arXiv subjects

István Szapudi

Publications and source records attributed to István Szapudi.

At least 73 records · Page 4Linked to original sources

arXiv2008

An Imprint of Super-Structures on the Microwave Background due to the Integrated Sachs-Wolfe Effect

We measure hot and cold spots on the microwave background associated with supercluster and supervoid structures identified in the Sloan Digital Sky Survey Luminous Red Galaxy catalog. The structures give a compelling visual imprint, with a mean temperature deviation of 9.6 +/- 2.2 microK, i.e. above 4 sigma. We interpret this as a detection of the late-time Integrated Sachs-Wolfe (ISW) effect, in which cosmic acceleration from dark energy causes gravitational potentials to decay, heating or cooling photons passing through density crests or troughs. In a flat universe, the linear ISW effect is a direct signal of dark energy.

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arXiv2007

Baryon oscillations in galaxy and matter power-spectrum covariance matrices

We investigate large-amplitude baryon acoustic oscillations (BAO's) in off-diagonal entries of cosmological power-spectrum covariance matrices. These covariance-matrix BAO's describe the increased attenuation of power-spectrum BAO's caused by upward fluctuations in large-scale power. We derive an analytic approximation to covariance-matrix entries in the BAO regime, and check the analytical predictions using N-body simulations. These BAO's look much stronger than the BAO's in the power spectrum, but seem detectable only at about a one-sigma level in gigaparsec-scale galaxy surveys. In estimating cosmological parameters using matter or galaxy power spectra, including the covariance-matrix BAO's can have a several-percent effect on error-bar widths for some parameters directly related to the BAO's, such as the baryon fraction. Also, we find that including the numerous galaxies in small haloes in a survey can reduce error bars in these cosmological parameters more than the simple reduction in shot noise might suggest.

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arXiv2007

Information content in the halo-model dark-matter power spectrum II: Multiple cosmological parameters

We investigate the cosmological Fisher information in the non-linear dark-matter power spectrum in the context of the halo model. We find that there is a plateau in information content on translinear scales which is generic to all cosmological parameters we tried. There is a rise in information on smaller scales, but we find that it is quite degenerate among different cosmological parameters (except, perhaps, the tilt). This suggests that it could be difficult to constrain cosmological parameters using the non-linear regime of the dark-matter power spectrum. We suggest ways to get around this problem, such as removing the largest haloes from consideration in survey analysis.

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arXiv2006

Information content in the halo-model dark-matter power spectrum

Using the halo model, we investigate the cosmological Fisher information in the non-linear dark-matter power spectrum about the initial amplitude of linear power. We find that there is little information on `translinear' scales (where the one- and two-halo terms are both significant) beyond what is on linear scales, but that additional information is present on small scales, where the one-halo term dominates. This behavior agrees with the surprising results that Rimes & Hamilton (2005, 2006) found using N-body simulations. We argue that the translinear plateau in cumulative information arises largely from fluctuations in the numbers of large haloes in a finite volume. This implies that more information could be extracted on non-linear scales if the masses of the largest haloes in a survey are known.

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arXiv2005

Introduction to Higher Order Spatial Statistics in Cosmology

In this lecture notes I concentrate on the classic and widely applicable characterization of higher order statistics by joint moments, a.k.a. higher order correlation functions, and directly related statistics. I put special emphasis on recent results, especially the connection of spatial statistics with symmetries.

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arXiv2005

Fast Edge Corrected Measurement of the Two-Point Correlation Function and the Power Spectrum

We present two related techniques to measure the two-point correlation function and the power spectrum with edge correction in any spatial dimensions. The underlying algorithm uses fast Fourier transforms for calculating the two-point function with an heuristically weighted edge corrected estimator. Once the correlation function is measured, we estimate the power spectrum via numerical integration of the Hankel transform connecting the two. We introduce an efficient numerical technique based on Gauss-Bessel-quadrature and double exponential transformation. This, combined with our, or any similar, two-point function estimator leads to a novel edge corrected estimator for power spectra. The pair of techniques presented are the Euclidean analogs of those developed and widely used in cosmic microwave background research for spherical maps.

