MAGIC MOORE-PENROSE INVERSES AND PHILATELIC MAGIC SQUARES WITH SPECIAL EMPHASIS ON THE DANIELS–ZLOBEC MAGIC SQUARE

We study singular magic matrices in which the numbers in the rows and columns and in the two main diagonals all add up to the same sum. Our interest focuses on such magic matrices for which the Moore– Penrose inverse is also magic. Special attention is given to the “Daniels–Zlobec magic square’’ introduced by the British magician and television performer Paul Daniels (b. 1938) and considered by Zlobec (2001); see also Murray (1989, pp. 30–32). We introduce the concept of a “philatelic magic square” as a square arrangement of images of postage stamps so that the associated nominal values form a magic square. Three philatelic magic squares with stamps especially chosen for Sanjo Zlobec are presented in celebration of his 70th birthday; most helpful in identifying these stamps was an Excel checklist by Männikkö (2009)

Efficiency of Nonlinear Particle Acceleration at Cosmic Structure Shocks

We have calculated the evolution of cosmic ray (CR) modified astrophysical shocks for a wide range of shock Mach numbers and shock speeds through numerical simulations of diffusive shock acceleration (DSA) in 1D quasi- parallel plane shocks. The simulations include thermal leakage injection of seed CRs, as well as pre-existing, upstream CR populations. Bohm-like diffusion is assumed. We model shocks similar to those expected around cosmic structure pancakes as well as other accretion shocks driven by flows with upstream gas temperatures in the range $T_0=10^4-10^{7.6}$K and shock Mach numbers spanning $M_s=2.4-133$. We show that CR modified shocks evolve to time-asymptotic states by the time injected particles are accelerated to moderately relativistic energies (p/mc \gsim 1), and that two shocks with the same Mach number, but with different shock speeds, evolve qualitatively similarly when the results are presented in terms of a characteristic diffusion length and diffusion time. For these models the time asymptotic value for the CR acceleration efficiency is controlled mainly by shock Mach number. The modeled high Mach number shocks all evolve towards efficiencies $\sim 50$%, regardless of the upstream CR pressure. On the other hand, the upstream CR pressure increases the overall CR energy in moderate strength shocks ($M_s \sim {\rm a few}$). (abridged)Comment: 23 pages, 12 ps figures, accepted for Astrophysical Journal (Feb. 10, 2005

Nonthermal Emission from a Supernova Remnant in a Molecular Cloud

In evolved supernova remnants (SNRs) interacting with molecular clouds, such as IC 443, W44, and 3C391, a highly inhomogeneous structure consisting of a forward shock of moderate Mach number, a cooling layer, a dense radiative shell and an interior region filled with hot tenuous plasma is expected. We present a kinetic model of nonthermal electron injection, acceleration and propagation in that environment and find that these SNRs are efficient electron accelerators and sources of hard X- and gamma-ray emission. The energy spectrum of the nonthermal electrons is shaped by the joint action of first and second order Fermi acceleration in a turbulent plasma with substantial Coulomb losses. Bremsstrahlung, synchrotron, and inverse Compton radiation of the nonthermal electrons produce multiwavelength photon spectra in quantitative agreement with the radio and the hard emission observed by ASCA and EGRET from IC 443. We distinguish interclump shock wave emission from molecular clump shock wave emission accounting for a complex structure of molecular cloud. Spatially resolved X- and gamma- ray spectra from the supernova remnants IC 443, W44, and 3C391 as might be observed with BeppoSAX, Chandra XRO, XMM, INTEGRAL and GLAST would distinguish the contribution of the energetic lepton component to the gamma-rays observed by EGRET.Comment: 14 pages, 4 figure, Astrophysical Journal, v.538, 2000 (in press

