arXiv subjects

R. Juszkiewicz

Publications and source records attributed to R. Juszkiewicz.

12 recordsLinked to original sources

arXiv2001

Gravity's smoking gun?

We present a new constraint on the biased galaxy formation picture. Gravitational instability theory predicts that the two-point mass density correlation function, ξ(r), has an inflection point at the separation r=r_0, corresponding to the boundary between the linear and nonlinear regime of clustering, ξ= 1. We show how this feature can be used to constrain the square of the biasing parameter, b^2 = ξ_g / ξon scales r = r_0, where ξ_g is the galaxy-galaxy correlation function, allowed to differ from ξ. We apply our method to real data: the ξ_g(r), estimated from the APM galaxy survey. Our results suggest that the APM galaxies trace the mass at separations r > 5 Mpc/h, where h is the Hubble constant in units of 100 km/s Mpc. The present results agree with earlier studies, based on comparing higher order correlations in the APM with weakly non-linear perturbation theory. Both approaches constrain the "b" factor to be within 20% of unity. If the existence of the feature we identified in the APM ξ_g(r) -- the inflection point near ξ_g = 1 -- is confirmed by more accurate surveys, we may have discovered gravity's smoking gun: the long awaited ``shoulder'' in ξ, predicted by Gott and Rees 25 years ago.

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arXiv2000

Evidence for a low-density Universe from the relative velocities of galaxies

The motions of galaxies can be used to constrain the cosmological density parameter Omega and the clustering amplitude of matter on large scales. The mean relative velocity of galaxy pairs, estimated from the Mark III survey, indicates that Omega = 0.35 +0.35/-0.25. If the clustering of galaxies is unbiased on large scales, Omega = 0.35 +/- 0.15, so that an unbiased Einstein-de Sitter model (Omega = 1) is inconsistent with the data.

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arXiv1999

Streaming velocities as a dynamical estimator of Omega

It is well known that estimating the pairwise velocity of galaxies, v_{12}, from the redshift space galaxy correlation function is difficult because this method is highly sensitive to the assumed model of the pairwise velocity dispersion. Here we propose an alternative method to estimate v_{12} directly from peculiar velocity samples, which contain redshift-independent distances as well as galaxy redshifts. In contrast to other dynamical measures which determine beta = sigma_8 x Omega^{0.6}, our method can provide an estimate of (sigma_8)^2 x Omega^{0.6} for a range of sigma_8 (here Omega is the cosmological mass density parameter while sigma_8 is the standard normalization parameter for the spectrum of matter density fluctuations). We demonstrate how to measure this quantity from realistic catalogues.

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arXiv1999

Measuring Omega with Galaxy Streaming Velocities

The mean pairwise velocity of galaxies has traditionally been estimated from the redshift space galaxy correlation function. This method is notorious for being highly sensitive to the assumed model of the pairwise velocity dispersion. Here we propose an alternative method to estimate the streaming velocity directly from peculiar velocity samples, which contain redshift-independent distances as well as galaxy redshifts. This method can provide an estimate of $Ω^{0.6}σ_8^2$ for a range of $σ_8$ where $Ω$ is the cosmological density parameter, while $σ_8$ is the standard normalization for the power spectrum of density fluctuations. We demonstrate how to measure this quantity from realistic catalogues and identify the main sources of bias and errors

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arXiv1998

Small-scale anisotropy of the cosmic background radiation and scattering by cloudy plasma

If the first stars formed soon after decoupling of baryons from the thermal cosmic background radiation (CBR), the radiation may have been last scattered in a cloudy plasma. We discuss the resulting small-scale anisotropy of the CBR in the limit where the plasma clouds are small compared to the mean distance between clouds along a line of sight. This complements the perturbative analysis valid for mildly nonlinear departures from homogeneity at last scattering. We conclude that reasonable choices for the cloud parameters imply CBR anisotropy consistent with the present experimental limits, in agreement with the perturbative approach. This means the remarkable isotropy of the CBR need not contradict the early small-scale structure formation predicted in some cosmogonies.

