Cosmic Ray Acceleration at Relativistic Shock Waves with a "Realistic" Magnetic Field Structure

The process of cosmic ray first-order Fermi acceleration at relativistic shock waves is studied with the method of Monte Carlo simulations. The simulations are based on numerical integration of particle equations of motion in a turbulent magnetic field near the shock. In comparison to earlier studies, a few "realistic" features of the magnetic field structure are included. The upstream field consists of a mean field component inclined at some angle to the shock normal with finite-amplitude sinusoidal perturbations imposed upon it. The perturbations are assumed to be static in the local plasma rest frame. Their flat or Kolmogorov spectra are constructed with randomly drawn wave vectors from a wide range $(k_{min}, k_{max})$. The downstream field structure is derived from the upstream one as compressed at the shock. We present particle spectra and angular distributions obtained at mildly relativistic sub- and superluminal shocks and also parallel shocks. We show that particle spectra diverge from a simple power-law, the exact shape of the spectrum depends on both the amplitude of the magnetic field perturbations and the wave power spectrum. Features such as spectrum hardening before the cut-off at oblique subluminal shocks and formation of power-law tails at superluminal ones are presented and discussed. At parallel shocks, the presence of finite-amplitude magnetic field perturbations leads to the formation of locally oblique field configurations at the shock and the respective magnetic field compressions. This results in the modification of the particle acceleration process, introducing some features present in oblique shocks, e.g., particle reflections from the shock. We demonstrate for parallel shocks a (nonmonotonic) variation of the particle spectral index with the turbulence amplitude.Comment: revised version (37 pages, 13 figures

Stochastic Acceleration in Relativistic Parallel Shocks

(abridged) We present results of test-particle simulations on both the first and the second order Fermi acceleration at relativistic parallel shock waves. We consider two scenarios for particle injection: (i) particles injected at the shock front, then accelerated at the shock by the first order mechanism and subsequently by the stochastic process in the downstream region; and (ii) particles injected uniformly throughout the downstream region to the stochastic process. We show that regardless of the injection scenario, depending on the magnetic field strength, plasma composition, and the employed turbulence model, the stochastic mechanism can have considerable effects on the particle spectrum on temporal and spatial scales too short to be resolved in extragalactic jets. Stochastic acceleration is shown to be able to produce spectra that are significantly flatter than the limiting case of particle energy spectral index -1 of the first order mechanism. Our study also reveals a possibility of re-acceleration of the stochastically accelerated spectrum at the shock, as particles at high energies become more and more mobile as their mean free path increases with energy. Our findings suggest that the role of the second order mechanism in the turbulent downstream of a relativistic shock with respect to the first order mechanism at the shock front has been underestimated in the past, and that the second order mechanism may have significant effects on the form of the particle spectra and its evolution.Comment: 14 pages, 11 figures (9 black/white and 2 color postscripts). To be published in the ApJ (accepted 6 Nov 2004

X-ray Emission Properties of Large Scale Jets, Hotspots and Lobes in Active Galactic Nuclei

We examine a systematic comparison of jet-knots, hotspots and radio lobes recently observed with Chandra and ASCA. This report will discuss the origin of their X-ray emissions and investigate the dynamics of the jets. The data was compiled at well sampled radio (5GHz) and X-ray frequencies (1keV) for more than 40 radio galaxies. We examined three models for the X-ray production: synchrotron (SYN), synchrotron self-Compton (SSC) and external Compton on CMB photons (EC). For the SYN sources -- mostly jet-knots in nearby low-luminosity radio galaxies -- X-ray photons are produced by ultrarelativistic electrons with energies 10-100 TeV that must be accelerated in situ. For the other objects, conservatively classified as SSC or EC sources, a simple formulation of calculating the ``expected'' X-ray fluxes under an equipartition hypothesis is presented. We confirmed that the observed X-ray fluxes are close to the expected ones for non-relativistic emitting plasma velocities in the case of radio lobes and majority of hotspots, whereas considerable fraction of jet-knots is too bright at X-rays to be explained in this way. We examined two possibilities to account for the discrepancy in a framework of the inverse-Compton model: (1) magnetic field is much smaller than the equipartition value, and (2) the jets are highly relativistic on kpc/Mpc scales. We concluded, that if the inverse-Compton model is the case, the X-ray bright jet-knots are most likely far from the minimum-power condition. We also briefly discuss the other possibility, namely that the observed X-ray emission from all of the jet-knots is synchrotron in origin.Comment: 20 pages, 10 figures, accepted for publication in the Astrophysical Journal, vol.62

Spectroscopic Survey of {\gamma} Doradus Stars I. Comprehensive atmospheric parameters and abundance analysis of {\gamma} Doradus stars

We present a spectroscopic survey of known and candidate $\gamma$\,Doradus stars. The high-resolution, high signal-to-noise spectra of 52 objects were collected by five different spectrographs. The spectral classification, atmospheric parameters (\teff, $\log g$, $\xi$), $v\sin i$ and chemical composition of the stars were derived. The stellar spectral and luminosity classes were found between G0-A7 and IV-V, respectively. The initial values for \teff\ and \logg\ were determined from the photometric indices and spectral energy distribution. Those parameters were improved by the analysis of hydrogen lines. The final values of \teff, \logg\ and $\xi$ were derived from the iron lines analysis. The \teff\ values were found between 6000\,K and 7900\,K, while \logg\,values range from 3.8 to 4.5\,dex. Chemical abundances and $v\sin i$ values were derived by the spectrum synthesis method. The $v\sin i$ values were found between 5 and 240\,km\,s$^{-1}$. The chemical abundance pattern of $\gamma$\,Doradus stars were compared with the pattern of non-pulsating stars. It turned out that there is no significant difference in abundance patterns between these two groups. Additionally, the relations between the atmospheric parameters and the pulsation quantities were checked. A strong correlation between the $v\sin i$ and the pulsation periods of $\gamma$\,Doradus variables was obtained. The accurate positions of the analysed stars in the H-R diagram have been shown. Most of our objects are located inside or close to the blue edge of the theoretical instability strip of $\gamma$\,Doradus.Comment: 18 pages, 13 figure

