Radio spectral study of the cluster of galaxies Abell 2255

Spectral index studies of halos, relics, and radio galaxies provide useful information on their origin and connection with merger processes. We present WSRT multi-wavelength observations of the galaxy cluster Abell 2255 at 25 cm, 85 cm, and 2 m. The spectral index images allowed us to study the integrated spectrum of halo and relic and to investigate the physical properties of the Beaver head-tail radio galaxy belonging to the cluster. In the radio halo, the spectral index is steeper at the center and flatter at the locations of the radio filaments, clearly detected at 25 cm. In the relics, the spectral index flattens, moving away from the cluster center. For the Beaver radio galaxy, the spectrum severely steepens from the head towards the end of the tail, because of the energy losses suffered by the relativistic particles. In the 2 m map, which is the first high-sensitivity image presented in the literature at such a long wavelength, a new Mpc-size emission region is detected between the known radio halo and the NW relic. Not detecting this feature in the more sensitive 85 cm observations implies that it must have a very steep spectrum (alpha <= -2.6). The observational properties of the radio halo suggest that either we are looking at a superposition of different structures (filaments in the foreground plus real halo in the background) seen in projection across the cluster center or that the halo is intrinsically peculiar. The newly detected extended region to the NW of the halo could be considered as an asymmetric extension of the halo itself. However, since radio halos are known in the literature as structures showing a regular morphology, the new feature could represent the first example of steep Mpc-size diffuse structures (MDS), detected around clusters at very low frequencies.Comment: 23 pages, 18 figures. A&A, in pres

A coupled bulk-surface model for cell polarisation

Several cellular activities, such as directed cell migration, are coordinated by an intricate network of biochemical reactions which lead to a polarised state of the cell, in which cellular symmetry is broken, causing the cell to have a well defined front and back. Recent work on balancing biological complexity with mathematical tractability resulted in the proposal and formulation of a famous minimal model for cell polarisation, known as the wave pinning model. In this study, we present a three-dimensional generalisation of this mathematical framework through the maturing theory of coupled bulk-surface semilinear partial differential equations in which protein compartmentalisation becomes natural. We show how a local perturbation over the surface can trigger propagating reactions, eventually stopped in a stable profile by the interplay with the bulk component. We describe the behaviour of the model through asymptotic and local perturbation analysis, in which the role of the geometry is investigated. The bulk-surface finite element method is used to generate numerical simulations over simple and complex geometries, which confirm our analysis, showing pattern formation due to propagation and pinning dynamics. The generality of our mathematical and computational framework allows to study more complex biochemical reactions and biomechanical properties associated with cell polarisation in multi-dimensions

Turbulence and Radio Mini-halos in the Sloshing Cores of Galaxy Clusters

A number of relaxed, cool-core galaxy clusters exhibit diffuse, steep-spectrum radio sources in their central regions, known as radio mini-halos. It has been proposed that the relativistic electrons responsible for the emission have been reaccelerated by turbulence generated by the sloshing of the cool core gas. We present a high-resolution MHD simulation of gas sloshing in a galaxy cluster coupled with subgrid simulations of relativistic electron acceleration to test this hypothesis. Our simulation shows that the sloshing motions generate turbulence on the order of $\delta{v} \sim$ 50-200 km s$^{-1}$ on spatial scales of $\sim$50-100 kpc and below in the cool core region within the envelope of the sloshing cold fronts, whereas outside the cold fronts, there is negligible turbulence. This turbulence is potentially strong enough to reaccelerate relativistic electron seeds (with initial $\gamma \sim 100-500$) to $\gamma \sim 10^4$ via damping of magnetosonic waves and non-resonant compression. The seed electrons could remain in the cluster from, e.g., past AGN activity. In combination with the magnetic field amplification in the core, these electrons then produce diffuse radio synchrotron emission that is coincident with the region bounded by the sloshing cold fronts, as indeed observed in X-rays and the radio. The result holds for different initial spatial distributions of preexisting relativistic electrons. The power and the steep spectral index ($\alpha \approx 1-2$) of the resulting radio emission are consistent with observations of minihalos, though the theoretical uncertainties of the acceleration mechanisms are high. We also produce simulated maps of inverse-Compton hard X-ray emission from the same population of relativistic electrons.Comment: 28 pages, 29 figures, in emulateapj format. Revised version accepted by the referee, conclusions unchange

Analytical Study of Diffusive Relativistic Shock Acceleration

Particle acceleration in relativistic shocks is studied analytically in the test-particle, small-angle scattering limit, for an arbitrary velocity-angle diffusion function D. Accurate analytic expressions for the spectral index s are derived using few (2-6) low-order moments of the shock-frame angular distribution. For isotropic diffusion, previous results are reproduced and justified. For anisotropic diffusion, s is shown to be sensitive to D, particularly downstream and at certain angles, and a wide range of s values is attainable. The analysis, confirmed numerically, can be used to test collisionless shock models and to observationally constrain D. For example, strongly forward- or backward-enhanced diffusion downstream is ruled out by GRB afterglow observations.Comment: 4 pages, 2 figures, PRL accepted, minor change

Deep Chandra observation and numerical studies of the nearest cluster cold front in the sky

