The ROSAT-ESO Flux-Limited X-Ray (REFLEX) Galaxy Cluster Survey VI: Constraints on the cosmic matter density from the KL power spectrum

The Karhunen-Lo\'{e}ve (KL) eigenvectors and eigenvalues of the sample correlation matrix are used to analyse the spatial fluctuations of the REFLEX clusters of galaxies. The method avoids the disturbing effects of correlated power spectral densities which affects all previous cluster measurements on Gpc scales. Comprehensive tests use a large set of independent REFLEX-like mock cluster samples extracted from the Hubble Volume Simulation. It is found that unbiased measurements on Gpc scales are possible with the REFLEX data. The distribution of the KL eigenvalues are consistent with a Gaussian random field on the 93.4% confidence level. Assuming spatially flat cold dark matter models, the marginalization of the likelihood contours over different sample volumes, fiducial cosmologies, mass/X-ray luminosity relations and baryon densities, yields the 95.4% confidence interval for the matter density of $0.03<\Omega_mh^2<0.19$. The N-body simulations show that cosmic variance, although difficult to estimate, is expected to increase the confidence intervals by about 50%.Comment: 11 pages, 7 figures, accepted for publication in MNRA

New Analyses of Double-Bang Events in the Atmosphere

We use CORSIKA+Herwig simulation code to produce ultra-high energy neutrino interactions in the atmosphere. Our aim is to reproduce extensive air showers originated by extragalactic tau-neutrinos. For charged current tau-neutrino interactions in the atmosphere, beside the air shower originated from the neutrino interaction, it is expected that a tau is created and may decay before reaching the ground. That phenomenon makes possible the generation of two related extensive air showers, the so called Double-Bang event. We make an analysis of the main characteristics of Double-Bang events in the atmosphere for mean values of the parameters involved in such phenomenon, like the inelasticity and tau decay length. We discuss what may happen for the ``out of the average'' cases and conclude that it may be possible to observe this kind of event in ultra-high energy cosmic ray observatories such as Pierre Auger or Telescope Array.Comment: 17 pages, 5 figures, final version to appear in BJ

A new estimate on Evans' Weak KAM approach

We consider a recent formulation of weak KAM theory proposed by Evans. As well as for classical integrability, for one dimensional mechanical Hamiltonian systems all the computations can be explicitly done. This allows us on the one hand to illustrate the geometric content of the theory, on the other hand to prove new lower bounds which extend also to the generic n degrees of freedom case

The extended ROSAT-ESO Flux Limited X-ray Galaxy Cluster Survey (REFLEX II)\\ II. Construction and Properties of the Survey

Galaxy clusters provide unique laboratories to study astrophysical processes on large scales and are important probes for cosmology. X-ray observations are currently the best means of detecting and characterizing galaxy clusters. In this paper we describe the construction of the REFLEX II galaxy cluster survey based on the southern part of the ROSAT All-Sky Survey. REFLEX II extends the REFLEX I survey by a factor of about two down to a flux limit of $1.8 \times 10^{-12}$ erg s$^{-1}$ cm$^{-2}$ (0.1 - 2.4 keV). We describe the determination of the X-ray parameters, the process of X-ray source identification, and the construction of the survey selection function. The REFLEX II cluster sample comprises currently 915 objects. A standard selection function is derived for a lower source count limit of 20 photons in addition to the flux limit. The median redshift of the sample is $z = 0.102$. Internal consistency checks and the comparison to several other galaxy cluster surveys imply that REFLEX II is better than 90\% complete with a contamination less than 10\%.Comment: Astronomy and Astrophysics Vol. 555, A30 - 15 pages, 20 figure