On random flights with non-uniformly distributed directions

This paper deals with a new class of random flights $\underline{\bf X}_d(t),t>0,$ defined in the real space $\mathbb{R}^d, d\geq 2,$ characterized by non-uniform probability distributions on the multidimensional sphere. These random motions differ from similar models appeared in literature which take directions according to the uniform law. The family of angular probability distributions introduced in this paper depends on a parameter $\nu\geq 0$ which gives the level of drift of the motion. Furthermore, we assume that the number of changes of direction performed by the random flight is fixed. The time lengths between two consecutive changes of orientation have joint probability distribution given by a Dirichlet density function. The analysis of $\underline{\bf X}_d(t),t>0,$ is not an easy task, because it involves the calculation of integrals which are not always solvable. Therefore, we analyze the random flight $\underline{\bf X}_m^d(t),t>0,$ obtained as projection onto the lower spaces $\mathbb{R}^m,m<d,$ of the original random motion in $\mathbb{R}^d$. Then we get the probability distribution of $\underline{\bf X}_m^d(t),t>0.$ Although, in its general framework, the analysis of $\underline{\bf X}_d(t),t>0,$ is very complicated, for some values of $\nu$, we can provide some results on the process. Indeed, for $\nu=1$, we obtain the characteristic function of the random flight moving in $\mathbb{R}^d$. Furthermore, by inverting the characteristic function, we are able to give the analytic form (up to some constants) of the probability distribution of $\underline{\bf X}_d(t),t>0.$Comment: 28 pages, 3 figure

Critical and Near-Critical Branching Processes

Scale-free dynamics in physical and biological systems can arise from a variety of causes. Here, we explore a branching process which leads to such dynamics. We find conditions for the appearance of power laws and study quantitatively what happens to these power laws when such conditions are violated. From a branching process model, we predict the behavior of two systems which seem to exhibit near scale-free behavior--rank-frequency distributions of number of subtaxa in biology, and abundance distributions of genotypes in an artificial life system. In the light of these, we discuss distributions of avalanche sizes in the Bak-Tang-Wiesenfeld sandpile model.Comment: 9 pages LaTex with 10 PS figures. v.1 of this paper contains results from non-critical sandpile simulations that were excised from the published versio

The 2HWC HAWC Observatory Gamma Ray Catalog

We present the first catalog of TeV gamma-ray sources realized with the recently completed High Altitude Water Cherenkov Observatory (HAWC). It is the most sensitive wide field-of-view TeV telescope currently in operation, with a 1-year survey sensitivity of ~5-10% of the flux of the Crab Nebula. With an instantaneous field of view >1.5 sr and >90% duty cycle, it continuously surveys and monitors the sky for gamma ray energies between hundreds GeV and tens of TeV. HAWC is located in Mexico at a latitude of 19 degree North and was completed in March 2015. Here, we present the 2HWC catalog, which is the result of the first source search realized with the complete HAWC detector. Realized with 507 days of data and represents the most sensitive TeV survey to date for such a large fraction of the sky. A total of 39 sources were detected, with an expected contamination of 0.5 due to background fluctuation. Out of these sources, 16 are more than one degree away from any previously reported TeV source. The source list, including the position measurement, spectrum measurement, and uncertainties, is reported. Seven of the detected sources may be associated with pulsar wind nebulae, two with supernova remnants, two with blazars, and the remaining 23 have no firm identification yet.Comment: Submitted 2017/02/09 to the Astrophysical Journa

The Sensitivity of HAWC to High-Mass Dark Matter Annihilations

The High Altitude Water Cherenkov (HAWC) observatory is a wide field-of-view detector sensitive to gamma rays of 100 GeV to a few hundred TeV. Located in central Mexico at 19 degrees North latitude and 4100 m above sea level, HAWC will observe gamma rays and cosmic rays with an array of water Cherenkov detectors. The full HAWC array is scheduled to be operational in Spring 2015. In this paper, we study the HAWC sensitivity to the gamma-ray signatures of high-mass (multi- TeV) dark matter annihilation. The HAWC observatory will be sensitive to diverse searches for dark matter annihilation, including annihilation from extended dark matter sources, the diffuse gamma-ray emission from dark matter annihilation, and gamma-ray emission from non-luminous dark matter subhalos. Here we consider the HAWC sensitivity to a subset of these sources, including dwarf galaxies, the M31 galaxy, the Virgo cluster, and the Galactic center. We simulate the HAWC response to gamma rays from these sources in several well-motivated dark matter annihilation channels. If no gamma-ray excess is observed, we show the limits HAWC can place on the dark matter cross-section from these sources. In particular, in the case of dark matter annihilation into gauge bosons, HAWC will be able to detect a narrow range of dark matter masses to cross-sections below thermal. HAWC should also be sensitive to non-thermal cross-sections for masses up to nearly 1000 TeV. The constraints placed by HAWC on the dark matter cross-section from known sources should be competitive with current limits in the mass range where HAWC has similar sensitivity. HAWC can additionally explore higher dark matter masses than are currently constrained.Comment: 15 pages, 4 figures, version to be published in PR

