Relativistic AGN jets III. Synthesis of synchrotron emission from Double-Double Radio Galaxies

The class of Double-Double Radio Galaxies (DDRGs) relates to episodic jet outbursts. How various regions and components add to the total intensity in radio images is less well known. In this paper we synthesize synchrotron images for DDRGs based on special relativistic hydrodynamic simulations, making advanced approximations for the magnetic fields. We study the synchrotron images for: Three different radial jet profiles; Ordered, entangled or mixed magnetic fields; Spectral ageing from synchrotron cooling; The contribution from different jet components; The viewing angle and Doppler (de-)boosting; The various epochs of the evolution of the DDRG. To link our results to observational data, we adopt to J1835+6204 as a reference source. In all cases the synthesized synchrotron images show two clear pairs of hotspots, in the inner and outer lobes. The best resemblance is obtained for the piecewise isochoric jet model, for a viewing angle of approximately $\vartheta \sim -71^{\circ}$, i.e. inclined with the lower jet towards the observer, with predominantly entangled ($\gtrsim 70$ per cent of the magnetic pressure) in turbulent, rather than ordered fields. The effects of spectral ageing become significant when the ratio of observation frequencies and cut-off frequency $\nu_{\rm obs}/\nu_{\infty,0} \gtrsim 10^{-3}$, corresponding to $\sim 3 \cdot 10^2$ MHz. For viewing angles $\vartheta \lesssim -30^{\circ}$, a DDRG morphology can no longer be recognized. The second jets must be injected within $\lesssim$ 4 per cent of the lifetime of the first jets for a DDRG structure to emerge, which is relevant for Active Galactic Nuclei feedback constraints.Comment: 24 pages, 8 figure

On the Structure and Scale of Cosmic Ray Modified Shocks

Strong astrophysical shocks, diffusively accelerating cosmic rays (CR) ought to develop CR precursors. The length of such precursor $L_{p}$ is believed to be set by the ratio of the CR mean free path $\lambda$ to the shock speed, i.e., $L_{p}\sim c\lambda/V_{sh}\sim cr_{g}/V_{sh}$, which is formally independent of the CR pressure $P_{c}$. However, the X-ray observations of supernova remnant shocks suggest that the precursor scale may be significantly shorter than $L_{p}$ which would question the above estimate unless the magnetic field is strongly amplified and the gyroradius $r_{g}$ is strongly reduced over a short (unresolved) spatial scale. We argue that while the CR pressure builds up ahead of the shock, the acceleration enters into a strongly nonlinear phase in which an acoustic instability, driven by the CR pressure gradient, dominates other instabilities (at least in the case of low $\beta$ plasma). In this regime the precursor steepens into a strongly nonlinear front whose size scales with \emph{the CR pressure}as $L_{f}\sim L_{p}\cdot(L_{s}/L_{p})^{2}(P_{c}/P_{g})^{2}$, where $L_{s}$ is the scale of the developed acoustic turbulence, and $P_{c}/P_{g}$ is the ratio of CR to gas pressure. Since $L_{s}\ll L_{p}$, the precursor scale reduction may be strong in the case of even a moderate gas heating by the CRs through the acoustic and (possibly also) the other instabilities driven by the CRs.Comment: EPS 2010 paper, to appear in PPC

On the mechanism for breaks in the cosmic ray spectrum

The proof of cosmic ray (CR) origin in supernova remnants (SNR) must hinge on full consistency of the CR acceleration theory with the observations; direct proof is impossible because of the orbit stochasticity of CR particles. Recent observations of a number of galactic SNR strongly support the SNR-CR connection in general and the Fermi mechanism of CR acceleration, in particular. However, many SNR expand into weakly ionized dense gases, and so a significant revision of the mechanism is required to fit the data. We argue that strong ion-neutral collisions in the remnant surrounding lead to the steepening of the energy spectrum of accelerated particles by \emph{exactly one power}. The spectral break is caused by a partial evanescence of Alfven waves that confine particles to the accelerator. The gamma-ray spectrum generated in collisions of the accelerated protons with the ambient gas is also calculated. Using the recent Fermi spacecraft observation of the SNR W44 as an example, we demonstrate that the parent proton spectrum is a classical test particle power law $\propto E^{-2}$, steepening to $E^{-3}$ at $E_{br}\approx7GeV$.Comment: APS talk to appear in PoP, 4 figure

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

Modeling Bell's Non-resonant Cosmic Ray Instability

We have studied the non-resonant streaming instability of charged energetic particles moving through a background plasma, discovered by Bell (2004). We confirm his numerical results regarding a significant magnetic field amplification in the system. A detailed physical picture of the instability development and of the magnetic field evolution is given.Comment: 12 pages, 4 figures, accepted to Ap

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

Extended Formulations in Mixed-integer Convex Programming

We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer approximation algorithms and generally faster solution times. First, we observe that all MICP instances from the MINLPLIB2 benchmark library are conic representable with standard symmetric and nonsymmetric cones. Conic reformulations are shown to be effective extended formulations themselves because they encode separability structure. For mixed-integer conic-representable problems, we provide the first outer approximation algorithm with finite-time convergence guarantees, opening a path for the use of conic solvers for continuous relaxations. We then connect the popular modeling framework of disciplined convex programming (DCP) to the existence of extended formulations independent of conic representability. We present evidence that our approach can yield significant gains in practice, with the solution of a number of open instances from the MINLPLIB2 benchmark library.Comment: To be presented at IPCO 201

The Heating of Thermal Electrons in Fast Collisionless Shocks: The Integral Role of Cosmic Rays

Understanding the heating of electrons to quasi-thermal energies at collisionless shocks has broad implications for plasma astrophysics. It directly impacts the interpretation of X-ray spectra from shocks, is important for understanding how energy is partitioned between the thermal and cosmic ray populations, and provides insight into the structure of the shock itself. In Ghavamian, Laming & Rakowski (2007) we presented observational evidence for an inverse square relation between the electron-to-proton temperature ratio and the shock speed at the outer blast waves of supernova remnants in partially neutral interstellar gas. There we outlined how lower hybrid waves generated in the cosmic ray precursor could produce such a relationship by heating the electrons to a common temperature independent of both shock speed and the strength of the ambient magnetic field. Here we explore the mechanism of lower hybrid wave heating of electrons in more detail. Specifically we examine the growth rate of the lower hybrid waves for both the kinetic (resonant) and reactive cases. We find that only the kinetic case exhibits a growing mode. At low Alfv\'en Mach numbers (~15) the growth of lower hybrid waves can be faster than the magnetic field amplification by modified Alfv\'en waves.Comment: Accepted to ApJ, 25 pages single column, 3 figure

Dark Matter in split extended supersymmetry

We consider the split extended (N=2) supersymmetry scenario recently proposed by Antoniadis et al. [hep-ph/0507192] as a realistic low energy framework arising from intersecting brane models. While all scalar superpartners and charged gauginos are naturally at a heavy scale, the model low energy spectrum contains a Higgsino-like chargino and a neutralino sector made out of two Higgsino and two Bino states. We show that the lightest neutralino is a viable dark matter candidate, finding regions in the parameter space where its thermal relic abundance matches the latest determination of the density of matter in the Universe by WMAP. We also discuss dark matter detection strategies within this model: we point out that current data on cosmic-ray antimatter already place significant constraints on the model, while direct detection is the most promising technique for the future. Analogies and differences with respect to the standard split SUSY scenario based on the MSSM are illustrated.Comment: 14 pages, references added, typos corrected, matches with the published versio