other three bursts gave the upper limits on the optical flux; their properties are briefly discussed. A more detailed analysis of GRB 100901A and GRB 100906A, supplemented by Swift data, provides the following results and indicates different origins for the prompt optical radiation in the two bursts. The light-curve patterns and spectral distributions suggest that there is a common production site for the prompt optical and high-energy emission in GRB 100901A. The results of the spectral fits for GRB 100901A in the range from optical to X-ray favour power-law energy distributions and a consistent value of the optical extinction in the host galaxy. GRB 100906A produced a smoothly peaking optical light curve, suggesting that the prompt optical radiation in this GRB originated in a front shock. This is supported by a spectral analysis. We have found that the Amati and Ghirlanda relations are satisfied for GRB 100906A. We obtain an upper limit on the value of the optical extinction on the host of GRB 100906A.

THE INFRARED JET IN 3C 31

We report the detection of infrared emission from the jet of the nearby FR I radio galaxy 3C 31. The jet was detected with the IRAC instrument on Spitzer at 4.5 micron, 5.8 micron, and 8.0 micron out to 30" (13 kpc) from the nucleus. We measure radio, infrared, optical, and X-ray fluxes in three regions along the jet determined by the infrared and X-ray morphology. Radio through X-ray spectra in these regions demonstrate that the emission can be interpreted as synchrotron emission from a broken power-law distribution of electron energies. We find significant differences in the high energy spectra with increasing distance from the nucleus. Specifically, the high energy slope increases from 0.86 to 1.72 from 1 kpc to 12 kpc along the jet, and the spectral break likewise increases in frequency along the jet from 10-100's of GHz to ~20 THz. Thus the ratio of IR to X-ray flux in the jet increases by at least an order of magnitude with increasing distance from the nucleus. We argue that these changes cannot simply be the result of spectral aging and that there is ongoing particle acceleration through this region of the jet. The effects of mass loading, turbulence, and jet deceleration, however these processes modify the jet flow in detail, must be causing a change in the electron energy distribution and the efficiency of particle acceleration.

FERMI constraints on the high energy, ~1 GeV, emission of long gamma ray bursts

We investigate the constraints imposed on the luminosity function (LF) of long duration Gamma Ray Bursts (LGRBs) by the flux distribution of bursts detected by the GBM at ~1 MeV, and the implications of the non detection of the vast majority, ~95%, of the LGRBs at higher energy, ~1 GeV, by the LAT detector. We find a LF that is consistent with those determined by BATSE and Swift. The non detections by LAT set upper limits on the ratio R of the prompt fluence at ~1 GeV to that at ~1 MeV. The upper limits are more stringent for brighter bursts, with R<{0.1,0.3,1} for {5,30,60}% of the bursts. This implies that for most bursts the prompt ~1 GeV emission may be comparable to the ~1 MeV emission, but can not dominate it. The value of R is not universal, with a spread of (at least) an order of magnitude around R~10^(-1). For several bright bursts with reliable determination of the photon spectral index at ~1 MeV, the LAT non detection implies an upper limit to the ~100 MeV flux which is <0.1 of the flux obtained by extrapolating the ~1 MeV flux to high energy. For the widely accepted models, in which the ~1 MeV power-law photon spectrum reflects the power-law energy distribution of fast cooling electrons, this suggests that either the electron energy distribution does not follow a power-law over a wide energy range, or that the high energy photons are absorbed. Requiring an order unity pair production optical depth at ~100 MeV sets an upper limit for the Lorentz factor, Gamma<=10^(2.5).

Proton beam Weibel instability simulations of energy transfer in gamma-ray bursts

Proton beam Weibel instability may explain key ingredients for Gamma-Ray Bursts (GRBs): amplified magnetic field, relativistic electron production and a power law energy distribution. By using particle-in-cell simulations, we demonstrate that a part of the directed kinetic energy of a proton beam is converted into kinetic energy of electrons, ions, electric and magnetic fields. A finite lifetime for the magnetic field is demonstrated, indicating a maximum for the GRB duration. An experiment probing the GRB environment is proposed.

Magnetostatic structures in collisionless plasma and their synchrotron radiation

The properties of the magnetostatic structures in a collisionless relativistic plasma found by exactly solving the nonlinear self-consistent kinetic and Maxwell equations using the method of invariants of particle motion are analyzed. These structures include individual neutral current sheets and cylindrically symmetric filaments as well as their ensembles, admitting a wide variety of types of particle energy distribution functions. Relationships are established between the possible parameters of the current sheets and filaments—their sizes, currents and magnetic fields, and the degree of anisotropy of the particle momentum distribution. The extent to which these parameters are conditioned by the properties of the Weibel instability that can produce these structure is also discussed. The spectral peculiarities of the synchrotron radiation from the particles that form the current sheets and filaments are investigated in the special case of power-law energy distribution functions.

