Bounds on the density of sources of ultra-high energy cosmic rays from the Pierre Auger Observatory

We derive lower bounds on the density of sources of ultra-high energy cosmic rays from the lack of significant clustering in the arrival directions of the highest energy events detected at the Pierre Auger Observatory. The density of uniformly distributed sources of equal intrinsic intensity was found to be larger than similar to (0.06 – 5) x 10(-4) Mpc(-3) at 95% CL, depending on the magnitude of the magnetic defections. Similar bounds, in the range (0.2 – 7) x 10(-4) Mpc(-3), were obtained for sources following the local matter distribution.
We are very grateful to the following agencies and organizations for financial support,: Comision Nacional de Energia Atomica, Fundacion Antorchas, Gobierno De La, Provincia de Ailendoza. Municipalidad de Malargile. INDM floldings and Valle Las Lenas, in gratitude for their continuing cooperation over land access. Argentina; the Australian Research Council; Conselho Nacional de Desenvolvimento Cientifico e 'Tecnologico (CNPq), Financiadora de Estudos e Projetos (FINEP), Fundacdo de Amparo a Pesquisa do Est ado de Rio de Janeiro (FAP HRJ), Fundacdo de Amparo Pesquisa do Estado de Sdo Paulo (FAPESP), Ministerio de Ciencia e Tecnologia (IVICT), Brazil; AVCR AVOZ10100502 and AVOZ10100522, GAAV KJB100100904, AISMT-CR LA08016, LG11044, 1VIEB111003, MSAI0021620859, LA08015, TACR TA01010517 and GA U.K. 119810, Czech Republic; Centre de Calcul I-N2P3/CNRS, Centre National de la -Recherche Scientifique ((1 NRS), Conseil Regional Ile-de-France, f)epartement, Physique Nuclealre et Corpusculaire (I N( Departement Sciences de l'Univers (SDU-INSU/CNRS), France; Bundesministerium fur Bildung und Forschung (BMBF), Deutsche Forschungsgemeinschaft (DITG), Finanzministerium Baden-Wurttemberg, flelmholtz-Gemeinschaft Deutscher Forschungszentren Ministerium fur Wissenschaft und Forschung, Nordrhein-Westfalen, Ministerimn fur Wissenschaft, Forschung und Kunst, Baden-WUrttemberg, Germany; Istituto Nazion ale di Fisica Nucleare (INFN), Ministero dell'Istruzione, delhLniversita e della Ricerca (MIUR), Italy: Consejo Nacional de Ciencia y Tecnologia (CONACYT), Mexico; Ministerie van Onden s Cultuur on NVetenschap Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Stichting voor Rmdamenteel Onderzoek der Materie (FOM), Netherlands; Ministry of Science and Higher Education, Grant Nos. N N202 200239 and N N202 207238, Poland; Portuguese national funds and FEDER funds within COMPETE - Programa Operacional Factores de Competitividade through Fundacao para a Ciencia e a Tecnologia, Portugal; Romanian Authority for Scientific Research ANCS, CNDI-UEFISETD1 partnership projects nr.20/2012 and nr.194/2012, project nr.1 /ASPERA2/20I2 ERA-NET and PN-IIRU-PD-2011-3-0145-17, Romania; Ministry for Higher Education, Science, and 'Technology, Slovenian Research Agency, Slovenia; Comunidad de Madrid, FEDER funds, Ministerio de Ciencia e Innovacion and Consolider-Ingenio 2010 (( PAN), X unta de Galicia Spain; Science and Technology Facilities Council, United kingdom; Department of Luergy, Contract Nos. DE-ACO2-07(11-111359, DE-FR02-04E1(41300, DE-FG02-99E1(41107, National Science Foundation, Grant No. 0450696, The Grainger Foundation U.S.A.; NAFOSTED, Vietnam; Marie Curie-IRSES/HPLANET, European Particle Physics Latin American Network, European Union 7th Frarneworlc Program. Grant No. IIRSES-2009-GA-246806; and UNESCO.