Nonlinear Gravitational Clustering: dreams of a paradigm

We discuss the late time evolution of the gravitational clustering in an expanding universe, based on the nonlinear scaling relations (NSR) which connect the nonlinear and linear two point correlation functions. The existence of critical indices for the NSR suggests that the evolution may proceed towards a universal profile which does not change its shape at late times. We begin by clarifying the relation between the density profiles of the individual halo and the slope of the correlation function and discuss the conditions under which the slopes of the correlation function at the extreme nonlinear end can be independent of the initial power spectrum. If the evolution should lead to a profile which preserves the shape at late times, then the correlation function should grow as $a^2$ [in a $\Omega=1$ universe] een at nonlinear scales. We prove that such exact solutions do not exist; however, ther e exists a class of solutions (``psuedo-linear profiles'', PLP's for short) which evolve as $a^2$ to a good approximation. It turns out that the PLP's are the correlation functions which arise if the individual halos are assumed to be isothermal spheres. They are also configurations of mass in which the nonlinear effects of gravitational clustering is a minimum and hence can act as building blocks of the nonlinear universe. We discuss the implicatios of this result.Comment: 32 Pages, Submitted to Ap

The scale of homogeneity in the Las Campanas Redshift Survey

We analyse the Las Campanas Redshift Survey using the integrated conditional density (or density of neighbors) in volume-limited subsamples up to unprecedented scales (200 Mpc/$h$) in order to determine without ambiguity the behavior of the density field. We find that the survey is well described by a fractal up to 20-30 Mpc/$h$, but flattens toward homogeneity at larger scales. Although the data are still insufficient to establish with high significance the expected homogeneous behavior, and therefore to rule out a fractal trend to larger scales, a fit with a CDM-like spectrum with high normalization well represents the data.Comment: 8 pages, 3 figures, accepted on Ap.J. Letter

Attraction of Acorn-Infesting \u3ci\u3eCydia Latiferreana\u3c/i\u3e (Lepidoptera: Tortricidae) to Pheromone-Baited Traps

Males of acorn-infesting Cydia latiferreana are attracted to an equilibrium mixture of the four isomers of 8, 10-dodecadien-l-ol acetate, the virgin female-produced pheromone. Trap height relative to the height of trees in which traps are placed seems to be a significant factor influencing moth catches at attractant-baited traps. In an oak woodlot and in an oak nursery, catches of male moths were greater in traps placed near the upper periphery of the canopy than at traps deployed at lower levels in the tree. Practical application of pheromone-baited traps in a forest situation will require further study on lure formulation and on trap deployment under forest conditions

Amplitude and Phase Fluctuations for Gravitational Waves Propagating through Inhomogeneous Mass Distribution in the Universe

When a gravitational wave (GW) from a distant source propagates through the universe, its amplitude and phase change due to gravitational lensing by the inhomogeneous mass distribution. We derive the amplitude and phase fluctuations, and calculate these variances in the limit of a weak gravitational field of density perturbation. If the scale of the perturbation is smaller than the Fresnel scale $\sim 100 {pc} (f/{mHz})^{-1/2}$ ($f$ is the GW frequency), the GW is not magnified due to the diffraction effect. The rms amplitude fluctuation is $1-10$ for $f > 10^{-10}$ Hz, but it is reduced less than 5% for a very low frequency of $f < 10^{-12}$ Hz. The rms phase fluctuation in the chirp signal is $\sim 10^{-3}$ radian at LISA frequency band ($10^{-5} - 10^{-1}$ Hz). Measurements of these fluctuations will provide information about the matter power spectrum on the Fresnel scale $\sim 100$ pc.Comment: 6 pages, 6 figures, refferences added, accepted for publication in Ap

Reionization Revisited: Secondary CMB Anisotropies and Polarization

Secondary CMB anisotropies and polarization provide a laboratory to study structure formation in the reionized epoch. We consider the kinetic Sunyaev-Zel'dovich effect from mildly nonlinear large-scale structure and show that it is a natural extension of the perturbative Vishniac effect. If the gas traces the dark matter to overdensities of order 10, as expected from simulations, this effect is at least comparable to the Vishniac effect at arcminute scales. On smaller scales, it may be used to study the thermal history-dependent clustering of the gas. Polarization is generated through Thomson scattering of primordial quadrupole anisotropies, kinetic (second order Doppler) quadrupole anisotropies and intrinsic scattering quadrupole anisotropies. Small scale polarization results from the density and ionization modulation of these sources. These effects generically produce comparable E and B-parity polarization, but of negligible amplitude (0.001-0.01 uK) in adiabatic CDM models. However, the primordial and kinetic quadrupoles are observationally comparable today so that a null detection of B-polarization would set constraints on the evolution and coherence of the velocity field. Conversely, a detection of a cosmological B-polarization even at large angles does not necessarily imply the presence of gravity waves or vorticity. For these calculations, we develop an all-sky generalization of the Limber equation that allows for an arbitrary local angular dependence of the source for both scalar and symmetric trace-free tensor fields on the sky.Comment: 14 pages, 12 figures, minor changes and typo fixes reflect published versio