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arXiv1996

Clustering statistics and dynamics

Since the appearance of the classical paper of Lifshitz almost half a century ago, linear stability analysis of cosmological models is textbook knowledge. Until recently, however, little was known about the behavior of higher than linear order terms in the perturbative expansion. These terms become important in the weakly nonlinear regime of gravitational clustering, when the rms mass density contrast is only slightly smaller than unity. In the past, theorists showed little interest in studying this regime, and for a good reason: only a decade ago, it would have been an academic excercise - at scales large enough to probe the weakly nonlinear regime, all measures of clustering were dominated by noise. This is no longer the case with present data. The purpose of this talk is to provide a brief summary of recent advances in weakly nonlinear perturbation theory. We present analytical perturbative results together with results of N-body experiments, conducted to test their accuracy. We compare perturbative predictions with measurements from galaxy surveys. Such comparisons can be used to test the gravitational instability theory and to constrain possible deviations from Gaussian statistics in the initial mass distribution; they can be also used to study the nature of physical processes that govern galaxy formation (``biasing''). We also show how future studies of velocity field statistics can provide a new way to determine the density parameter, $Ω$.

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arXiv1994

Redshift Distortions of Clustering: A Lagrangian Approach

We study the effects of peculiar velocities on statistical measures of galaxy clustering. These effects occur when distances to the galaxies are estimated from their redshifts. It is assumed that the clustering pattern results from the gravitational instability of initially Gaussian, small-amplitude perturbations of a Friedman-Lemaitre cosmological model. Explicit expressions are given for an arbitrary density parameter Ωof the model, both when the cosmological constant, Λ, is zero, and when the model is spatially flat, Ω+ Λ/3H^2 =1. We show how to compute the skewness, or third moment of the density field, in redshift space, and its Fourier space counterpart, the bispectrum. We rely on a perturbative expansion of particle trajectories in Lagrangian coordinates. This formalism extends to higher orders the Zel'dovich first order solution (1970). We show that a physically consistent and quantitatively accurate analysis of the growth skewness in redshift space can be obtained from second-order Lagrangian theory. We also study the effects of spatial smoothing of the evolved density field. We give analytic expressions for the gravitationally induced skewness as a function of the power spectrum and of Ω, for a spherical top-hat and a Gaussian smoothing filter. We compare our analytical predictions with measurements performed in numerical simulations, and find good agreement. These results should then prove useful in analyzing large scale redshift surveys. In particular, our results, in conjunction with the recent suggestion of Fry (1994), may help to break the coupling between the bias and the cosmological

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arXiv1994

Perturbative Lagrangian Approach to Gravitational Instability

This paper deals with the time evolution in the matter era of perturbations in Friedman-Lemaitre models with arbitrary density parameter $Ω$, with either a zero cosmological constant, $Λ= 0$, or with a non-zero cosmological constant in a spatially flat Universe. Unlike the classical Eulerian approach where the density contrast is expanded in a perturbative series, this analysis relies instead on a perturbative expansion of particles trajectories in Lagrangian coordinates. This brings a number of advantages over the classical analysis. In particular, it enables the description of stronger density contrasts. Indeed the linear term is the famous Zel'dovich approximate solution (1970). We present here a systematic and detailed account of this approach. We give analytical results (or fits to numerical results) up to the third order. We then proceed to explore the link between the lagrangian description and statistical measures. We show in particular that Lagrangian perturbation theory provides a natural framework to compute the effect of redshift distortions, using the skewness of the density distribution function as an example. Finally, we show how well the second order theory does as compared to other approximat- ions in the case of spherically symmetric perturbations. We also compare this second order approximation and Zel'dovich solution to N-body simulations in the description of large-scale structure formation starting from a power law (n=-2) power spectrum of Gaussian perturbation. We find that second order theory is both simple and powerful.

