Observational Constraints on Higher Order Clustering up to $z\simeq 1

Constraints on the validity of the hierarchical gravitational instability theory and the evolution of biasing are presented based upon measurements of higher order clustering statistics in the Deeprange Survey, a catalog of $\sim710,000$ galaxies with $I_{AB} \le 24$ derived from a KPNO 4m CCD imaging survey of a contiguous $4^{\circ} \times 4^{\circ}$ region. We compute the 3-point and 4-point angular correlation functions using a direct estimation for the former and the counts-in-cells technique for both. The skewness $s_3$ decreases by a factor of $\simeq 3-4$ as galaxy magnitude increases over the range $17 \le I \le 22.5$ ($0.1 \lesssim z \lesssim 0.8$). This decrease is consistent with a small {\it increase} of the bias with increasing redshift, but not by more than a factor of 2 for the highest redshifts probed. Our results are strongly inconsistent, at about the $3.5-4 \sigma$ level, with typical cosmic string models in which the initial perturbations follow a non-Gaussian distribution - such models generally predict an opposite trend in the degree of bias as a function of redshift. We also find that the scaling relation between the 3-point and 4-point correlation functions remains approximately invariant over the above magnitude range. The simplest model that is consistent with these constraints is a universe in which an initially Gaussian perturbation spectrum evolves under the influence of gravity combined with a low level of bias between the matter and the galaxies that decreases slightly from $z \sim 0.8$ to the current epoch.Comment: 28 pages, 4 figures included, ApJ, accepted, minor change

Macedonio Melloni between physics and political commitment

Macedonio Melloni is an outstanding figure in the scientific world of the nineteenth century. His life can be divided into two main periods, and the interruption is due to his deep involvement in the political risings that shaked Europe in 1831. In the first period, he was a professor at the School of Physics of the University of Parma. Since the very beginning, he devoted a special attention to the properties of radiant heat, and the theoretical insights about the nature of Thermal phenomena were doubled by a smart attitude in improving the laboratory tools. The political events of 1830-31 caused stir inside the University of Parma. Melloni delivered a celebrated speech, leading to stormy meetings, the closure of the School of Physics of the University, the arrests and deportations of students. Nevertheless they gained support from the whole town: Parma in fact rose up and a provisional government was formed of which Melloni himself became a member. Accounts on these events can be found in the documents of the Archivio di Stato (the Public Records Office), as well as in the diary of Lombardini, the Chancellor of the University, and in the short stories by Gallenga (a deported student), besides letters and memories of Melloni himself. The subsequent exile, apart from difficulties in private and familiar life, gave him the chance of establishing relations and collaborations with the scientific European circles. Thus, the 1831 uprising caused both dramatic changes and rich opportunities in the career of a patriot who, as others in the same period, was divided between political engagement and scientific passion

Fluid-loaded metasurfaces

We consider wave propagation along fluid-loaded structures which take the form of an elastic plate augmented by an array of resonators forming a metasurface, that is, a surface structured with sub-wavelength resonators. Such surfaces have had considerable recent success for the control of wave propagation in electromagnetism and acoustics, by combining the vision of sub-wavelength wave manipulation, with the design, fabrication and size advantages associated with surface excitation. We explore one aspect of recent interest in this field: graded metasurfaces, but within the context of fluid-loaded structures. Graded metasurfaces allow for selective spatial frequency separation and are often referred to as exhibiting rainbow trapping. Experiments, and theory, have been developed for acoustic, electromagnetic, and even elastic, rainbow devices but this has not been approached for fluid-loaded structures that support surface waves coupled with the acoustic field in a bulk fluid. This surface wave, coupled with the fluid, can be used to create an additional effect by designing a metasurface to mode convert from surface to bulk waves. We demonstrate that sub-wavelength control is possible and that one can create both rainbow trapping and mode conversion phenomena for a fluid-loaded elastic plate model.Comment: 13 pages, 10 figure

Hyperextended Cosmological Perturbation Theory: Predicting Non-linear Clustering Amplitudes

We consider the long-standing problem of predicting the hierarchical clustering amplitudes $S_p$ in the strongly non-linear regime of gravitational evolution. N-body results for the non-linear evolution of the bispectrum (the Fourier transform of the three-point density correlation function) suggest a physically motivated ansatz that yields the strongly non-linear behavior of the skewness, $S_3$, starting from leading-order perturbation theory. When generalized to higher-order ($p>3$) polyspectra or correlation functions, this ansatz leads to a good description of non-linear amplitudes in the strongly non-linear regime for both scale-free and cold dark matter models. Furthermore, these results allow us to provide a general fitting formula for the non-linear evolution of the bispectrum that interpolates between the weakly and strongly non-linear regimes, analogous to previous expressions for the power spectrum.Comment: 20 pages, 6 figures. Final version accepted by ApJ. Includes new paragraphs on factorizable hierarchical models and agreement of HEPT with the excursion set model for white-noise Gaussian fluctuation

