Is the Weibel instability enhanced by the suprathermal populations, or not?

The kinetic instabilities of the Weibel-type are presently invoked in a large variety of astrophysical scenarios because anisotropic plasma structures are ubiquitous in space. The Weibel instability is driven by a temperature anisotropy which is commonly modeled by a bi-axis distribution function, such as a bi-Maxwellian or a generalized bi-Kappa. Previous studies have been limited to a bi-Kappa distribution and found a suppression of this instability in the presence of suprathermal tails. In the present paper it is shown that the Weibel growth rate is rather more sensitive to the shape of the anisotropic distribution function. In order to illustrate the distinguishing properties of this instability a \emph{product-bi-Kappa distribution} is introduced, with the advantage that this distribution function enables the use of different values of the spectral index in the two directions, $\kappa_{\parallel} \ne \kappa_{\perp}$. The growth rates and the instability threshold are derived and contrasted with those for a simple bi-Kappa and a bi-Maxwellian. Thus, while the maximum growth rates reached at the saturation are found to be higher, the threshold is drastically reduced making the anisotropic product-bi-Kappa (with small kappas) highly susceptible to the Weibel instability. This effect could also rise questions on the temperature or the temperature anisotropy that seems to be not an exclusive source of free energy for this instability, and definition of these notions for such Kappa distributions must probably be reconsidered

Scattering of Cosmic Rays by Magnetohydrodynamic Interstellar Turbulence

Recent advances in understanding of magnetohydrodynamic (MHD) turbulence call for substantial revisions in our understanding of cosmic ray transport. In this paper we use gyroresonance recently obtained scaling laws for MHD modes to calculate the scattering frequency for cosmic rays in the ISM. We consider gyroresonance with MHD modes (Alfvenic, slow and fast) and transit-time damping (TTD) by fast modes. We conclude that the gyroresonance with fast modes is the dominant contribution to cosmic ray scattering for the typical interstellar conditions. In contrast to earlier studies, we find that Alfvenic and slow modes are inefficient because they are far from isotropy usually assumed.Comment: 4 pages, 2 figures, Phys. Rev. Lett. in press, minor change

Interplay of Kinetic Plasma Instabilities

<a href="http://www.intechopen.com/books/wave-propagation-in-materials-for-modern-applications/interplay-of-kinetic-plasma-instabilities" title="interplay-of-kinetic-plasma-instabilities">Interplay of Kinetic Plasma Instabilities</a>status: publishe

Limits on the AGN activities in X-ray underluminous galaxy groups

We have observed four X-ray underluminous groups of galaxies using the Giant Meterwave RadioTelescope. The groups NGC 524, 720, 3607, and 4697 are underluminous in relation to the extrapolation of the Lx - T relation from rich clusters and do not show any evidence of current AGN activities that can account for such a departure. The GMRT observations carried out at low frequencies (235 and 610 MHz) were aimed at detecting low surface brightness, steep-spectrum sources indicative of past AGN activities in these groups. No such radio emissions were detected in any of these four groups. The corresponding upper limits on the total energy in relativistic particles is about 3 X 10$^{57}$ erg. This value is more than a factor of 100 less than that required to account for the decreased X-ray luminosities (or, enhanced entropies) of these four groups in the AGN-heating scenario. Alternatively, the AGN activity must have ceased about 4 Gyr ago, allowing the relativistic particles to diffuse out to such a large extent (about 250 kpc) that their radio emission could have been undetected by the current observations. If the latter scenario is correct, the ICM was pre-heated before the assembly of galaxy clusters.Comment: 10 pages, 3 figures, accepted for publication in ApJ Letter

Non-linear Weibel-type Soliton Modes

Discussion is given of non-linear soliton behavior including coupling between electrostatic and electromagnetic potentials for non-relativistic, weakly relativistic, and fully relativistic plasmas. For plasma distribution functions that are independent of the canonical momenta perpendicular to the soliton spatial structure direction there are, in fact, no soliton behaviors allowed because transverse currents are zero. Dependence on the transverse canonical momenta is necessary. When such is the case, it is shown that the presence or absence of a soliton is intimately connected to the functional form assumed for the particle distribution functions. Except for simple situations, the coupled non-linear equations for the electrostatic and electromagnetic potentials would seem to require numerical solution procedures. Examples are given to illustrate all of these points for non-relativistic, weakly relativistic, and fully relativistic plasmas.Comment: Accepted for publication at Journal of Physics A: Mathematical and Theoretica

Cosmic magnetization: from spontaneously emitted aperiodic turbulent to ordered equipartition fields