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arXiv1994

Omega from the skewness of the cosmic velocity divergence

We propose a method for measuring the cosmological density parameter $Ω$ from the statistics of the divergence field, $θ\equiv H^{-1} ÷v$, the divergence of peculiar velocity, expressed in units of the Hubble constant, $H \equiv 100 h km/s/Mpc$. The velocity field is spatially smoothed over $\sim 10 h^{-1} Mpc$ to remove strongly nonlinear effects. Assuming weakly-nonlinear gravitational evolution from Gaussian initial fluctuations, and using second-order perturbative analysis, we show that $ <θ^3> \propto -Ω^{-0.6} <θ^2>^2$. The constant of proportionality depends on the smoothing window. For a top-hat of radius R and volume-weighted smoothing, this constant is $26/7-γ$, where $γ=-d\log <θ^2> / d\log R$. If the power spectrum is a power law, $P(k)\propto k^n$, then $γ=3+n$. A Gaussian window yields similar results. The resulting method for measuring $Ω$ is independent of any assumed biasing relation between galaxies and mass. The method has been successfully tested with numerical simulations. A preliminary application to real data, provided by the POTENT recovery procedure from observed velocities favors $Ω\sim 1$. However, because of an uncertain sampling error, this result should be treated as an assessment of the feasibility of our method rather than a definitive measurement of $Ω$.

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arXiv1993

Perturbation Theory Confronts Observations~: Implications for the ``Initial'' Conditions and Omega

This paper covers the material of our two talks. We describe a series of projects based upon perturbative expansions to follow the gravitational evolution of the one point probability distribution functions (PDFs) for the density contrast field and for the divergence of the corresponding velocity field. The Edgeworth expansion greatly simplifies the problem. Indeed, the PDF can be described through several low order moments, with the first non-trivial contribution coming from the skewness, or third moment. Gaussian initial conditions imply that the skewness of the smoothed density field is proportional to the square of the variance. The constant of proportionality is then a function of the logarithmic slope of the variance versus scale, and is otherwise independent of scale. This constant is also practically independent of the density parameter $Ω$, and has very nearly the same value when distances are estimated by redshifts. To show the latter property, we also briefly discuss our Lagrangian approach to perturbation theory. Finally, the observed skewness does depend, of course, on the relation between the distribution of light and mass; we describe the case of local biasing. For the divergence of the velocity field, the skewness of its PDF is also proportional to the square of its variance, but the ratio now strongly depends on the value of $Ω$. This offers a new method to determine the density parameter which does not involve comparisons

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arXiv1993

Weakly Non-Linear Gaussian Fluctuations and the Edgeworth Expansion

We calculate the cosmological evolution of the 1-point probability distribution function (PDF), using an analytic approximation that combines gravitational perturbation theory with the Edgeworth expansion of the PDF. Our method applies directly to a smoothed mass density field or to the divergence of a smoothed peculiar velocity field, provided that rms fluctuations are small compared to unity on the smoothing scale, and that the primordial fluctuations that seed the growth of structure are Gaussian. We use this `Edgeworth approximation' to compute the evolution of $<δ|δ|>$ and $<|delta|>$; these measures are similar to the skewness and kurtosis of the density field, but they are less sensitive to tails of the probability distribution, so they may be more accurately estimated from surveys of limited volume. We compare our analytic calculations to cosmological N-body simulations in order to assess their range of validity. When $σ\ll 1$, the numerical simulations and perturbation theory agree precisely, demonstrating that the N-body method can yield accurate results in the regime of weakly non-linear clustering. We show analytically that `biased' galaxy formation preserves the relation $<δ^3> \propto <δ^2>^2$ predicted by second-order perturbation theory, provided that the galaxy density is a local function of the underlying mass density.

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arXiv1993

Skewness Induced by Gravity

Large-scale structures, observed today, are generally believed to have grown from random, small-amplitude inhomogeneities, present in the early Universe. We investigate how gravitational instability drives the distribution of these fluctuations away from the initial state, assumed to be Gaussian. Using second order perturbation theory, we calculate the skewness factor, $S_3 \equiv \langle δ^3 \rangle \, /\, \langle δ^2 \rangle^2$. Here the brackets, $\langle \ldots \rangle$, denote an ensemble average, and $δ$ is the density contrast field, smoothed with a low pass spatial filter. We show that $S_3$ decreases with the slope of the fluctuation power spectrum; it depends only weakly on $Ω$, the cosmological density parameter. We compare perturbative calculations with N-body experiments and find excellent agreement over a wide dynamic range. If galaxies trace the mass, measurements of $S_3$ can be used to distinguish models with Gaussian initial conditions from their non-Gaussian alternatives.

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