Large-Scale Structure of the Universe and Cosmological Perturbation Theory

We review the formalism and applications of non-linear perturbation theory (PT) to understanding the large-scale structure of the Universe. We first discuss the dynamics of gravitational instability, from the linear to the non-linear regime. This includes Eulerian and Lagrangian PT, non-linear approximations, and a brief description of numerical simulation techniques. We then cover the basic statistical tools used in cosmology to describe cosmic fields, such as correlations functions in real and Fourier space, probability distribution functions, cumulants and generating functions. In subsequent sections we review the use of PT to make quantitative predictions about these statistics according to initial conditions, including effects of possible non Gaussianity of the primordial fields. Results are illustrated by detailed comparisons of PT predictions with numerical simulations. The last sections deal with applications to observations. First we review in detail practical estimators of statistics in galaxy catalogs and related errors, including traditional approaches and more recent developments. Then, we consider the effects of the bias between the galaxy distribution and the matter distribution, the treatment of redshift distortions in three-dimensional surveys and of projection effects in angular catalogs, and some applications to weak gravitational lensing. We finally review the current observational situation regarding statistics in galaxy catalogs and what the future generation of galaxy surveys promises to deliver

Measuring the Redshift Evolution of Clustering: the Hubble Deep Field South

We present an analysis of the evolution of galaxy clustering in the redshift interval 0<z<4.5 in the HDF-S. The HST optical data are combined with infrared ISAAC/VLT observations, and photometric redshifts are used for all the galaxies brighter than I_AB<27.5. The clustering signal is obtained in different redshift bins using two different approaches: a standard one, which uses the best redshift estimate of each object, and a second one, which takes into account the redshift probability function of each object. This second method makes it possible to improve the information in the redshift intervals where contamination from objects with insecure redshifts is important. With both methods, we find that the clustering strength up to z~3.5 in the HDF-S is consistent with the previous results in the HDF-N. While at redshift lower than z~1 the HDF galaxy population is un/anti-biased (b<1) with respect to the underlying dark matter, at high redshift the bias increases up to b~2-3, depending on the cosmological model. These results support previous claims that, at high redshift, galaxies are preferentially located in massive haloes, as predicted by the biased galaxy formation scenario. The impact of cosmic errors on our analyses has been quantified, showing that errors in the clustering measurements in the HDF surveys are indeed dominated by shot-noise in most regimes. Future observations with instruments like the ACS on HST will improve the S/N by at least a factor of two and more detailed analyses of the errors will be required. In fact, pure shot-noise will give a smaller contribution with respect to other sources of errors, such as finite volume effects or non-Poissonian discreteness effects.Comment: 17 pages Latex, with 12 PostScript figures, Accepted for publication in MNRA

Biased-estimations of the Variance and Skewness

Nonlinear combinations of direct observables are often used to estimate quantities of theoretical interest. Without sufficient caution, this could lead to biased estimations. An example of great interest is the skewness $S_3$ of the galaxy distribution, defined as the ratio of the third moment \xibar_3 and the variance squared \xibar_2^2. Suppose one is given unbiased estimators for \xibar_3 and \xibar_2^2 respectively, taking a ratio of the two does not necessarily result in an unbiased estimator of $S_3$. Exactly such an estimation-bias affects most existing measurements of $S_3$. Furthermore, common estimators for \xibar_3 and \xibar_2 suffer also from this kind of estimation-bias themselves: for \xibar_2, it is equivalent to what is commonly known as the integral constraint. We present a unifying treatment allowing all these estimation-biases to be calculated analytically. They are in general negative, and decrease in significance as the survey volume increases, for a given smoothing scale. We present a re-analysis of some existing measurements of the variance and skewness and show that most of the well-known systematic discrepancies between surveys with similar selection criteria, but different sizes, can be attributed to the volume-dependent estimation-biases. This affects the inference of the galaxy-bias(es) from these surveys. Our methodology can be adapted to measurements of analogous quantities in quasar spectra and weak-lensing maps. We suggest methods to reduce the above estimation-biases, and point out other examples in LSS studies which might suffer from the same type of a nonlinear-estimation-bias.Comment: 28 pages of text, 9 ps figures, submitted to Ap

Source-lens clustering effects on the skewness of the lensing convergence

The correlation between source galaxies and lensing potentials causes a systematic effect on measurements of cosmic shear statistics, known as the source-lens clustering (SLC) effect. The SLC effect on the skewness of lensing convergence, $S_3$, is examined using a nonlinear semi-analytic approach and is checked against numerical simulations. The semi-analytic calculations have been performed in a wide variety of generic models for the redshift distribution of source galaxies and power-law models for the bias parameter between the galaxy and dark matter distributions. The semi-analytic predictions are tested successfully against numerical simulations. We find the relative amplitude of the SLC effect on $S_3$ to be of the order of five to forty per cent. It depends significantly on the redshift distribution of sources and on the way the bias parameter evolves. We discuss possible measurement strategies to minimize the SLC effects.Comment: 14 pages, 14 figures, accepted for publication in MNRA