Growth rates of the Weibel and tearing mode instabilities in a relativistic pair plasma

We present an algorithm for solving the linear dispersion relation in an inhomogeneous, magnetised, relativistic plasma. The method is a generalisation of a previously reported algorithm that was limited to the homogeneous case. The extension involves projecting the spatial dependence of the perturbations onto a set of basis functions that satisfy the boundary conditions (spectral Galerkin method). To test this algorithm in the homogeneous case, we derive an analytical expression for the growth rate of the Weibel instability for a relativistic Maxwellian distribution and compare it with the numerical results. In the inhomogeneous case, we present solutions of the dispersion relation for the relativistic tearing mode, making no assumption about the thickness of the current sheet, and check the numerical method against the analytical expression.Comment: Accepted by PPC

Navier-Stokes hydrodynamics of thermal collapse in a freely cooling granular gas

We employ Navier-Stokes granular hydrodynamics to investigate the long-time behavior of clustering instability in a freely cooling dilute granular gas in two dimensions. We find that, in circular containers, the homogeneous cooling state (HCS) of the gas loses its stability via a sub-critical pitchfork bifurcation. There are no time-independent solutions for the gas density in the supercritical region, and we present analytical and numerical evidence that the gas develops thermal collapse unarrested by heat diffusion. To get more insight, we switch to a simpler geometry of a narrow-sector-shaped container. Here the HCS loses its stability via a transcritical bifurcation. For some initial conditions a time-independent inhomogeneous density profile sets in, qualitatively similar to that previously found in a narrow-channel geometry. For other initial conditions, however, the dilute gas develops thermal collapse unarrested by heat diffusion. We determine the dynamic scalings of the flow close to collapse analytically and verify them in hydrodynamic simulations. The results of this work imply that, in dimension higher than one, Navier-Stokes hydrodynamics of a dilute granular gas is prone to finite-time density blowups. This provides a natural explanation to the formation of densely packed clusters of particles in a variety of initially dilute granular flows.Comment: 18 pages, 19 figure

Differential Form of the Collision Integral for a Relativistic Plasma

The differential formulation of the Landau-Fokker-Planck collision integral is developed for the case of relativistic electromagnetic interactions.Comment: Plain TeX, 5 page

Ultra-relativistic electrostatic Bernstein waves

A new general form of the dispersion relation for electrostatic Bernstein waves in ultra-relativistic pair plasmas, characterized by a−1 = kBT/(mec2)  1, is derived in this paper. The parameter Sp = aΩ0/ωp, where Ω0 is the rest cyclotron frequency for electrons or positrons and ωp is the electron (or positron) plasma frequency, plays a crucial role in characterizing these waves. In particular, Sp has a restricted range for permitted wave solutions; this range is effectively unlimited for classical plasmas, but is significant for the ultra-relativistic case. The characterization of these waves is applied in particular to the presence of such plasmas in pulsar atmospheres

Stereoscopic electron spectroscopy of solar hard X-ray flares with a single spacecraft

Hard X-ray (HXR) spectroscopy is the most direct method of diagnosing energetic electrons in solar flares. Here we present a technique which allows us to use a single HXR spectrum to determine an effectively stereoscopic electron energy distribution. Considering the Sun's surface to act as a 'Compton mirror' allows us to look at emitting electrons also from behind the source, providing vital information on downward-propagating particles. Using this technique we determine simultaneously the electron spectra of downward and upward directed electrons for two solar flares observed by the Ramaty High Energy Solar Spectroscopic Imager (RHESSI). The results reveal surprisingly near-isotropic electron distributions, which contrast strongly with the expectations from the standard model which invokes strong downward beaming, including collisional thick-target model.Comment: 7 pages, 3 figures, accepted to Astrophysical Journal Letter

Classical dilute relativistic plasma in equilibrium. Two-particle distribution function

We consider here a dilute hot plasma which is homogeneous and in equilibrium in the framework of classical relativistic statistical mechanics as formulated recently by the authors. No external fields are present. The two-particle distribution function of the plasma is calculated for any temperature. This distribution will be physically significant, as long as the creation of pairs can be neglected. Several limits which apply at low or high temperatures are discussed. Comparison with previous work from several authors is made

The exact Darwin Lagrangian

Darwin (1920) noted that when radiation can be neglected it should be possible to eliminate the radiation degrees-of-freedom from the action of classical electrodynamics and keep the discrete particle degrees-of-freedom only. Darwin derived his well known Lagrangian by series expansion in $v/c$ keeping terms up to order $(v/c)^2$. Since radiation is due to acceleration the assumption of low speed should not be necessary. A Lagrangian is suggested that neglects radiation without assuming low speed. It cures deficiencies of the Darwin Lagrangian in the ultra-relativistic regime.Comment: 2.5 pages, no figure

Magnetic Field Limitations on Advection Dominated Flows

Recent papers discussing advection dominated accretion flows (ADAF) as a solution for astrophysical accretion problems should be treated with some caution because of their uncertain physical basis. The suggestions underlying ADAF involve ignoring the magnetic field reconnection in heating of the plasma flow, assuming electron heating due only to binary Coulomb collisions with ions. Here, we analyze the physical processes in optically thin accretion flows at low accretion rates including the influence of an equipartition turbulent magnetic field. For these conditions there is continuous destruction of magnetic flux by reconnection. The reconnection is expected to significantly heat the electrons which can efficiently emit magnetobremstrahlung radiation. Because of this electron emission, the radiative efficiency of the ADAF is not small. We suggest that the small luminosities of nearby galactic black holes is due to outflows rather than ADAF accretion.Comment: 7 pages, 3 figures, Submitted to Ap

Blue spectra and induced formation of primordial black holes

We investigate the statistical properties of primordial black hole (PBH) formation in the very early Universe. We show that the high level of inhomogeneity of the early Universe leads to the formation of the first generation PBHs. %The existence of these PBHs This causes later the appearance of a dust-like phase of the cosmological expansion. We discuss here a new mechanism for the second generation of PBH formation during the dust-like phase. This mechanism is based on the coagulation process. We demonstrate that the blue power spectrum of initial adiabatic perturbations after inflation leads to overproduction of primordial black holes with $10^9$g$\le M\le10^{15}$g if the power index is $n\ge1.2$.Comment: 16 pages, 2 figure

The Particle Content of Extragalactic Jets

Recent x-ray and radio data from radio sources in galaxy clusters are used to show that the pdV work required to inflate the radio lobes exceeds all other energy estimates deduced from the radio emission. If the required jet energy density has an isotropic pressure, then in almost all cases the jet cannot be confined by an external medium. This problem can be resolved with jets dominated by cold protons, but even here the accompanying energy density in relativistic electons can cause decollimation. Electron-positron jets cannot solve this problem unless they are highly beamed with unusual energy distributions. Poynting flux jets may be a viable alternative.Comment: 14 pages, 3 figures, to be published in Ap