It is shown that an unmagnetized nonrelativistic thermal electron-proton plasma spontaneously emits aperiodic turbulent magnetic field fluctuations of strength $|\delta B|=9\beta_eg^{1/3}W_e^{1/2}$ G, where $\beta_e$ is the normalized thermal electron temperature, $W_e$ the thermal plasma energy density and $g$ the plasma parameter. Aperiodic modes fluctuate only in space, but are not propagating. For the unmagnetized intergalactic medium, immediately after the reionization onset, the field strength from this mechanism is about $4.7\cdot 10^{-16}$ G, too weak to affect the dynamics of the plasma. The shear and/or compression of the intergalactic medium exerted by the first supernova explosions amplify these seed fields and make them anisotropic, until the magnetic restoring forces affect the gas dynamics at ordered plasma betas near unity.Comment: 4 pages, 1 figur

On the Momentum Diffusion of Radiating Ultrarelativistic Electrons in a Turbulent Magnetic Field

Here we investigate some aspects of stochastic acceleration of ultrarelativistic electrons by magnetic turbulence. In particular, we discuss the steady-state energy spectra of particles undergoing momentum diffusion due to resonant interactions with turbulent MHD modes, taking rigorously into account direct energy losses connected with different radiative cooling processes. For the magnetic turbulence we assume a given power spectrum of the type $W(k) \propto k^{-q}$. In contrast to the previous approaches, however, we assume a finite range of turbulent wavevectors $k$, consider a variety of turbulence spectral indexes $1 =< q =< 2$, and concentrate on the case of a very inefficient particle escape from the acceleration site. We find that for different cooling and injection conditions, stochastic acceleration processes tend to establish a modified ultrarelativistic Maxwellian distribution of radiating particles, with the high-energy exponential cut-off shaped by the interplay between cooling and acceleration rates. For example, if the timescale for the dominant radiative process scales with the electron momentum as $\propto p^r$, the resulting electron energy distribution is of the form $n_e(p) \propto p^2 exp[ - (1 / a) (p / p_eq)^a]$, where $a = 2-q-r$, and $p_eq$ is the equilibrium momentum defined by the balance between stochastic acceleration and energy losses timescales. We also discuss in more detail the synchrotron and inverse-Compton emission spectra produced by such an electron energy distribution, taking into account Klein-Nishina effects. We point out that the curvature of the high frequency segments of these spectra, even though being produced by the same population of electrons, may be substantially different between the synchrotron and inverse-Compton components.Comment: 42 pages, 14 figures included. Slightly modified version, accepted for publication in Ap

Some properties of synchrotron radio and inverse-Compton gamma-ray images of supernova remnants

The synchrotron radio maps of supernova remnants (SNRs) in uniform interstellar medium and interstellar magnetic field (ISMF) are analyzed, allowing different `sensitivity' of injection efficiency to the shock obliquity. The very-high energy gamma-ray maps due to inverse Compton process are also synthesized. The properties of images in these different wavelength bands are compared, with particular emphasis on the location of the bright limbs in bilateral SNRs. Recent H.E.S.S. observations of SN 1006 show that the radio and IC gamma-ray limbs coincide, and we found that this may happen if: i) injection is isotropic but the variation of the maximum energy of electrons is rather quick to compensate for differences in magnetic field; ii) obliquity dependence of injection (either quasi-parallel or quasi-perpendicular) and the electron maximum energy is strong enough to dominate magnetic field variation. In the latter case, the obliquity dependence of the injection and the maximum energy should not be opposite. We argue that the position of the limbs alone and even their coincidence in radio, X-rays and gamma-rays, as it is discovered by H.E.S.S. in SN 1006, cannot be conclusive about the dependence of the electron injection efficiency, the compression/amplification of ISMF and the electron maximum energy on the obliquity angle.Comment: Accepted for publication in MNRA

Nonthermal Emissions from Particles Accelerated by Turbulence in Clusters of Galaxies

We consider nonthermal emission from clusters of galaxies produced by particle acceleration by resonant scattering of Alfv\'{e}n waves driven by fluid turbulence through the Lighthill mechanism in the intracluster medium. We assume that the turbulence is driven by cluster mergers. We find that the resonant Alfv\'{e}n waves can accelerate electrons up to \gamma ~10^5 through resonant scattering. We also find that the turbulent resonant acceleration can give enough energy to electrons to produce the observed diffuse radio relic emission from clusters if the clusters have a pool of electrons with \gamma ~10^3. This mechanism can also explain the observed hard X-ray emission from clusters if the magnetic field in a cluster is small enough (~< \mu G) or the fluid turbulence spectrum is flatter than the Kolmogorov law. The fluid turbulence could be observed with Astro-E2 in the regions where diffuse radio emission is observed. Although non-gravitational heating before cluster formation (preheating) steepens a relation between radio luminosity and X-ray temperature, our predicted relation is still flatter than the observed one.Comment: 33 pages, accepted for publication on Ap