Power-law Energy Distribution Of Electrons Research Articles

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.

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.

Polarization of radiation of electrons in highly turbulent magnetic fields

We study the polarization properties of the jitter and synchrotron radiation produced by electrons in highly turbulent anisotropic magnetic fields. The net polarization is provided by the geometry of the magnetic field the directions of which are parallel to a certain plane. Such conditions may appear in the relativistic shocks during the amplification of the magnetic field through the so-called Weibel instability. While the polarization properties of the jitter radiation allows extraction of direct information on the turbulence spectrum as well as the geometry of magnetic field, the polarization of the synchrotron radiation reflects the distribution of the magnetic field over its strength. For the isotropic distribution of monoenergetic electrons, we found that the degree of polarization of the synchrotron radiation is larger than the polarization of the jitter radiation. For the power-law energy distribution of electrons the relation between the degree of polarization of synchrotron and jitter radiation depends on the spectral index of the distribution.

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).

X‐Ray and Optical Emission from Radio Hot Spots of Powerful Quasars

In a survey with Chandra and HST of a sample of 17 radio sources with bright radio jets (16 powerful FR II and one nearby FR I), we detected X-ray and optical emission from a number of radio hot spots and lobes. Six hot spots on the near sides of powerful FR II galaxies (as determined from the jet asymmetry) were detected at X-rays, while none were detected on the far side, suggesting that high-energy emission from hot spots is anisotropic. In the nearby FR I galaxy 0836+299 (the only FR I in our sample) both hot spots are detected in X-rays, in agreement with the symmetric radio morphology. In the latter case the spectral energy distributions (SEDs) of both hot spots can be modeled from radio to X-rays with synchrotron emission from a single power-law energy distribution of electrons with Lorentz factors up to ~2 × 107. For the six hot spots of powerful FR II galaxies the X-ray flux lies above the extrapolation from the radio-to-optical continuum. Modeling the SEDs with a one-zone synchrotron self-Compton model, we find that equipartition is strongly violated, with the particle energy density dominating over the magnetic field one by 1-2 orders of magnitude. We discuss alternatives to this simple model, concluding that a viable alternative is that the X-ray emission is produced in the still-relativistic (Doppler factor δ = 3-6) terminal part of the jet by inverse Compton (IC) scattering on the CMB or synchrotron photons emitted by plasma flowing with a small velocity. X-ray emission from some of the lobes is detected on the side opposite to the jet, suggesting the possible relevance of back-scattered central radiation in providing seed photons for the IC process.

Fast electron slowing-down and diffusion in a high temperature coronal X-ray source

Finite thermal velocity modifications to electron slowing-down rates may be important for the deduction of solar flare total electron energy. Here we treat both slowing-down and velocity diffusion of electrons in the corona at flare temperatures, for the case of a simple, spatially homogeneous source. Including velocity diffusion yields a consistent treatment of both `accelerated' and `thermal' electrons. It also emphasises that one may not invoke finite thermal velocity target effects on electron lifetimes without simultaneously treating the contribution to the observed X-ray spectrum from thermal electrons. We present model calculations of the X-ray spectra resulting from injection of a power-law energy distribution of electrons into a source with finite temperature. Reducing the power-law distribution low-energy cutoff to lower and lower energies only increases the relative magnitude of the thermal component of the spectrum, because the lowest energy electrons simply join the background thermal distribution. Acceptable fits to RHESSI flare data are obtained using this model. These also demonstrate, however, that observed spectra may in consequence be acceptably consistent with rather a wide range of injected electron parameters.

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)

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.

Gamma-ray bursts: afterglows from cylindrical jets

Nearly all previous discussion on beaming effects in GRBs have assumed a conical geometry. However, more and more observations on relativistic jets in radio galaxies, active galactic nuclei, and microquasars in the Galaxy have shown that many of these outflows are not conical, but cylindrical, i.e., they maintain constant cross sections at large scales. Thus it is necessary to discuss the possibility that GRBs may be due to highly collimated cylindrical jets, not conical ones. Here we study the dynamical evolution of cylindrical jets and discuss their afterglows. Both analytical and numerical results are presented. It is shown that when the lateral expansion is not taken into account, a cylindrical jet typically remains to be highly relativistic for \sim 10^8 - 10^9 s. During this relativistic phase, the optical afterglow decays as \propto t^{-p/2} at first, where p is the index characterizing the power-law energy distribution of electrons. Then the light curve steepens to be \propto t^{-(p+1)/2} due to cooling of electrons. After entering the non-relativistic phase (i.e., t > 10^{11} s), the afterglow is \propto t^{-(5p-4)/6}. But if the cylindrical jet expands laterally at co-moving sound speed, then the decay becomes \propto t^{-p} and \propto t^{-(15p-21)/10} - t^{-(15p-20)/10} in the ultra-relativistic and non-relativistic phase respectively. Note that in both cases, the light curve turns flatter after the relativistic-Newtonian transition point, which differs markedly from the behaviour of a conical jet. It is suggested that some GRBs with afterglows decaying as t^{-1.1} - t^{-1.3} may be due to cylindrical jets, not necessarily isotropic fireballs.

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.

Detection of a sub-milliarcsecond radio component in the RS CVn system HR 1099

The RS CVn system HR 1099 was observed with a five station VLBI array at a frequency of 8.4 GHz during a strong radio outburst of approximately 400 mJy. The data are consistent with a circular Gaussian source of 0.8 + or - 0.12 milli-arcsec (FWHM), corresponding to a linear size of 4 + or - 0.6 x 10 to the 11th cm. This is comparable to the distance between the surfaces of the two stars, or to 75 percent of the diameter of the chromospherically active K star. Extrapolation of published photometric data shows that the starspot formation of HR 1099 was facing toward the observers at the times of observations. The high equivalent brightness temperature, approximately 10 billion K, is consistent with gyrosynchrotron emission from a power-law energy distribution of electrons in a magnetic field of strength about 30 gauss.

VLBI observations of the RS Canum Venaticorum binary systems UX ARIETIS and HR 1099 at 1.65 GHz

VLBI observations of the RS CVn binaries UX Arietis and HR 1099 have been made at 1.65 GHz using a three-element array with a minimum fringe spacing of 11.5 milli-arcsec. Both sources were found to be unresolved within measurement uncertainties. In both cases, the derived upper limit to the source size was comparable to the overall size of each binary system. The lower limits to the brightness temperature were 1.4 x 10 to the 10th K for UX Arietis and 2.9 x 10 to the 10th K for HR 1099. Simultaneous polarization measurements at the VLA showed 4-8 percent circular polarization and less than 2 percent linear polarization. It is found that the data are consistent with gyrosynchrotron emission from a power-law energy distribution of electrons in a magnetic field B less than or approximately equal to 6 gauss.

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.