Features of electron current layers: Comparison between three‐dimensional particle‐in‐cell simulations and Cluster observations

Wygant et al. (2005) and more recently Chen et al. (2008) reported Cluster observations on some basic features of electron current layers (ECL) in the magnetotail. These features include (1) a bifurcated ECL consisting of two layers with relatively large currents separated by a region of small current, (2) peaked density at the ECL center bordered by extended low‐density regions, (3) bipolar Hall electric fields (EHall), (4) fine‐scale, large‐amplitude spiky turbulence in the electric fields normal to the plane of the ECL (En), (5) energized electrons that become increasingly isotropized toward the ECL central region, (6) cold electrons bordering the ECL, (7) ions accelerated by the Hall electric field, and (8) ions counterstreaming against the ions accelerated by EHall on both the north and south sides of the neutral sheet at the ECL midplane. We compare all these features with results from fully three‐dimensional particle‐in‐cell simulations of an ECL. Simulations reveal that the fine structures in the electric fields inside the ECL are created by the ECL‐driven electrostatic instabilities, which are instrumental in rapid heating and isotropization of the electrons with power law energy distribution, Fe(E) ≈ E−0.7. The heated electrons set up ambipolar electric fields (Ea) in the central part of the ECL, reflecting ions accelerated by EHall. The overall structures in the normal electric fields result from the superposition of EHall, Ea, and the instability‐generated electric fields.

Photo-Induced In-Gap States in SrTiO3Probed by Photoemission Spectroscopy under Ultraviolet Illumination

We report on an electronic structure study of SrTiO 3 under ultraviolet illumination. Photoemission measurements at 20 K under ultraviolet illumination show that the illumination induces electronic states within the band gap. The photo-induced in-gap states show the power-law energy distribution with exponent of 3.4–3.7 and weakly depends on the strength of illumination. The photo-induced in-gap states indicate that most of the photo-excited electrons are trapped by local lattice distortions with various size scale. We argue that the free carriers in the Ti 3 d band and the localized Ti 3 d electrons and O 2 p holes within the band gap contribute to the photoconductivity and the ferroelectricity under the ultraviolet illumination, respectively.

Particle acceleration in supernova remnants

Supernova remnants (SNR) are the most likely source of galactic cosmic rays (CRs) up to the ‘knee’ in the spectrum at a few PeV. The theory of diffusive shock acceleration nicely supplies a power law energy distribution with approximately the desired spectral index and with suitably high efficiency. For a SNR blast wave expanding into a typical interstellar magnetic field the predicted maximum CR energy falls short of 1 PeV, but a non-resonant plasma instability allows the CRs themselves to amplify the magnetic field by orders of magnitude to a level capable of accelerating CRs to the knee.

Acceleration and transport of ions in turbulent current sheets: formation of non-maxwelian energy distribution

Abstract. The paper is devoted to particle acceleration in turbulent current sheet (CS). Our results show that the mechanism of CS particle interaction with electromagnetic turbulence can explain the formation of power law energy distributions. We study the ratio between adiabatic acceleration of particles in electric field in the presence of stationary turbulence and acceleration due to electric field in the case of dynamic turbulence. The correlation between average energy gained by particles and average particle residence time in the vicinity of the neutral sheet is discussed. It is also demonstrated that particle velocity distributions formed by particle-turbulence interaction are similar in essence to the ones observed near the far reconnection region in the Earth's magnetotail.

KLEIN–NISHINA EFFECTS ON OPTICALLY THIN SYNCHROTRON AND SYNCHROTRON SELF-COMPTON SPECTRUM

We present analytic approximations to the optically thin synchrotron and synchrotron self-Compton (SSC) spectra when Klein-Nishina (KN) effects are important and pair production and external radiation fields can be neglected. This theory is useful for analytical treatment of radiation from astrophysical sources, such as gamma-ray bursts (GRBs), active galactic nuclei, and pulsar wind nebula, where KN effects may be important. We consider a source with continuous injection of relativistic electrons with a power-law energy distribution above some typical injection energy. We find that the synchrotron-SSC spectra can be described by a broken power law, and provide analytic estimates for the break frequencies and power-law indices. In general, we show that the dependence of the KN cross section on the energy of the upscattering electron results in a hardening of the energy distribution of fast cooling electrons and therefore in a hardening of the observed synchrotron spectrum. As a result the synchrotron spectrum of fast cooling electrons, below the typical injection energy, can be as hard as F_ν α ν^0, instead of the classical ν^(–1/2) when KN effects are neglected. The synchrotron energy output can be dominated by electrons with energy above the typical injection energy. We solve self-consistently for the cooling frequency and find that the transition between synchrotron and SSC cooling can result in discontinuous variations of the cooling frequency and the synchrotron and SSC spectra. We demonstrate the application of our results to theory by applying them to prompt and afterglow emission models of GRBs.