VAMOS: a Pathfinder for the HAWC Gamma-Ray Observatory

VAMOS was a prototype detector built in 2011 at an altitude of 4100m a.s.l. in the state of Puebla, Mexico. The aim of VAMOS was to finalize the design, construction techniques and data acquisition system of the HAWC observatory. HAWC is an air-shower array currently under construction at the same site of VAMOS with the purpose to study the TeV sky. The VAMOS setup included six water Cherenkov detectors and two different data acquisition systems. It was in operation between October 2011 and May 2012 with an average live time of 30%. Besides the scientific verification purposes, the eight months of data were used to obtain the results presented in this paper: the detector response to the Forbush decrease of March 2012, and the analysis of possible emission, at energies above 30 GeV, for long gamma-ray bursts GRB111016B and GRB120328B.Comment: Accepted for pubblication in Astroparticle Physics Journal (20 pages, 10 figures). Corresponding authors: A.Marinelli and D.Zaboro

Highlights from the Pierre Auger Observatory

The Pierre Auger Observatory is the world's largest cosmic ray observatory. Our current exposure reaches nearly 40,000 km$^2$ str and provides us with an unprecedented quality data set. The performance and stability of the detectors and their enhancements are described. Data analyses have led to a number of major breakthroughs. Among these we discuss the energy spectrum and the searches for large-scale anisotropies. We present analyses of our X$_{max}$ data and show how it can be interpreted in terms of mass composition. We also describe some new analyses that extract mass sensitive parameters from the 100% duty cycle SD data. A coherent interpretation of all these recent results opens new directions. The consequences regarding the cosmic ray composition and the properties of UHECR sources are briefly discussed.Comment: 9 pages, 12 figures, talk given at the 33rd International Cosmic Ray Conference, Rio de Janeiro 201

A search for point sources of EeV photons

Measurements of air showers made using the hybrid technique developed with the fluorescence and surface detectors of the Pierre Auger Observatory allow a sensitive search for point sources of EeV photons anywhere in the exposed sky. A multivariate analysis reduces the background of hadronic cosmic rays. The search is sensitive to a declination band from -85{\deg} to +20{\deg}, in an energy range from 10^17.3 eV to 10^18.5 eV. No photon point source has been detected. An upper limit on the photon flux has been derived for every direction. The mean value of the energy flux limit that results from this, assuming a photon spectral index of -2, is 0.06 eV cm^-2 s^-1, and no celestial direction exceeds 0.25 eV cm^-2 s^-1. These upper limits constrain scenarios in which EeV cosmic ray protons are emitted by non-transient sources in the Galaxy.Comment: 28 pages, 10 figures, accepted for publication in The Astrophysical Journa

Reconstruction of inclined air showers detected with the Pierre Auger Observatory

We describe the method devised to reconstruct inclined cosmic-ray air showers with zenith angles greater than $60^\circ$ detected with the surface array of the Pierre Auger Observatory. The measured signals at the ground level are fitted to muon density distributions predicted with atmospheric cascade models to obtain the relative shower size as an overall normalization parameter. The method is evaluated using simulated showers to test its performance. The energy of the cosmic rays is calibrated using a sub-sample of events reconstructed with both the fluorescence and surface array techniques. The reconstruction method described here provides the basis of complementary analyses including an independent measurement of the energy spectrum of ultra-high energy cosmic rays using very inclined events collected by the Pierre Auger Observatory.Comment: 27 pages, 19 figures, accepted for publication in Journal of Cosmology and Astroparticle Physics (JCAP

Multi-resolution anisotropy studies of ultrahigh-energy cosmic rays detected at the Pierre Auger Observatory

We report a multi-resolution search for anisotropies in the arrival directions of cosmic rays detected at the Pierre Auger Observatory with local zenith angles up to $80^\circ$ and energies in excess of 4 EeV ($4 \times 10^{18}$ eV). This search is conducted by measuring the angular power spectrum and performing a needlet wavelet analysis in two independent energy ranges. Both analyses are complementary since the angular power spectrum achieves a better performance in identifying large-scale patterns while the needlet wavelet analysis, considering the parameters used in this work, presents a higher efficiency in detecting smaller-scale anisotropies, potentially providing directional information on any observed anisotropies. No deviation from isotropy is observed on any angular scale in the energy range between 4 and 8 EeV. Above 8 EeV, an indication for a dipole moment is captured; while no other deviation from isotropy is observed for moments beyond the dipole one. The corresponding $p$-values obtained after accounting for searches blindly performed at several angular scales, are $1.3 \times 10^{-5}$ in the case of the angular power spectrum, and $2.5 \times 10^{-3}$ in the case of the needlet analysis. While these results are consistent with previous reports making use of the same data set, they provide extensions of the previous works through the thorough scans of the angular scales.Comment: Published version. Added journal reference and DOI. Added Report Numbe