Simulating cosmic rays in clusters of galaxies - II. A unified scheme for radio halos and relics with predictions of the gamma-ray emission

The thermal plasma of galaxy clusters lost most of its information on how structure formation proceeded as a result of dissipative processes. In contrast, non-equilibrium distributions of cosmic rays (CR) preserve the information about their injection and transport processes and provide thus a unique window of current and past structure formation processes. This information can be unveiled by observations of non-thermal radiative processes, including radio synchrotron, hard X-ray, and gamma-ray emission. To explore this, we use high-resolution simulations of a sample of galaxy clusters spanning a mass range of about two orders of magnitudes, and follow self-consistent CR physics on top of the radiative hydrodynamics. We model CR electrons that are accelerated at cosmological structure formation shocks and those that are produced in hadronic interactions of CRs with ambient gas protons. We find that CR protons trace the time integrated non-equilibrium activities of clusters while shock-accelerated CR electrons probe current accretion and merging shock waves. The resulting inhomogeneous synchrotron emission matches the properties of observed radio relics. We propose a unified model for the generation of radio halos. Giant radio halos are dominated in the centre by secondary synchrotron emission with a transition to the synchrotron radiation emitted from shock-accelerated electrons in the cluster periphery. This model is able to explain the observed correlation of mergers with radio halos, the larger peripheral variation of the spectral index, and the large scatter in the scaling relation between cluster mass and synchrotron emission. Future low-frequency radio telescopes (LOFAR, GMRT, MWA, LWA) are expected to probe the accretion shocks of clusters. [abridged]Comment: 32 pages, 19 figures, small changes to match the version to be published by MNRAS, full resolution version available at http://www.cita.utoronto.ca/~pfrommer/Publications/CRs_non-thermal.pd

A maximum-entropy method for reconstructing the projected mass distribution of gravitational lenses

The maximum-entropy method is applied to the problem of reconstructing the projected mass density of a galaxy cluster using its gravitational lensing effects on background galaxies. We demonstrate the method by reconstructing the mass distribution in a model cluster using simulated shear and magnification data to which Gaussian noise is added. The mass distribution is reconstructed directly and the inversion is regularised using the entropic prior for this positive additive distribution. For realistic noise levels, we find that the method faithfully reproduces the main features of the cluster mass distribution not only within the observed field but also slightly beyond it. We estimate the uncertainties on the reconstruction by calculating an analytic approximation to the covariance matrix of the reconstruction values of each pixel. This result is compared with error estimates derived from Monte-Carlo simulations for different noise realisations and found to be in good agreement.Comment: Version accepted by MNRAS. New figure showing power spectrum and auto correlation function of the residual map; other minor changes. 10 pages including 9 figure

Sequential Design with Mutual Information for Computer Experiments (MICE): Emulation of a Tsunami Model

Computer simulators can be computationally intensive to run over a large number of input values, as required for optimization and various uncertainty quantification tasks. The standard paradigm for the design and analysis of computer experiments is to employ Gaussian random fields to model computer simulators. Gaussian process models are trained on input-output data obtained from simulation runs at various input values. Following this approach, we propose a sequential design algorithm, MICE (Mutual Information for Computer Experiments), that adaptively selects the input values at which to run the computer simulator, in order to maximize the expected information gain (mutual information) over the input space. The superior computational efficiency of the MICE algorithm compared to other algorithms is demonstrated by test functions, and a tsunami simulator with overall gains of up to 20% in that case

A Note on the Ruelle Pressure for a Dilute Disordered Sinai Billiard

The topological pressure is evaluated for a dilute random Lorentz gas, in the approximation that takes into account only uncorrelated collisions between the moving particle and fixed, hard sphere scatterers. The pressure is obtained analytically as a function of a temperature-like parameter, beta, and of the density of scatterers. The effects of correlated collisions on the topological pressure can be described qualitatively, at least, and they significantly modify the results obtained by considering only uncorrelated collision sequences. As a consequence, for large systems, the range of beta-values over which our expressions for the topological pressure are valid becomes very small, approaching zero, in most cases, as the inverse of the logarithm of system size.Comment: 15 pages RevTeX with 2 figures. Final version with some typo's correcte

Three-Dimensional Simulations of Bi-Directed Magnetohydrodynamic Jets Interacting with Cluster Environments

We report on a series of three-dimensional magnetohydrodynamic simulations of active galactic nucleus (AGN) jet propagation in realistic models of magnetized galaxy clusters. We are primarily interested in the details of energy transfer between jets and the intracluster medium (ICM) to help clarify what role such flows could have in the reheating of cluster cores. Our simulated jets feature a range of intermittency behaviors, including intermittent jets that periodically switch on and off and one model jet that shuts down completely, naturally creating a relic plume. The ICM into which these jets propagate incorporates tangled magnetic field geometries and density substructure designed to mimic some likely features of real galaxy clusters. We find that our jets are characteristically at least 60% efficient at transferring thermal energy to the ICM. Irreversible heat energy is not uniformly distributed, however, instead residing preferentially in regions very near the jet/cocoon boundaries. While intermittency affects the details of how, when, and where this energy is deposited, all of our models generically fail to heat the cluster cores uniformly. Both the detailed density structure and nominally weak magnetic fields in the ICM play interesting roles in perturbing the flows, particularly when the jets are non-steady. Still, this perturbation is never sufficient to isotropize the jet energy deposition, suggesting that some other ingredient is required for AGN jets to successfully reheat cluster cores.Comment: 19 pages, 18 figures, Accepted for publication in the Astrophysical Journa