The Steep Nekhoroshev's Theorem

Revising Nekhoroshev's geometry of resonances, we provide a fully constructive and quantitative proof of Nekhoroshev's theorem for steep Hamiltonian systems proving, in particular, that the exponential stability exponent can be taken to be $1/ (2n \alpha_1\cdots\alpha_{n-2}$) ($\alpha_i$'s being Nekhoroshev's steepness indices and $n\ge 3$ the number of degrees of freedom)

Improving the modelling of redshift-space distortions: I. A bivariate Gaussian description for the galaxy pairwise velocity distributions

As a step towards a more accurate modelling of redshift-space distortions in galaxy surveys, we develop a general description of the probability distribution function of galaxy pairwise velocities within the framework of the so-called streaming model. For a given galaxy separation $\vec{r}$, such function can be described as a superposition of virtually infinite local distributions. We characterize these in terms of their moments and then consider the specific case in which they are Gaussian functions, each with its own mean $\mu$ and dispersion $\sigma$. Based on physical considerations, we make the further crucial assumption that these two parameters are in turn distributed according to a bivariate Gaussian, with its own mean and covariance matrix. Tests using numerical simulations explicitly show that with this compact description one can correctly model redshift-space distorsions on all scales, fully capturing the overall linear and nonlinear dynamics of the galaxy flow at different separations. In particular, we naturally obtain Gaussian/exponential, skewed/unskewed distribution functions, depending on separation as observed in simulations and data. Also, the recently proposed single-Gaussian description of redshift-space distortions is included in this model as a limiting case, when the bivariate Gaussian is collapsed to a two-dimensional Dirac delta function. We also show how this description naturally allows for the Taylor expansion of $1+\xi_S(\vec{s})$ around $1+\xi_R(r)$, which leads to the Kaiser linear formula when truncated to second order, expliciting its connection with the moments of the velocity distribution functions. More work is needed, but these results indicate a very promising path to make definitive progress in our program to improve RSD estimators.Comment: 11 pages, 3 figures, 2 table

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

The Clustering Characteristics of HI-Selected Galaxies from the 40% ALFALFA Survey

The 40% Arecibo Legacy Fast ALFA (ALFALFA) survey catalog (\alpha.40) of approximately 10,150 HI-selected galaxies is used to analyze the clustering properties of gas-rich galaxies. By employing the Landy-Szalay estimator and a full covariance analysis for the two-point galaxy-galaxy correlation function, we obtain the real-space correlation function and model it as a power law, \xi(r) = (r/r_0)^(-\gamma), on scales less than 10 h^{-1} Mpc. As the largest sample of blindly HI-selected galaxies to date, \alpha.40 provides detailed understanding of the clustering of this population. We find \gamma = 1.51 +/- 0.09 and r_0 = 3.3 +0.3, -0.2 h^{-1} Mpc, reinforcing the understanding that gas-rich galaxies represent the most weakly clustered galaxy population known; we also observe a departure from a pure power law shape at intermediate scales, as predicted in \Lambda CDM halo occupation distribution models. Furthermore, we measure the bias parameter for the \alpha.40 galaxy sample and find that HI galaxies are severely antibiased on small scales, but only weakly antibiased on large scales. The robust measurement of the correlation function for gas-rich galaxies obtained via the \alpha.40 sample constrains models of the distribution of HI in simulated galaxies, and will be employed to better understand the role of gas in environmentally-dependent galaxy evolution.Comment: 30 pages, 10 figures, accepted by Ap

Accurate fitting functions for peculiar velocity spectra in standard and massive-neutrino cosmologies

We estimate the velocity field in a large set of $N$-body simulations including massive neutrino particles, and measure the auto-power spectrum of the velocity divergence field as well as the cross-power spectrum between the cold dark matter density and the velocity divergence. We perform these measurements at four different redshifts and within four different cosmological scenarios, covering a wide range in neutrino masses. We find that the nonlinear correction to the velocity power spectra largely depend on the degree of nonlinear evolution with no specific dependence on the value of neutrino mass. We provide a fitting formula, based on the value of the r.m.s. of the matter fluctuations in spheres of $8h^{-1}$Mpc, describing the nonlinear corrections with 3\% accuracy on scales below $k=0.7\; h$ Mpc$^{-1}$.Comment: 8 pages, 5 figures, accepted by A&A, typos corrected in equation 1