PtrA is required for coordinate regulation of gene expression during phosphate stress in a marine Synechococcus

Previous microarray analyses have shown a key role for the two-component system PhoBR (SYNW0947, SYNW0948) in the regulation of P transport and metabolism in the marine cyanobacterium Synechococcus sp. WH8102. However, there is some evidence that another regulator, SYNW1019 (PtrA), probably under the control of PhoBR, is involved in the response to P depletion. PtrA is a member of the cAMP receptor protein transcriptional regulator family that shows homology to NtcA, the global nitrogen regulator in cyanobacteria. To define the role of this regulator, we constructed a mutant by insertional inactivation and compared the physiology of wild-type Synechcococcus sp. WH8102 with the ptrA mutant under P-replete and P-stress conditions. In response to P stress the ptrA mutant failed to upregulate phosphatase activity. Microarrays and quantitative RT-PCR indicate that a subset of the Pho regulon is controlled by PtrA, including two phosphatases, a predicted phytase and a gene of unknown function psip1 (SYNW0165), all of which are highly upregulated during P limitation. Electrophoretic mobility shift assays indicate binding of overexpressed PtrA to promoter sequences upstream of the induced genes. This work suggests a two-tiered response to P depletion in this strain, the first being PhoB-dependent induction of high-affinity PO4 transporters, and the second the PtrA-dependent induction of phosphatases for scavenging organic P. The levels of numerous other transcripts are also directly or indirectly influenced by PtrA, including those involved in cell-surface modification, metal uptake, photosynthesis, stress responses and other metabolic processes, which may indicate a wider role for PtrA in cellular regulation in marine picocyanobacteria

Maximum Likelihood Estimation in Gaussian Chain Graph Models under the Alternative Markov Property

The AMP Markov property is a recently proposed alternative Markov property for chain graphs. In the case of continuous variables with a joint multivariate Gaussian distribution, it is the AMP rather than the earlier introduced LWF Markov property that is coherent with data-generation by natural block-recursive regressions. In this paper, we show that maximum likelihood estimates in Gaussian AMP chain graph models can be obtained by combining generalized least squares and iterative proportional fitting to an iterative algorithm. In an appendix, we give useful convergence results for iterative partial maximization algorithms that apply in particular to the described algorithm.Comment: 15 pages, article will appear in Scandinavian Journal of Statistic

Simple and Nearly Optimal Polynomial Root-finding by Means of Root Radii Approximation

We propose a new simple but nearly optimal algorithm for the approximation of all sufficiently well isolated complex roots and root clusters of a univariate polynomial. Quite typically the known root-finders at first compute some crude but reasonably good approximations to well-conditioned roots (that is, those isolated from the other roots) and then refine the approximations very fast, by using Boolean time which is nearly optimal, up to a polylogarithmic factor. By combining and extending some old root-finding techniques, the geometry of the complex plane, and randomized parametrization, we accelerate the initial stage of obtaining crude to all well-conditioned simple and multiple roots as well as isolated root clusters. Our algorithm performs this stage at a Boolean cost dominated by the nearly optimal cost of subsequent refinement of these approximations, which we can perform concurrently, with minimum processor communication and synchronization. Our techniques are quite simple and elementary; their power and application range may increase in their combination with the known efficient root-finding methods.Comment: 12 pages, 1 figur

The Electron Energy Distribution in the Hotspots of Cygnus A: Filling the Gap with the Spitzer Space Telescope

Here we present Spitzer Space Telescope imaging of Cyg A with the Infrared Array Camera, resulting in the detection of the high-energy tails or cut-offs in the synchrotron spectra for all four hotspots of this archetype radio galaxy. When combined with the other data collected from the literature, our observations allow for detailed modeling of the broad-band emission for the brightest spots A and D. We confirm that the X-ray flux detected previously from these features is consistent with the synchrotron self-Compton radiation for the magnetic field intensity 170 muG in spot A, and 270 muG in spot D. We also find that the energy density of the emitting electrons is most likely larger by a factor of a few than the energy density of the hotspots' magnetic field. We construct energy spectra of the radiating ultrarelativistic electrons. We find that for both hotspots A and D these spectra are consistent with a broken power-law extending from at least 100 MeV up to 100 GeV, and that the spectral break corresponds almost exactly to the proton rest energy of 1 GeV. We argue that the shape of the electron continuum reflects two different regimes of the electron acceleration process at mildly relativistic shocks, rather than resulting from radiative cooling and/or absorption effects. In this picture the protons' inertia defines the critical energy for the hotspot electrons above which Fermi-type acceleration processes may play a major role, but below which the operating acceleration mechanism has to be of a different type. At energies >100 GeV, the electron spectra cut-off/steepen again, most likely as a result of spectral aging due to radiative loss effects. We discuss several implications of the presented analysis for the physics of extragalactic jets.Comment: 29 pages, 8 figures and 2 tables included. Accepted for publication in Ap

Particle-unstable nuclei in the Hartree-Fock theory

Ground state energies and decay widths of particle unstable nuclei are calculated within the Hartree-Fock approximation by performing a complex scaling of the many-body Hamiltonian. Through this transformation, the wave functions of the resonant states become square integrable. The method is implemented with Skyrme effective interactions. Several Skyrme parametrizations are tested on four unstable nuclei: 10He, 12O, 26O and 28O.Comment: 5 pages, LaTeX, submitted to Phys. Rev. Let