Symmetric coupling of angular momenta, quadratic algebras and discrete polynomials

Eigenvalues and eigenfunctions of the volume operator, associated with the symmetric coupling of three SU(2) angular momentum operators, can be analyzed on the basis of a discrete Schroedinger-like equation which provides a semiclassical Hamiltonian picture of the evolution of a `quantum of space', as shown by the authors in a recent paper. Emphasis is given here to the formalization in terms of a quadratic symmetry algebra and its automorphism group. This view is related to the Askey scheme, the hierarchical structure which includes all hypergeometric polynomials of one (discrete or continuous) variable. Key tool for this comparative analysis is the duality operation defined on the generators of the quadratic algebra and suitably extended to the various families of overlap functions (generalized recoupling coefficients). These families, recognized as lying at the top level of the Askey scheme, are classified and a few limiting cases are addressed.Comment: 10 pages, talk given at "Physics and Mathematics of Nonlinear Phenomena" (PMNP2013), to appear in J. Phys. Conf. Serie

Diffuse cosmic rays shining in the Galactic center: A novel interpretation of H.E.S.S. and Fermi-LAT gamma-ray data

We present a novel interpretation of the $\gamma$-ray diffuse emission measured by Fermi-LAT and H.E.S.S. in the Galactic center (GC) region and the Galactic ridge (GR). In the first part we perform a data-driven analysis based on PASS8 Fermi-LAT data: we extend down to few GeV the spectra measured by H.E.S.S. and infer the primary cosmic-ray (CR) radial distribution between 0.1 and 3 TeV. In the second part we adopt a CR transport model based on a position-dependent diffusion coefficient. Such behavior reproduces the radial dependence of the CR spectral index recently inferred from the Fermi-LAT observations. We find that the bulk of the GR emission can be naturally explained by the interaction of the diffuse steady-state Galactic CR sea with the gas present in the Central Molecular Zone. Although our results leave room for a residual radial-dependent emission associated with a central source, the relevance of the large-scale background prevents from a solid evidence of a GC Pevatron.Comment: 5 pages, 3 figures, accepted for publication in Physical Review Letter

How many Ultra High Energy Cosmic Rays could we expect from Centaurus A?

The Pierre Auger Observatory has associated a few ultra high energy cosmic rays with the direction of Centaurus A. This source has been deeply studied in radio, infrared, X-ray and $\gamma$-rays (MeV-TeV) because it is the nearest radio-loud active galactic nuclei. Its spectral energy distribution or spectrum shows two main peaks, the low energy peak, at an energy of $10^{-2}$ eV, and the high energy peak, at about 150 keV. There is also a faint very high energy (E $\geq$ 100 GeV) $\gamma$-ray emission fully detected by the High Energy Stereoscopic System experiment. In this work we describe the entire spectrum, the two main peaks with a Synchrotron/Self-Synchrotron Compton model and, the Very High Energy emission with a hadronic model. We consider p$\gamma$ and $pp$ interactions. For the p$\gamma$ interaction, we assume that the target photons are those produced at 150 keV in the leptonic processes. On the other hand, for the pp interaction we consider as targets the thermal particle densities in the lobes. Requiring a satisfactory description of the spectra at very high energies with p$\gamma$ interaction we obtain an excessive luminosity in ultra high energy cosmic rays (even exceeding the Eddington luminosity). However, when considering pp interaction to describe the $\gamma$-spectrum, the obtained number of ultra high energy cosmic rays are in agreement with Pierre Auger observations. Moreover, we calculate the possible neutrino signal from pp interactions on a Km$^3$ neutrino telescope using Monte Carlo simulations.Comment: Accepted in Ap

Study of TeV variability of Mrk 421 from 3 years of monitoring with the Milagro Observatory

The Milagro experiment was a TeV gamma-ray observatory designed to continuously monitor the overhead sky in the 0.1-100 TeV energy range. It operated from 2000 and 2008 and was characterized by a large field of view ($\sim$ 2 sr) and a high duty cycle ($\geq$ 90$\%$). Here we report on the long-term monitoring of the blazar Mrk 421 with Milagro over the period from September 21, 2005 to March 15, 2008. We present a study of the TeV variability of the source and provide upper limits for the measured flux for different time scales, ranging from one week up to one year.Comment: 3 pages, 2 figures. Paper to appear in the Proceedings of the Thirteen Marcel Grossmann Meeting, held in Stockholm, Sweden, on July 2012, World Scientific, Singapore, in pres