Three-Point Statistics from a New Perspective

Multipole expansion of spatial three-point statistics is introduced as a tool for investigating and displaying configuration dependence. The novel parametrization renders the relation between bi-spectrum and three-point correlation function especially transparent as a set of two-dimensional Hankel transforms. It is expected on theoretical grounds, that three-point statistics can be described accurately with only a few multipoles. In particular, we show that in the weakly non-linear regime, the multipoles of the reduced bispectrum, $Q_l$, are significant only up to quadrupole. Moreover, the non-linear bias in the weakly non-linear regime only affects the monopole order of these statistics. As a consequence, a simple, novel set of estimators can be constructed to constrain galaxy bias. In addition, the quadrupole to dipole ratio is independent of the bias, thus it becomes a novel diagnostic of the underlying theoretical assumptions: weakly non-linear gravity and perturbative local bias. To illustrate the use of our approach, we present predictions based on both power law, and CDM models. We show that the presently favoured SDSS-WMAP concordance model displays strong ``baryon bumps'' in the $Q_l$'s. Finally, we sketch out three practical techniques estimate these novel quantities: they amount to new, and for the first time edge corrected, estimators for the bispectrum.Comment: 5 pages 6 figures, ApL accepte

The FIR/submm window on galaxy formation

Our view on the deep universe has been so far biased towards optically bright galaxies. Now, the measurement of the Cosmic Infrared Background in FIRAS and DIRBE residuals, and the observations of FIR/submm sources by the ISOPHOT and SCUBA instruments begin unveiling the ``optically dark side'' of galaxy formation. Though the origin of dust heating is still unsolved, it appears very likely that a large fraction of the FIR/submm emission is due to heavily-extinguished star formation. Consequently, the level of the CIRB implies that about 2/3 of galaxy/star formation in the universe is hidden by dust shrouds. In this review, we introduce a new modeling of galaxy formation and evolution that provides us with specific predictions in FIR/submm wavebands. These predictions are compared with the current status of the observations. Finally, the capabilities of current and forthcoming instruments for all-sky and deep surveys of FIR/submm sources are briefly described.Comment: 10 pages, Latex, 5 postscript figures, to appear in ``The Birth of Galaxies'', 1999, B. Guiderdoni, F.R. Bouchet, T.X. Thuan & J. Tran Thanh Van (eds), Editions Frontiere

Previrialization

We propose a method to solve the "previrialization" problem of whether the non-linear interactions between perturbations at different scales increase or decrease the rate of growth of structure. As a measure of this effect we calculate the weakly non-linear corrections to the variance of the probability distribution function of the density field. We assume Gaussian initial conditions and use perturbative expansions to calculate these corrections for scale-free initial power spectra. As a realistic example, we also compute the corrections for the spectrum proposed by Peacock \& Dodds (1994). The calculations are performed for both a Gaussian and a top-hat smoothing of the evolved fields. We show that the effect of weakly non-linear interactions depends strongly on the spectral index; they increase the variance for the spectral index n=-2, but decrease it for n \ge -1. Finally, we compare our perturbative calculations to N-body simulations and a formula of a type proposed by Hamilton et al. (1991)

The Omega dependence of the velocity divergence distribution

Analytical studies based on perturbative theory have shown that the moments of the Probability Distribution Function (PDF) of the local smoothed velocity divergence are expected to have a very specific dependence on the density parameter Omega in the quasi-linear regime. This dependence is particularly interesting as it does not involve the possible bias between the galaxy spatial distribution and the underlying mass distribution. This implies a new and promising method for determining a bias-independent value of Omega based on a reliable determination of the velocity divergence PDF. In this paper we study the Omega dependence of the velocity divergence PDF and its first moments in a set of N-body simulations, using the so-called Voronoi and Delaunay methods. We show that this dependence is in agreement with the theoretical prediction, even while the number density of velocity field tracers has been diluted to a value comparable to that available in current galaxy catalogues. In addition, we demonstrate that a sufficiently reliable determination of these statistical quantities is also possible when the measurement of the galaxy peculiar velocities is restricted to the one component along the line-of-sight. Under ideal, noise-free circumstances we can successfully discriminate between low and high Omega.Comment: 12 pages, LaTex file, 5 figures. Revised version with significant extensions of the numerical studies, accepted for publication in MNRA

