Comment on: Diffusion through a slab

Mahan [J. Math. Phys. 36, 6758 (1995)] has calculated the transmission coefficient and angular distribution of particles which enter a thick slab at normal incidence and which diffuse in the slab with linear anisotropic, non-absorbing, scattering. Using orthogonality relations derived by McCormick & Kuscer [J. Math. Phys. 6, 1939 (1965); 7, 2036 (1966)] for the eigenfunctions of the problem, this calculation is generalised to a boundary condition with particle input at arbitrary angles. It is also shown how to use the orthogonality relations to relax in a simple way the restriction to a thick slab.Comment: 3 pages, LaTeX, uses RevTe

Particle acceleration at ultrarelativistic shocks: an eigenfunction method

We extend the eigenfunction method of computing the power-law spectrum of particles accelerated at a relativistic shock fronts to apply to shocks of arbitrarily high Lorentz factor. In agreement with the findings of Monte-Carlo simulations, we find the index of the power-law distribution of accelerated particles which undergo isotropic diffusion in angle at an ultrarelativistic, unmagnetized shock is s=4.23 (where s=-d(ln f)/dp with f the Lorentz invariant phase-space density and p the momentum). This corresponds to a synchrotron index for uncooled electrons of a=0.62 (taking cooling into account a=1.12), where a=-d(ln F)/dn, F is the radiation flux and n the frequency. We also present an approximate analytic expression for the angular distribution of accelerated particles, which displays the effect of particle trapping by the shock: compared with the non-relativistic case the angular distribution is weighted more towards the plane of the shock and away from its normal. We investigate the sensitivity of our results to the transport properties of the particles and the presence of a magnetic field. Shocks in which the ratio of Poynting to kinetic energy flux upstream is not small are less compressive and lead to larger values of $s$.Comment: Minor additions on publicatio

X-Ray Spectral Variability of Extreme BL Lac AGN H1426+428

Between 7 March 2002 and 15 June 2002, intensive X-ray observations were carried out on the extreme BL Lac object H1426+428 with instruments on board the Rossi X-ray Timing Explorer (RXTE). These instruments provide measurements of H1426+428 in the crucial energy range that characterizes the first peak of its spectral energy distribution. This peak, which is almost certainly due to synchrotron emission, has previously been inferred to be in excess of 100 keV. By taking frequent observations over a four-month campaign, which included $\sim$450 ksec of RXTE time, studies of flux and spectral variability on multiple timescales were performed, along with studies of spectral hysteresis. The 3-24 keV X-ray flux and spectra exhibited significant variability, implying variability in the location of the first peak of the spectral energy distribution. Hysteresis patterns were observed, and their characteristics have been discussed within the context of emission models.Comment: accepted for publication in Astrophysical Journa

On Spectral and Temporal Variability in Blazars and Gamma Ray Bursts

A simple model for variability in relativistic plasma outflows is studied, in which nonthermal electrons are continuously and uniformly injected in the comoving frame over a time interval dt. The evolution of the electron distribution is assumed to be dominated by synchrotron losses, and the energy- and time-dependence of the synchrotron and synchrotron self-Compton (SSC) fluxes are calculated for a power-law electron injection function with index s = 2. The mean time of a flare or pulse measured at photon energy E with respect to the onset of the injection event varies as E^{-1/2} and E^{-1/4} for synchrotron and SSC processes, respectively, until the time approaches the limiting intrinsic mean time (1+z)dt/(2 D), where z is the redshift and D is the Doppler factor. This dependence is in accord with recent analyses of blazar and GRB emissions, and suggests a method to discriminate between external Compton and SSC models of high-energy gamma radiation from blazars and GRBs. The qualititative behavior of the X-ray spectral index/flux relation observed from BL Lac objects can be explained with this model. This demonstrates that synchrotron losses are primarily responsible for the X-ray variability behavior and strengthens a new test for beaming from correlated hard X-ray/TeV observations.Comment: 10 pages, 2 figures, accepted for publication in Astrophysical Journal Letters; uses aaspp4.sty, epsf.st

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

Impact craters on Venus: An overview from Magellan observations

Magellan has revealed an ensemble of impact craters on Venus that is unique in many important ways. We have compiled a database describing 842 craters on 89 percent of the planet's surface mapped through orbit 2578 (the craters range in diameter from 1.5 to 280 km). We have studied the distribution, size-frequency, morphology, and geology of these craters both in aggregate and, for some craters, in more detail. We have found the following: (1) the spatial distribution of craters is highly uniform; (2) the size-density distribution of craters with diameters greater than or equal to 35 km is consistent with a 'production' population having a surprisingly young age of about 0.5 Ga (based on the estimated population of Venus-crossing asteroids); (3) the spectrum of crater modification differs greatly from that on other planets--62 percent of all craters are pristine, only 4 percent volcanically embayed, and the remainder affected by tectonism, but none are severely and progressively depleted based on size-density distribution extrapolated from larger craters; (4) large craters have a progression of morphologies generally similar to those on other planets, but small craters are typically irregular or multiple rather than bowl shaped; (5) diffuse radar-bright or -dark features surround some craters, and about 370 similar diffuse 'splotches' with no central crater are observed whose size-density distribution is similar to that of small craters; and (6) other features unique to Venus include radar-bright or -dark parabolic arcs opening westward and extensive outflows originating in crater ejecta

New constraints on Planck-scale Lorentz Violation in QED from the Crab Nebula

We set constraints on O(E/M) Lorentz Violation in QED in an effective field theory framework. A major consequence of such assumptions is the modification of the dispersion relations for electrons/positrons and photons, which in turn can affect the electromagnetic output of astrophysical objects. We compare the information provided by multiwavelength observations with a full and self-consistent computation of the broad-band spectrum of the Crab Nebula. We cast constraints of order 10^{-5} at 95% confidence level on the lepton Lorentz Violation parameters.Comment: 23 pages, 9 figures. v2: added comments and references, matches version accepted by JCA