Anisotropic inverse Compton scattering from the trans-relativistic to the ultra-relativistic regime and application to the radio galaxies

The problem of the anisotropic Inverse Compton scattering between a monochromatic photon beam and relativistic electrons is revisited and formally solved without approximations. Solutions are given for the single scattering with an electron beam and with a population of electrons isotropically distributed, under the assumption that the energy distribution of the relativistic particles follows a simple power law as it is the case in many astrophysical applications. Both the Thomson approximation and the Klein-Nishina regime are considered for the scattering of an unpolarized photon beam. The equations are obtained without the ultra-relativistic approximation and are compared with the ultra-relativistic solutions given in the literature. The main characteristics of the power distribution and spectra of the scattered radiation are discussed for relevant examples. In the Thomson case for an isotropic electron population simple formulae holding down to mildly-relativistic energies are given. As an application the formulae of the anisotropic inverse Compton scattering are used to predict the properties of the X and $\gamma$-ray spectra from the radio lobes of strong FR II radio galaxies due to the interaction of the relativistic electrons with the incoming photons from the nucleus. The dependence of the emitted power on the relativistic electron energy distribution and on its evolution with time is discussed.Comment: 35 pages, 17 .ps figures, LaTex, to appear in Astroparticle Physic

Giant radio halos in galaxy clusters as probes of particle acceleration in turbulent regions

Giant radio halos in galaxy clusters probe mechanisms of particle acceleration connected with cluster merger events. Shocks and turbulence are driven in the inter-galactic-medium (IGM) during clusters mergers and may have a deep impact on the non-thermal properties of galaxy clusters. Models of turbulent (re)acceleration of relativistic particles allow good correspondence with present observations, from radio halos to gamma-ray upper limits, although several aspects of this complex scenario remain still poorly understood. After providing basic motivations for turbulent acceleration in galaxy clusters, we discuss relevant aspects of the physics of particle acceleration by MHD turbulence and the expected broad--band non-thermal emission from galaxy clusters. We discuss (in brief) the most important results of turbulent (re)acceleration models, the open problems, and the possibilities to test models with future observations. In this respect, further constraints on the origin of giant nearby radio halos can also be obtained by combining their (spectral and morphological) properties with the constraints from gamma-ray observations of their parent clusters.Comment: 10 pages, 2 figures, Invited talk at the conference "Diffuse Relativistic Plasmas", Bangalore, March 2011. J. Astrophys. Astr. in pres

Optimization as a design strategy. Considerations based on building simulation-assisted experiments about problem decomposition

In this article the most fundamental decomposition-based optimization method - block coordinate search, based on the sequential decomposition of problems in subproblems - and building performance simulation programs are used to reason about a building design process at micro-urban scale and strategies are defined to make the search more efficient. Cyclic overlapping block coordinate search is here considered in its double nature of optimization method and surrogate model (and metaphore) of a sequential design process. Heuristic indicators apt to support the design of search structures suited to that method are developed from building-simulation-assisted computational experiments, aimed to choose the form and position of a small building in a plot. Those indicators link the sharing of structure between subspaces ("commonality") to recursive recombination, measured as freshness of the search wake and novelty of the search moves. The aim of these indicators is to measure the relative effectiveness of decomposition-based design moves and create efficient block searches. Implications of a possible use of these indicators in genetic algorithms are also highlighted.Comment: 48 pages. 12 figures, 3 table

Particle reacceleration by compressible turbulence in galaxy clusters: effects of reduced mean free path

Direct evidence for in situ particle acceleration mechanisms in the inter-galactic-medium (IGM) is provided by the diffuse Mpc--scale synchrotron emissions observed from galaxy clusters. It has been proposed that MHD turbulence, generated during cluster-cluster mergers, may be a source of particle reacceleration in the IGM. Calculations of turbulent acceleration must account self-consistently for the complex non--linear coupling between turbulent waves and particles. This has been calculated in some detail under the assumption that turbulence interacts in a collisionless way with the IGM. In this paper we explore a different picture of acceleration by compressible turbulence in galaxy clusters, where the interaction between turbulence and the IGM is mediated by plasma instabilities and maintained collisional at scales much smaller than the Coulomb mean free path. In this regime most of the energy of fast modes is channeled into the reacceleration of relativistic particles and the acceleration process approaches a universal behaviour being self-regulated by the back-reaction of the accelerated particles on turbulence itself. Assuming that relativistic protons contribute to several percent (or less) of the cluster energy, consistent with the FERMI observations of nearby clusters, we find that compressible turbulence at the level of a few percent of the thermal energy can reaccelerate relativistic electrons at GeV energies, that are necessary to explain the observed diffuse radio emission in the form of giant radio halos.Comment: 8 pages, 3 figures. Accepted in MNRAS (October 28, 2010

Remarks on time-energy uncertainty relations

Using a recent construction of observables characterizing the time of occurence of an effect in quantum theory, we present a rigorous derivation of the standard time-energy uncertainty relation. In addition, we prove an uncertainty relation for time measurements only.Comment: 9 pages, to be pubblished in Rev. Math. Phys. issue in honor of H. Arak