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arXiv2001

Higher Order Moments of the Angular Distribution of Galaxies from Early SDSS Data

We present initial results for counts in cells statistics of the angular distribution of galaxies in early data from the Sloan Digital Sky Survey (SDSS). We analyze a rectangular stripe $2.5^\circ$ wide, covering approximately 160 sq. degrees, containing over $10^6$ galaxies in the apparent magnitude range $18 < r^\prime < 22$, with areas of bad seeing, contamination from bright stars, ghosts, and high galactic extinction masked out. This survey region, which forms part of the SDSS Early Data Release, is the same as that for which two-point angular clustering statistics have recently been computed. The third and fourth moments of the cell counts, $s_3$ (skewness) and $s_4$ (kurtosis), constitute the most accurate measurements to date of these quantities (for $r^\prime < 21$) over angular scales $0.015^\circ-0.3^\circ$. They display the approximate hierarchical scaling expected from non-linear structure formation models and are in reasonable agreement with the predictions of $Λ$-dominated cold dark matter models with galaxy biasing that suppresses higher order correlations at small scales. The results are in general consistent with previous measurements in the APM, EDSGC, and Deeprange surveys. These results suggest that the SDSS imaging data are free of systematics to a high degree and will therefore enable determination of the skewness and kurtosis to 1% and less then 10%, as predicted by Colombi, Szapudi, & Szalay (1998).

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arXiv2001

The 3D Power Spectrum from Angular Clustering of Galaxies in Early SDSS Data

Early photometric data from the Sloan Digital Sky Survey (SDSS) contain angular positions for 1.5 million galaxies. In companion papers, the angular correlation function $w(θ)$ and 2D power spectrum $C_l$ of these galaxies are presented. Here we invert Limber's equation to extract the 3D power spectrum from the angular results. We accomplish this using an estimate of $dn/dz$, the redshift distribution of galaxies in four different magnitude slices in the SDSS photometric catalog. The resulting 3D power spectrum estimates from $w(θ)$ and $C_l$ agree with each other and with previous estimates over a range in wavenumbers $0.03 < k/{\rm h Mpc}^{-1} < 1$. The galaxies in the faintest magnitude bin ($21 < \rstar < 22$, which have median redshift $z_m=0.43$) are less clustered than the galaxies in the brightest magnitude bin ($18 < \rstar < 19$ with $z_m=0.17$), especially on scales where nonlinearities are important. The derived power spectrum agrees with that of Szalay et al. (2001) who go directly from the raw data to a parametric estimate of the power spectrum. The strongest constraints on the shape parameter $Γ$ come from the faintest galaxies (in the magnitude bin $21 < \rstar < 22$), from which we infer $Γ= 0.14^{+0.11}_{-0.06}$ (95% C.L.).

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arXiv2000

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 $3.5-4 σ$ 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.

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arXiv2000

The luminosity dependence of clustering and higher order correlations in the PSCz survey

We investigate the spatial clustering of galaxies in the PSCz galaxy redshift survey, as revealed by the two-point correlation function, the luminosity mark correlations, and the moments of counts-in-cells. We construct volume-limited subsamples at different depths, and search for a luminosity dependence of the clustering pattern. We find no statistically significant effect in either the two-point correlation function or the mark correlations and so we take each subsample (of different characteristic luminosity) as representing the same statistical process. We then carry out a counts-in-cells analysis of the volume-limited subsamples, including a rigorous error calculation based on the recent theory of Szapudi, Colombi and Bernardeau. In this way, we derive the best estimates to date of the skewness and kurtosis of IRAS galaxies in redshift space. Our results agree well with previous measurements in both the parent angular catalogue, and in the derived redshift surveys. This is in contrast with smaller, optically selected surveys, were there is a discrepancy between the redshift space and projected measurements. Predictions from cold dark matter theory, obtained using the recent semi-analytical model of galaxy formation of Benson {\it et al}, provide an excellent description of our clustering data.