Nonlinear shock acceleration beyond the Bohm limit

We suggest a physical mechanism whereby the acceleration time of cosmic rays by shock waves can be significantly reduced. This creates the possibility of particle acceleration beyond the knee energy at ~10^15eV. The acceleration results from a nonlinear modification of the flow ahead of the shock supported by particles already accelerated to the knee momentum at p ~ p_*. The particles gain energy by bouncing off converging magnetic irregularities frozen into the flow in the shock precursor and not so much by re-crossing the shock itself. The acceleration rate is thus determined by the gradient of the flow velocity and turns out to be formally independent of the particle mean free path (m.f.p.). The velocity gradient is, in turn, set by the knee-particles at p ~ p_* as having the dominant contribution to the CR pressure. Since it is independent of the m.f.p., the acceleration rate of particles above the knee does not decrease with energy, unlike in the linear acceleration regime. The reason for the knee formation at p ~ p_* is that particles with $p > p_*$ are effectively confined to the shock precursor only while they are within limited domains in the momentum space, while other particles fall into ``loss-islands'', similar to the ``loss-cone'' of magnetic traps. This structure of the momentum space is due to the character of the scattering magnetic irregularities. They are formed by a train of shock waves that naturally emerge from unstably growing and steepening magnetosonic waves or as a result of acoustic instability of the CR precursor. These losses steepen the spectrum above the knee, which also prevents the shock width from increasing with the maximum particle energy.Comment: aastex, 13 eps figure

When non-activists care: group efficacy mediates the effect of social identification and perceived instability on the legitimacy of collective action

In recent years, multiple social movements have emerged around the world. In addition, public surveys indicate the highest recorded levels of support for protest. In this context of acceptance of collective action, we examine the role of non-activists in the legitimacy of social movements, as this ‘passive’ support can contribute to social change. Given that antecedents of legitimacy have been neglected in the literature, we carried out a survey (N = 605) among a general sample of the population in Chile to shed light on this issue. We found that social identification with movements and perceived instability predicted the perceived legitimacy of protests by social movements, and that both variables had only indirect effects, through group efficacy. This suggests that perceiving social movements as able to achieve success can lead non-activists to perceive their actions as legitimate, highlighting the importance to movements of being seen to be effective

Cosmological Shocks in Adaptive Mesh Refinement Simulations and the Acceleration of Cosmic Rays

We present new results characterizing cosmological shocks within adaptive mesh refinement N-Body/hydrodynamic simulations that are used to predict non-thermal components of large-scale structure. This represents the first study of shocks using adaptive mesh refinement. We propose a modified algorithm for finding shocks from those used on unigrid simulations that reduces the shock frequency of low Mach number shocks by a factor of ~3. We then apply our new technique to a large, (512 Mpc/h)^3, cosmological volume and study the shock Mach number (M) distribution as a function of pre-shock temperature, density, and redshift. Because of the large volume of the simulation, we have superb statistics that results from having thousands of galaxy clusters. We find that the Mach number evolution can be interpreted as a method to visualize large-scale structure formation. Shocks with Mach<5 typically trace mergers and complex flows, while 520 generally follow accretion onto filaments and galaxy clusters, respectively. By applying results from nonlinear diffusive shock acceleration models using the first-order Fermi process, we calculate the amount of kinetic energy that is converted into cosmic ray protons. The acceleration of cosmic ray protons is large enough that in order to use galaxy clusters as cosmological probes, the dynamic response of the gas to the cosmic rays must be included in future numerical simulations.Comment: 15 pages, 14 figures, Accepted to ApJ, minor changes mad

The Contribution of Different Supernova Populations to the Galactic Gamma-Ray Background