DYNAMIC MAGNETOGRAPHY OF SOLAR FLARING LOOPS

We develop a practical forward fitting method based on the SIMPLEX algorithm with shaking, which allows the derivation of the magnetic field and other parameters along a solar flaring loop using microwave imaging spectroscopy of gyrosynchrotron emission. We illustrate the method using a model loop with spatially varying magnetic field, filled with uniform ambient density and an evenly distributed fast electron population with an isotropic, power-law energy distribution.

Primordial globular clusters, X-ray binaries and cosmological reionization

Globular clusters are dense stellar systems that have typical ages of � 13 billion years, implying that they formed during the early epochs of galaxy formation at redshifts of z � 6. Massive stars in newly formed or primordial globular clusters could have played an important role during the epoch of cosmological reionisation (z � 6) as sources of energetic, neutral hydrogen ionising UV photons. We investigate whether or not these stars could have been as important in death as sources of energetic X-ray photons as they were during their main sequence lives. Most massive stars are expected to form in binaries, and an appreciable fraction of these (as much as � 30%) will evolve into X-ray luminous (LX � 10 38 erg/s) high-mass X-ray binaries (HMXBs). These sources would have made a contribution to the X-ray background at z � 6. Using Monte Carlo models of a globular cluster, we estimate the total X-ray luminosity of a population of HMXBs. We compare and contrast this with the total UV luminosity of the massive stars during their main sequence lives. For reasonable estimates, we find that the bolometric luminosity of the cluster peaks at � 10 42 erg/s during the first few million years, but declines to � 10 41 erg/s after � 5 million years as the most massive stars evolve off the main sequence. From this time onwards, the total bolometric luminosity is dominated by HMXBs and falls gradually to � 10 40 erg/s after � 50 million years. Assuming a power-law spectral energy distribution for the HMXBs, we calculate the effective number of neutral hydrogen ionisations per HMXB and show that HMXBs can be as important as sources of ionising radiation as massive stars. Finally we discuss the implications of our results for modelling galaxy formation at high redshift and the prospects of using globular clusters as probes of reionisation.

ELECTRON ENERGY AND MAGNETIC FIELD DERIVED FROM SOLAR MICROWAVE BURST SPECTRA

Microwave bursts during solar flares are known to be sensitive to high-energy electrons and magnetic field, both of which are important ingredients of solar flare physics. This paper presents such information derived from the microwave bursts of the 412 flares that were measured with the Owens Valley Solar Array. We assumed that these bursts are predominantly due to gyrosynchrotron radiation by nonthermal electrons in a single power-law energy distribution to use the simplified formulae for gyrosynchrotron radiation in the data analysis. A second major assumption was that statistical properties of flare electrons derived from this microwave database should agree with an earlier result based on the hard X-ray burst spectrometer on Solar Maximum Mission. Magnetic field information was obtained in the form of a scaling law between the average magnetic field and the total source area, which turns out to be a narrow distribution around ~400 G. The derived nonthermal electron energy is related to the peak flux, peak frequency, and spectral index, through a multistep regression fit, which can be used for a quick estimate for the nonthermal electron energy from spatially integrated microwave spectral observations.

RELATIVISTIC PARTICLE ACCELERATION IN DEVELOPING ALFVÉN TURBULENCE

A new particle acceleration process in a developing Alfv\'{e}n turbulence in the course of successive parametric instabilities of a relativistic pair plasma is investigated by utilyzing one-dimensional electromagnetic full particle code. Coherent wave-particle interactions result in efficient particle acceleration leading to a power-law like energy distribution function. In the simulation high energy particles having large relativistic masses are preferentially accelerated as the turbulence spectrum evolves in time. Main acceleration mechanism is simultaneous relativistic resonance between a particle and two different waves. An analytical expression of maximum attainable energy in such wave-particle interactions is derived.