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arXiv1999

Experimental Cosmic Statistics I: Variance

Counts-in-cells are measured in the $τ$CDM Virgo Hubble Volume simulation. This large N-body experiment has 10^9 particles in a cubic box of size 2000 h^{-1} Mpc. The unprecedented combination of size and resolution allows for the first time a realistic numerical analysis of the cosmic errors and cosmic correlations of statistics related to counts-in-cells measurements, such as the probability distribution function P_N itself, its factorial moments F_k and the related cumulants $\xiav$ and S_N's. These statistics are extracted from the whole simulation cube, as well as from 4096 sub-cubes of size 125 h^{-1}Mpc, each representing a virtual random realization of the local universe. The measurements and their scatter over the sub-volumes are compared to the theoretical predictions of Colombi, Bouchet & Schaeffer (1995) for P_0, and of Szapudi & Colombi (1996, SC) and Szapudi, Colombi & Bernardeau (1999a, SCB) for the factorial moments and the cumulants. The general behavior of experimental variance and cross-correlations as functions of scale and order is well described by theoretical predictions, with a few percent accuracy in the weakly non-linear regime for the cosmic error on factorial moments. (... more in paper >...)

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arXiv1999

Experimental Cosmic Statistics II: Distribution

Colombi et al. 1999 (paper I) investigated the counts-in-cells statistics and their respective errors in the $τ$CDM Virgo Hubble Volume simulation. This extremely large $N$-body experiment also allows a numerical investigation of the {\em cosmic distribution function}, $Υ(\tA)$ itself for the first time. For a statistic $A$, $Υ(\tA)$ is the probability density of measuring the value $\tA$ in a finite galaxy catalog. $Υ$ was evaluated for the distribution of counts-in-cells, $P_N$, the factorial moments, $F_k$, and the cumulants, $\xiav$ and $S_N$'s, using the same subsamples as paper I. While paper I concentrated on the first two moments of $Υ$, i.e. the mean, the cosmic error and the cross-correlations, here the function $Υ$ is studied in its full generality, including a preliminary analysis of joint distributions $Υ(\tA,\tB)$. The most significant, and reassuring result for the analyses of future galaxy data is that the cosmic distribution function is nearly Gaussian provided its variance is small. A good practical criterion for the relative cosmic error is that $ΔA/A \la 0.2$. This means that for accurate measurements, the theory of the cosmic errors, presented by Szapudi & Colombi (1996) and Szapudi, Colombi & Bernardeau (1999), and confirmed empirically by paper I, is sufficient for a full statistical description and thus for a maximum likelihood rating of models. As the cosmic error increases, the cosmic distribution function $Υ$ becomes increasingly skewed and is well described by a generalization of the lognormal distribution. The cosmic skewness is introduced as an additional free parameter. (...more in paper...)

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arXiv1998

Cumulant Correlators from the APM

This work presents a set of new statistics, the cumulant correlators, aimed at high precision analysis of the galaxy distribution. They form a symmetric matrix, $Q_{NM}$, related to moment correlators the same way as cumulants are related to the moments of the distribution. They encode more information than the usual cumulants, $S_N$'s, and their extraction from data is similar to the calculation of the two-point correlation function. Perturbation theory (PT), its generalization, the extended perturbation theory (EPT), and the hierarchical assumption (HA) have simple predictions for these statistics. As an example, the factorial moment correlators measured by Szapudi, Dalton, Efstathiou & Szalay (1996) in the APM catalog are reanalyzed using this technique. While the previous analysis assumed hierarchical structure constants, this method can directly investigate the validity of HA, along with PT, and EPT. The results in agreement with previous findings indicate that, at the small scales used for this analysis, the APM data supports HA. When all non-linear corrections are taken into account it is a good approximation at the 20 percent level. It appears that PT, and a natural generalization of EPT for cumulant correlators does not provide such a good fit for the APM at small scales. Once the validity the HA is approximately established, cumulant correlators can separate the amplitudes of different tree-types in the hierarchy up to fifth order. As an example, the weights for the fourth order tree topologies are calculated including all non-linear corrections.