Power Spectrum Correlations Induced by Non-Linear Clustering

Gravitational clustering is an intrinsically non-linear process that generates significant non-Gaussian signatures in the density field. We consider how these affect power spectrum determinations from galaxy and weak-lensing surveys. Non-Gaussian effects not only increase the individual error bars compared to the Gaussian case but, most importantly, lead to non-trivial cross-correlations between different band-powers. We calculate the power-spectrum covariance matrix in non-linear perturbation theory (weakly non-linear regime), in the hierarchical model (strongly non-linear regime), and from numerical simulations in real and redshift space. We discuss the impact of these results on parameter estimation from power spectrum measurements and their dependence on the size of the survey and the choice of band-powers. We show that the non-Gaussian terms in the covariance matrix become dominant for scales smaller than the non-linear scale, depending somewhat on power normalization. Furthermore, we find that cross-correlations mostly deteriorate the determination of the amplitude of a rescaled power spectrum, whereas its shape is less affected. In weak lensing surveys the projection tends to reduce the importance of non-Gaussian effects. Even so, for background galaxies at redshift z=1, the non-Gaussian contribution rises significantly around l=1000, and could become comparable to the Gaussian terms depending upon the power spectrum normalization and cosmology. The projection has another interesting effect: the ratio between non-Gaussian and Gaussian contributions saturates and can even decrease at small enough angular scales if the power spectrum of the 3D field falls faster than 1/k^2.Comment: 34 pages, 15 figures. Revised version, includes a clearer explanation of why the hierarchical ansatz does not provide a good model of the covariance matrix in the non-linear regime, and new constraints on the amplitudes Ra and Rb for general 4-pt function configurations in the non-linear regim

Correlation between the Mean Matter Density and the Width of the Saturated Lyman Alpha Absorption

We report a scaling of the mean matter density with the width of the saturated Lyman alpha absorptions. This property is established using the ``pseudo-hydro'' technique (Croft et al. 1998). It provides a constraint for the inversion of the Lyman alpha forest, which encounters difficulty in the saturated region. With a Gaussian density profile and the scaling relation, a simple inversion of the simulated Lyman alpha forests shows that the one-dimensional mass power spectrum is well recovered on scales above 2 Mpc/h, or roughly k < 0.03 s/km, at z=3. The recovery underestimates the power on small scales, but improvement is possible with a more sophisticated algorithm.Comment: 7 pages, 9 figures, accepted for publication in MNRAS, replaced by the version after proo

Cluster Correlation in Mixed Models

We evaluate the dependence of the cluster correlation length r_c on the mean intercluster separation D_c, for three models with critical matter density, vanishing vacuum energy (Lambda = 0) and COBE normalized: a tilted CDM (tCDM) model (n=0.8) and two blue mixed models with two light massive neutrinos yielding Omega_h = 0.26 and 0.14 (MDM1 and MDM2, respectively). All models approach the observational value of sigma_8 (and, henceforth, the observed cluster abundance) and are consistent with the observed abundance of Damped Lyman_alpha systems. Mixed models have a motivation in recent results of neutrino physics; they also agree with the observed value of the ratio sigma_8/sigma_25, yielding the spectral slope parameter Gamma, and nicely fit LCRS reconstructed spectra. We use parallel AP3M simulations, performed in a wide box (side 360/h Mpc) and with high mass and distance resolution, enabling us to build artificial samples of clusters, whose total number and mass range allow to cover the same D_c interval inspected through APM and Abell cluster clustering data. We find that the tCDM model performs substantially better than n=1 critical density CDM models. Our main finding, however, is that mixed models provide a surprisingly good fit of cluster clustering data.Comment: 22 pages + 10 Postscript figures. Accepted for publication in Ap

A technique for correcting ERTS data for solar and atmospheric effects

The author has identified the following significant results. Based on processing ERTS CCTs and ground truth measurements collected on Michigan test site for January through June 1973 the following results are reported: (1) atmospheric transmittance varies from: 70 to 85% in band 4, 77 to 90% in band 5, 80 to 94% in band 6, and 84 to 97% in band 7 for one air mass; (2) a simple technique was established to determine atmospheric scattering seen by ERTS-1 from ground-based measurements of sky radiance. For March this scattering was found to be equivalent to that produced by a target having a reflectance of 11% in band 4, 5% in band 5, 3% in band 6, and 1% in band 7; (3) computer ability to classify targets under various atmospheric conditions was determined. Classification accuracy on some targets (i.e. bare soil, tended grass, etc.) hold up even under the most severe atmospheres encountered, while performance on other targets (trees, urban, rangeland, etc.) degrades rapidly when atmospheric conditions change by the smallest amount

A Closure Theory for Non-linear Evolution of Cosmological Power Spectra

We apply a non-linear statistical method in turbulence to the cosmological perturbation theory and derive a closed set of evolution equations for matter power spectra. The resultant closure equations consistently recover the one-loop results of standard perturbation theory and beyond that, it is still capable of treating the non-linear evolution of matter power spectra. We find the exact integral expressions for the solutions of closure equations. These analytic expressions coincide with the renormalized one-loop results presented by Crocce & Scoccimarro (2006,2007). By constructing the non-linear propagator, we analytically evaluate the non-linear matter power spectra based on the first-order Born approximation of the integral expressions and compare it with those of the renormalized perturbation theory.Comment: 22 pages, 4 figures, accepted for publication in Ap