1,358 research outputs found
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
galaxies with derived from a KPNO 4m CCD imaging
survey of a contiguous 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
decreases by a factor of as galaxy magnitude increases over the
range (). 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 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 to the current epoch.Comment: 28 pages, 4 figures included, ApJ, accepted, minor change
Extended Perturbation Theory for the Local Density Distribution Function
Perturbation theory makes it possible to calculate the probability
distribution function (PDF) of the large scale density field in the small
variance limit. For top hat smoothing and scale-free Gaussian initial
fluctuations, the result depends only on the linear variance, sigma_linear, and
its logarithmic derivative with respect to the filtering scale
-(n_linear+3)=dlog sigma_linear^2/dlog L (Bernardeau 1994). In this paper, we
measure the PDF and its low-order moments in scale-free simulations evolved
well into the nonlinear regime and compare the results with the above
predictions, assuming that the spectral index and the variance are adjustable
parameters, n_eff and sigma_eff=sigma, where sigma is the true, nonlinear
variance. With these additional degrees of freedom, results from perturbation
theory provide a good fit of the PDFs, even in the highly nonlinear regime. The
value of n_eff is of course equal to n_linear when sigma << 1, and it decreases
with increasing sigma. A nearly flat plateau is reached when sigma >> 1. In
this regime, the difference between n_eff and n_linear increases when n_linear
decreases. For initial power-spectra with n_linear=-2,-1,0,+1, we find n_eff ~
-9,-3,-1,-0.5 when sigma^2 ~ 100.Comment: 13 pages, 6 figures, Latex (MN format), submitted to MNRA
Self-similarity and scaling behavior of scale-free gravitational clustering
We measure the scaling properties of the probability distribution of the
smoothed density field in -body simulations of expanding universes with
scale-free initial power-spectra, with particular attention to the predictions
of the stable clustering hypothesis. We concentrate our analysis on the ratios
, , where is the averaged -body correlation function over a cell of radius
. The behavior of the higher order correlations is studied through that
of the void probability distribution function.
As functions of , the quantities , ,
exhibit two plateaus separated by a smooth transition around . In the weakly nonlinear regime, {\bar \xi}_2 \la 1, the results are in
reasonable agreement with the predictions of perturbation theory. In the
nonlinear regime, , the function is
larger than in the weakly nonlinear regime, and increasingly so with . It
is well-fitted by the expression $S_Q= ({\bar \xi}_2/100)^{0.045(Q-2)}\
{\widetilde S}_Qn. This weak dependence on scale proves {\em a
small, but significant departure from the stable clustering predictions} at
least for n=0n=+1P_0S_Qn=-2n=-1$. In these two cases, our measurements are not accurate enough to be
discriminant.Comment: 31 pages, postscript file, figure 1 missing. Postscript file
including figure 1 available at
ftp://ftp-astro-theory.fnal.gov:/pub/Publications/Pub-95-256-
A Count Probability Cookbook: Spurious Effects and the Scaling Model
We study the errors brought by finite volume effects and dilution effects on
the practical determination of the count probability distribution function
P_N(n,L), which is the probability of having N objects in a cell of volume L^3
for a set of average number density n. Dilution effects are particularly
relevant to the so-called sparse sampling strategy. This work is mainly done in
the framework of the scaling model (Balian \& Schaeffer 1989), which assumes
that the Q-body correlation functions obey the scaling relation xi_Q(K r_1,...,
K r_Q) = K^{-(Q-1) gamma} xi_N(r_1,..., r_Q). We use three synthetic samples as
references to perform our analysis: a fractal generated by a Rayleigh-L\'evy
random walk with 3.10^4 objects, a sample dominated by a spherical power-law
cluster with 3.10^4 objects and a cold dark matter (CDM) universe involving
3.10^5 matter particles.Comment: 44 pages, uuencoded compressed postcript file, FERMILAB-Pub-94/229-A,
accepted in ApJ
Adaptive Gravitational Force Representation for Fast Trajectory Propagation Near Small Bodies
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76253/1/AIAA-32559-372.pd
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
Hyperextended Cosmological Perturbation Theory: Predicting Non-linear Clustering Amplitudes
We consider the long-standing problem of predicting the hierarchical
clustering amplitudes 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, , starting from leading-order perturbation theory. When
generalized to higher-order () 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
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 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 . Exactly such an
estimation-bias affects most existing measurements of . 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
Cosmological Perturbation Theory Using the Schr\"odinger Equation
We introduce the theory of non-linear cosmological perturbations using the
correspondence limit of the Schr\"odinger equation. The resulting formalism is
equivalent to using the collisionless Boltzman (or Vlasov) equations which
remain valid during the whole evolution, even after shell crossing. Other
formulations of perturbation theory explicitly break down at shell crossing,
e.g. Eulerean perturbation theory, which describes gravitational collapse in
the fluid limit. This paper lays the groundwork by introducing the new
formalism, calculating the perturbation theory kernels which form the basis of
all subsequent calculations. We also establish the connection with conventional
perturbation theories, by showing that third order tree level results, such as
bispectrum, skewness, cumulant correlators, three-point function are exactly
reproduced in the appropriate expansion of our results. We explicitly show that
cumulants up to N=5 predicted by Eulerian perturbation theory for the dark
matter field are exactly recovered in the corresponding limit. A
logarithmic mapping of the field naturally arises in the Schr\"odinger context,
which means that tree level perturbation theory translates into (possibly
incomplete) loop corrections for the conventional perturbation theory. We show
that the first loop correction for the variance is for a field with spectral index . This yields 1.86 and
0.86 for respectively, and to be compared with the exact loop order
corrections 1.82, and 0.88. Thus our tree-level theory recovers the dominant
part of first order loop corrections of the conventional theory, while
including (partial) loop corrections to infinite order in terms of .Comment: 5 pages, submitted to ApJ Letter
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