Results of WEBT, VLBA and RXTE monitoring of 3C 279 during 2006–2007

Context. The quasar 3C 279 is among the most extreme blazars in terms of luminosity and variability of flux at all wavebands. Its vari ations in flux and polarization are quite complex and therefore require intensive monitoring observations at multiple wavebands to characterise and interpret the observed changes. Aims. In this paper, we present radio-to-optical data taken by the WEBT, supplemented by our VLBA and RXTE observations, of 3C 279. Our goal is to use this extensive database to draw inferences regarding the physics of the relativistic jet. Methods. We assemble multifrequency light curves with data from 30 ground-based observatories and the space-based instruments SWIFT (UVOT) and RXTE, along with linear polarization vs. time in the optical R band. In addition, we present a sequence of 22 images (with polarization vectors) at 43 GHz at resolution 0.15 milliarcse c, obtained with the VLBA. We analyse the light curves and polarization, as well as the spectral energy distributions at different epochs, corresponding to different brightness states. Results. We find that the IR-optical-UV continuum spectrum of the vari able component corresponds to a power law with a constant slope of−1.6, while in the 2.4‐10 keV X-ray band it varies in slope from−1.1 to−1.6. The steepest X-ray spectrum occurs at a flux minimum. Durin g a decline in flux from maximum in late 2006, the optical and 43 GHz core po larization vectors rotate by∼ 300 ◦ . Conclusions. The continuum spectrum agrees with steady injection of relativistic electrons with a power-law energy distribution of slope−3.2 that is steepened to−4.2 at high energies by radiative losses. The X-ray emission at flux minimum comes most likely from a new component that starts in an upstream section of the jet where inverse Compton scattering of seed photons from outside the jet is important. The rotation of the polarization vector implies that the jet contains a helical magnetic field that extends ∼ 20 pc past the 43 GHz core.

The Outburst of the Blazar AO 0235+164 in 2006 December: Shock‐in‐Jet Interpretation

We present the results of polarimetric (R-band) and multicolor photometric (BH RI J H K) observations of the blazar AO 0235+16 during an outburst in 2006 December. The data reveal a short timescale of variability (several hours), which increases from optical to near-IR wavelengths; even shorter variations are detected in polarization. The flux density correlates with the degree of polarization, and at the maximum degree of polarization the electric vector tends to align with the parsec-scale jet direction. We find that a variable component with a steady power-law spectral energy distribution and very high optical polarization (30%-50%) is responsible for the variability. We interpret these properties of the blazar within a model of a transverse shock propagating down the jet. In this case a small change in the viewing angle of the jet, by 1°, and a decrease in the shocked plasma compression by a factor of ~1.5 are sufficient to account for the variability.

Relaxation of Relativistic Plasmas Under the Effect of Wave‐Particle Interactions

We simulate the acceleration of electrons to relativistic energies due to the interaction of electrons with waves generated by longitudinal (i.e., electrostatic) streaming instabilities in plasmas. Two equal systems undergoing a streaming instability evolve, one according to the classical Newton's law and one according to the special relativity dynamics equation. The system that obeys Newton's law relaxes to a Maxwellian equilibrium distribution. In the case of the relativistic dynamics, the equilibrium distribution exhibits peaks in the phase space at high momenta and a larger number of particles at high energies. This steady electron population at higher energies could explain power-law energy distribution in many plasma physics and astrophysical systems.

The reddest ISO-2MASS quasar

Context. While there is growing consensus on the existence of numerous dust-enshrouded red quasars, their discovery and detailed exploration is still an observational challenge. In the course of the near-mid-infrared AGN search combining the 6.7 μm ISOCAM Parallel Survey and 2MASS we have discovered 24 type-1 quasars about a third of which are too red to be discriminated by optical/UV search techniques. Aims. Here we report on a detailed case study of the reddest type-1 quasar of our sample, 2MASS J23410667−0914327 (for short J2341) at redshift z = 0.236 with M_K = −25.8 and J − K_s = 1.95. This source has a very red optical appearance but lacks the far-infrared emission typically seen in known dust enshrouded AGN. Therefore we here explore its enigmatic nature. Methods. We performed spectroscopy in the optical with VLT/FORS1 and in the mid-infrared (5–38 μm) with the Spitzer Space Telescope as well as near-infrared (NIR) imaging with ISPI at the CTIO 4m-telescope. To explain the red optical continuum of the quasar we examine nuclear dust reddening of an intrinsically blue quasar continuum in combination with dilution by stellar light of the host galaxy. Results. The optical and NIR observations reveal a star forming emission-line galaxy at the same redshift as the quasar with a projected linear separation of 1.8 (6.7 kpc). The quasar and its companion are embedded in diffuse extended continuum emission. Compared with its companion the quasar exhibits redder optical-NIR colours, which we attribute to hot nuclear dust. The mid-infrared spectrum shows only few emission lines superimposed on a power-law spectral energy distribution typically seen in type-1 AGN. However, the lack of strong far-infrared emission suggests that our potentially interacting object contains much less gas and dust and is in a stage different from dust reddened ULIRG-AGN like Mrk 231. The optical spectrum shows signatures for reddening in the emission-lines and no post-starburst stellar population is detected in the host galaxy of the quasar. The optical continuum emission of the active nucleus appears absorbed and diluted. Conclusions. Even the combination of absorption and host dilution is not able to match J2341 with standard quasar templates.While the BLR shows only a rather moderate absorption of E_(B−V) = 0.3, the continuum shorter than 4500 A requires strong obscuration with E_(B−V) = 0.7, clearly exceeding the constraints from the low upper limit on the silicate 9.7 μm absorption. This leads us to conclude that the continuum of the quasar J2341 is intrinsically redder than that of typical quasars.