The contribution of Source Cosmic Rays (SCRs), accelerated and still confined in Supernova Remnants (SNRs), to the diffuse high energy \gr emission above 1 GeV from the Galactic disk is studied. The \grs produced by the SCRs have a much harder spectrum than those generated by the Galactic Cosmic Rays (GCRs). Extending a previous paper, a simple SNR population synthesis is considered and the Inverse Compton emission from the SCR electrons is evaluated in greater detail. Then the combined spectrum of \gr emission from the Galactic Supernova Remnant population is calculated and this emission at low Galactic latitudes is compared with the diffuse \gr emission observed by the EGRET and ground based instruments. The average contribution of SCRs is comparable to the GCR contribution already at GeV energies, due to Supernovae of types II and Ib exploding into the wind bubbles of quite massive progenitor stars, and becomes dominant at \gr energies above 100 GeV. At TeV energies the dominant contribution is from SCRs in SNRs that expand into a uniform interstellar medium. In fact, the sum of hadronic and Inverse Compton \grs would exceed the limits given by the existing experimental data, unless the confinement time $T_{SN}$, i.e. the time until which SNRs confine the main fraction of accelerated SCRs, is as small as $T_{SN}\sim 10^4$ yr and the typical magnetic field strength in SNRs as large as 30 $\mu$G. Both situations are however possible as a result of field amplification through CR backreaction in the acceleration process. It is pointed out that accurate measurements of the low-latitude diffuse Galactic \gr spectrum at TeV-energies can serve as a unique consistency test for CR origin from the Supernova Remnant population as a whole.Comment: To appear in Astrophysical Journa

The effect of cosmic-ray diffusion on the Parker instability

The Parker instability, which has been considered as a process governing the structure of the interstellar medium, is induced by the buoyancy of magnetic fields and cosmic rays. In previous studies, while the magnetic field has been fully incorporated in the context of isothermal magnetohydrodynamics, cosmic rays have normally been treated with the simplifying assumption of infinite diffusion along magnetic field lines but no diffusion across them. The cosmic-ray diffusion is, however, finite. In this work, we fully take into account the diffusion process of cosmic rays in a linear stability analysis of the Parker instability. Cosmic rays are described with the diffusion-convection equation. With realistic values of cosmic-ray diffusion coefficients expected in the interstellar medium, we show that the result of previous studies with the simplifying assumption about cosmic-ray diffusion applies well. The finiteness of the parallel diffusion decreases the growth rate of the Parker instability, while the relatively smaller perpendicular diffusion has no significant effect. We discuss the implication of our result on the role of the Parker instability in the interstellar mediumopen373

Cosmic Ray Protons and Magnetic Fields in Clusters of Galaxies and their Cosmological Consequences

The masses of clusters of galaxies estimated by gravitational lensing exceed in many cases the mass estimates based on hydrostatic equilibrium. This may suggest the existence of nonthermal pressure. We ask if radio galaxies can heat and support the cluster gas with injected cosmic ray protons and magnetic field densities, which are permitted by Faraday rotation and gamma ray observations of clusters of galaxies. We conclude that they are powerful enough to do this within a cluster radius of roughly 1 Mpc. If present, nonthermal pressures could lead to a revised estimate of the ratio of baryonic mass to total mass, and the apparent baryonic overdensity in clusters would disappear. In consequence, $\Omega_{\rm cold}$, the clumping part of the cosmological density $\Omega_{o}$, would be larger than $0.4\,h_{50}^{-1/2}$.Comment: Accepted by ApJ, 16 pages, LaTeX, 2 figures, epsfig.sty, aaspp4.st

Understanding hadronic gamma-ray emission from supernova remnants

We aim to test the plausibility of a theoretical framework in which the gamma-ray emission detected from supernova remnants may be of hadronic origin, i.e., due to the decay of neutral pions produced in nuclear collisions involving relativistic nuclei. In particular, we investigate the effects induced by magnetic field amplification on the expected particle spectra, outlining a phenomenological scenario consistent with both the underlying Physics and the larger and larger amount of observational data provided by the present generation of gamma experiments, which seem to indicate rather steep spectra for the accelerated particles. In addition, in order to study to study how pre-supernova winds might affect the expected emission in this class of sources, the time-dependent gamma-ray luminosity of a remnant with a massive progenitor is worked out. Solid points and limitations of the proposed scenario are finally discussed in a critical way.Comment: 30 pages, 5 figures; Several comments, references and a figure added. Some typos correcte