We present the results of a very deep (500 ks) Chandra observation, along with tailored numerical simulations, of the nearest, best resolved cluster cold front in the sky, which lies 90 kpc (19 arcmin) to the north-west of M 87. The northern part of the front appears the sharpest, with a width smaller than 2.5 kpc (1.5 Coulomb mean free paths; at 99 per cent confidence). Everywhere along the front, the temperature discontinuity is narrower than 4–8 kpc and the metallicity gradient is narrower than 6 kpc, indicating that diffusion, conduction and mixing are suppressed across the interface. Such transport processes can be naturally suppressed by magnetic fields aligned with the cold front. Interestingly, comparison to magnetohydrodynamic simulations indicates that in order to maintain the observed sharp density and temperature discontinuities, conduction must also be suppressed along the magnetic field lines. However, the northwestern part of the cold front is observed to have a non-zero width. While other explanations are possible, the broadening is consistent with the presence of Kelvin–Helmholtz instabilities (KHI) on length-scales of a few kpc. Based on comparison with simulations, the presence of KHI would imply that the effective viscosity of the intracluster medium is suppressed by more than an order of magnitude with respect to the isotropic Spitzer-like temperature dependent viscosity. Underneath the cold front, we observe quasi-linear features that are ∼10 per cent brighter than the surrounding gas and are separated by ∼15 kpc from each other in projection. Comparison to tailored numerical simulations suggests that the observed phenomena may be due to the amplification of magnetic fields by gas sloshing in wide layers below the cold front, where the magnetic pressure reaches ∼5–10 per cent of the thermal pressure, reducing the gas density between the bright features

Phase-Transition in Binary Sequences with Long-Range Correlations

Motivated by novel results in the theory of correlated sequences, we analyze the dynamics of random walks with long-term memory (binary chains with long-range correlations). In our model, the probability for a unit bit in a binary string depends on the fraction of unities preceding it. We show that the system undergoes a dynamical phase-transition from normal diffusion, in which the variance D_L scales as the string's length L, into a super-diffusion phase (D_L ~ L^{1+|alpha|}), when the correlation strength exceeds a critical value. We demonstrate the generality of our results with respect to alternative models, and discuss their applicability to various data, such as coarse-grained DNA sequences, written texts, and financial data.Comment: 4 pages, 4 figure

Ion dynamics and acceleration in relativistic shocks

Ab-initio numerical study of collisionless shocks in electron-ion unmagnetized plasmas is performed with fully relativistic particle in cell simulations. The main properties of the shock are shown, focusing on the implications for particle acceleration. Results from previous works with a distinct numerical framework are recovered, including the shock structure and the overall acceleration features. Particle tracking is then used to analyze in detail the particle dynamics and the acceleration process. We observe an energy growth in time that can be reproduced by a Fermi-like mechanism with a reduced number of scatterings, in which the time between collisions increases as the particle gains energy, and the average acceleration efficiency is not ideal. The in depth analysis of the underlying physics is relevant to understand the generation of high energy cosmic rays, the impact on the astrophysical shock dynamics, and the consequent emission of radiation.Comment: 5 pages, 3 figure

Asymptotic Spectroscopy of Rotating Black Holes

We calculate analytically the transmission and reflection amplitudes for waves incident on a rotating black hole in d=4, analytically continued to asymptotically large, nearly imaginary frequency. These amplitudes determine the asymptotic resonant frequencies of the black hole, including quasinormal modes, total-transmission modes and total-reflection modes. We identify these modes with semiclassical bound states of a one-dimensional Schrodinger equation, localized along contours in the complexified r-plane which connect turning points of corresponding null geodesics. Each family of modes has a characteristic temperature and chemical potential. The relations between them provide hints about the microscopic description of the black hole in this asymptotic regime.Comment: References adde

Self-Similar Collisionless Shocks

Observations of gamma-ray burst afterglows suggest that the correlation length of magnetic field fluctuations downstream of relativistic non-magnetized collisionless shocks grows with distance from the shock to scales much larger than the plasma skin depth. We argue that this indicates that the plasma properties are described by a self-similar solution, and derive constraints on the scaling properties of the solution. For example, we find that the scaling of the characteristic magnetic field amplitude with distance from the shock is B \propto D^{s_B} with -1<s_B<=0, that the spectrum of accelerated particles is dn/dE \propto E^{-2/(s_B+1)}, and that the scaling of the magnetic correlation function is \propto x^{2s_B} (for x>>D). We show that the plasma may be approximated as a combination of two self-similar components: a kinetic component of energetic particles and an MHD-like component representing "thermal" particles. We argue that the latter may be considered as infinitely conducting, in which case s_B=0 and the scalings are completely determined (e.g. dn/dE \propto E^{-2} and B \propto D^0). Similar claims apply to non- relativistic shocks such as in supernova remnants, if the upstream magnetic field can be neglected. Self-similarity has important implications for any model of particle acceleration and/or field generation. For example, we show that the diffusion function in the angle \mu of momentum p in diffusive shock acceleration models must satisfy D_{\mu\mu}(p,D) = D^{-1}D'_{\mu\mu}(p/D), and that a previously suggested model for the generation of large scale magnetic fields through a hierarchical merger of current-filaments should be generalized. A numerical experiment testing our analysis is outlined (Abridged).Comment: 16 pages, 1 figure, accepted for publication in Ap

Large-scale Motions in the Perseus Galaxy Cluster

By combining large-scale mosaics of ROSAT PSPC, XMM-Newton, and Suzaku X-ray observations, we present evidence for large-scale motions in the intracluster medium of the nearby, X-ray bright Perseus Cluster. These motions are suggested by several alternating and interleaved X-ray bright, low-temperature, low-entropy arcs located along the east-west axis, at radii ranging from ~10 kpc to over a Mpc. Thermodynamic features qualitatively similar to these have previously been observed in the centers of cool core clusters, and were successfully modeled as a consequence of the gas sloshing/swirling motions induced by minor mergers. Our observations indicate that such sloshing/swirling can extend out to larger radii than previously thought, on scales approaching the virial radius.Comment: 6 pages, 6 figures, accepted for publication in Ap