Semi-analytic modelling of galaxy evolution in the IR/submm range

This paper proposes a new semi-analytic modelling of galaxy properties in the IR/submm wavelength range, which is explicitly set in a cosmological framework. This type of approach has had some success in reproducing the optical properties of galaxies. We hereafter propose a simple extension to the IR/submm range. We estimate the IR/submm luminosities of ``luminous UV/IR galaxies'', and we explore how much star formation could be hidden in heavily--extinguished, ``ultraluminous IR galaxies'' by designing a family of evolutionary scenarios which are consistent with the current status of the ``cosmic constraints'', as well as with the IRAS luminosity function and faint counts, but with different high-z IR luminosity densities. However, these scenarios generate a Cosmic Infrared Background whose spectrum falls within the range of the isotropic IR component detected by Puget et al. (1996) and revisited by Guiderdoni et al. (1997). We give predictions for the faint galaxy counts and redshift distributions at IR and submm wavelengths. The submm range is very sensitive to the details of the evolutionary scenarios. As a result, the on-going and forthcoming observations with ISO and SCUBA (and later with SIRTF, SOFIA, FIRST and PLANCK) will put strong constraints on the evolution of galaxies at z=1 and beyond.Comment: 21 pages, Latex, 20 postscript figures, accepted for publication in Month. Not. Roy. Astron. So

Numerical Analyses of Weakly Nonlinear Velocity-Density Coupling

We study evolution of various statistical quantities of smoothed cosmic density and velocity fields using N-body simulations. The parameter $C\equiv /( )$ characterizes nonlinear coupling of these two fields and determines behavior of bulk velocity dispersion as a function of local density contrast. It is found that this parameter depends strongly on the smoothing scale even in quasi-linear regimes where the skewness parameter $S_3$ is nearly constant and close to the predicted value by the second-order perturbation theory. We also analyze weakly nonlinear effects caused by an adaptive smoothing known as the gather approach.Comment: 22 pages, 4 figures, to appear in ApJ (558, Sep 10

The Bispectrum of IRAS Galaxies

We compute the bispectrum for the galaxy distribution in the IRAS QDOT, 2Jy, and 1.2Jy redshift catalogs for wavenumbers 0.05<k<0.2 h/Mpc and compare the results with predictions from gravitational instability in perturbation theory. Taking into account redshift space distortions, nonlinear evolution, the survey selection function, and discreteness and finite volume effects, all three catalogs show evidence for the dependence of the bispectrum on configuration shape predicted by gravitational instability. Assuming Gaussian initial conditions and local biasing parametrized by linear and non-linear bias parameters b_1 and b_2, a likelihood analysis yields 1/b_1 = 1.32^{+0.36}_{-0.58}, 1.15^{+0.39}_{-0.39} and b_2/b_1^2=-0.57^{+0.45}_{-0.30}, -0.50^{+0.31}_{-0.51}, for the for the 2Jy and 1.2Jy samples, respectively. This implies that IRAS galaxies trace dark matter increasingly weakly as the density contrast increases, consistent with their being under-represented in clusters. In a model with chi^2 non-Gaussian initial conditions, the bispectrum displays an amplitude and scale dependence different than that found in the Gaussian case; if IRAS galaxies do not have bias b_1> 1 at large scales, \chi^2 non-Gaussian initial conditions are ruled out at the 95% confidence level. The IRAS data do not distinguish between Lagrangian or Eulerian local bias.Comment: 30 pages, 11 figure

Simulations of the Microwave Sky and of its ``Observations''

Here follows a preliminary report on the construction of fake millimeter and sub-millimeter skies, as observed by virtual instruments, e.g. the COBRA/SAMBA mission, using theoretical modeling and data extrapolations. Our goal is to create maps as realistic as possible of the relevant physical contributions which may contribute to the detected signals. This astrophysical modeling is followed by simulations of the measurement process itself by a given instrumental configuration. This will enable a precise determination of what can and cannot be achieved with a particular experimental configuration, and provide a feedback on how to improve the overall design. It is a key step on the way to define procedures for the separation of the different physical processes in the future observed maps. Note that this tool will also prove useful in preparing and analyzing current (\eg\ balloon borne) Microwave Background experiments. Keywords: Cosmology -- Microwave Background Anisotropies.Comment: 6 pages of uuencoded compressed postscript (1.2 Mb uncompressed), to appear in the proceedings of the meeting "Far Infrared and Sub-millimeter Space Missions in the Next Decade'', Paris, France, Eds. M. Sauvage, Space Science Revie

Reconstructing baryon oscillations

The baryon acoustic oscillation (BAO) method for constraining the expansion history is adversely affected by non-linear structure formation, which washes out the correlation function peak created at decoupling. To increase the constraining power of low z BAO experiments, it has been proposed that one use the observed distribution of galaxies to "reconstruct'' the acoustic peak. Recently Padmanabhan, White and Cohn provided an analytic formalism for understanding how reconstruction works within the context of Lagrangian perturbation theory. We extend that formalism to include the case of biased tracers of the mass and, because the quantitative validity of LPT is questionable, we investigate reconstruction in N-body simulations. We find that LPT does a good job of explaining the trends seen in simulations for both the mass and for biased tracers and comment upon the implications this has for reconstruction.Comment: 9 pages, 8 figure