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arXiv1997

Comparison of the Large Scale Clustering in the APM and the EDSGC Galaxy Surveys

Clustering statistics are compared in the Automatic Plate Machine (APM) and the Edinburgh/Durham Southern Galaxy Catalogue (EDSGC) angular galaxy surveys. Both surveys were independently constructed from scans of the same adjacent UK IIIa--J Schmidt photographic plates with the APM and COSMOS microdensitometers, respectively. The comparison of these catalogs is a rare practical opportunity to study systematic errors, which cannot be achieved via simulations or theoretical methods. On intermediate scales, $0.1^\circ < θ< 0.5^\circ$, we find good agreement for the cumulants or reduced moments of counts in cells up to sixth order. On larger scales there is a small disagreement due to edge effects in the EDSGC, which covers a smaller area. On smaller scales, we find a significant disagreement that can only be attributed to differences in the construction of the surveys, most likely the dissimilar deblending of crowded fields. The overall agreement of the APM and EDSGC is encouraging, and shows that the results for intermediate scales should be fairly robust. On the other hand, the systematic deviations found at small scales are significant in a regime, where comparison with theory and simulations is possible. This is an important fact to bear in mind when planning the construction of future digitized galaxy catalogs.

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arXiv1997

A New Class of Estimators for the N-point Correlations

A class of improved estimators is proposed for N-point correlation functions of galaxy clustering, and for discrete spatial random processes in general. In the limit of weak clustering, the variance of the unbiased estimator converges to the continuum value much faster than with any alternative, all terms giving rise to a slower convergence exactly cancel. Explicit variance formulae are provided for both Poisson and multinomial point processes using techniques for spatial statistics reported by Ripley (1988). The formalism naturally includes most previously used statistical tools such as N-point correlation functions and their Fourier counterparts, moments of counts-in-cells, and moment correlators. For all these, and perhaps some other statistics our estimator provides a straightforward means for efficient edge corrections.

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arXiv1996

Higher Order Statistics from the EDSGC Survey I: Counts in Cells

Counts in cells are used to analyse the higher order properties of the statistics of the EDSGC survey. The probability distribution is obtained from an equal area projection source catalog with infinite oversampling over the range $0.015^\circ-2^\circ$. The factorial moments of the resulting distribution and the $s_N$'s characterizing the non-Gaussian nature of the distribution are extracted. These results are compared to previous results from the APM survey, and to theoretical results from perturbation theory. The deprojected 3D values corresponding to the $s_N$'s are also determined. We find that the 3D values match the scaling relation for strongly nonlinear clustering found in N-body simulations remarkably well, suggesting that the galaxies are reliable tracers of the underlying mass distribution.

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arXiv1995

Cosmic Error and the Statistics of Large Scale Structure

We examine the errors on counts in cells extracted from galaxy surveys. The measurement error, related to the finite number of sampling cells, is disentangled from the ``cosmic error'', due to the finiteness of the survey. Using the hierarchical model and assuming locally Poisson behavior, we identified three contributions to the cosmic error: The finite volume effect is proportional to the average of the two-point correlation function over the whole survey. It accounts for possible fluctuations of the density field at scales larger than the sample size. The edge effect is related to the geometry of the survey. It accounts for the fact that objects near the boundary carry less statistical weight than those further away from it. The discreteness effect is due to the fact that the underlying smooth random field is sampled with finite number of objects. This is the ``shot noise'' error. Measurements of errors in artificial hierarchical samples showed excellent agreement with our predictions. The probability distribution of errors is increasingly skewed when the order $N$ and/or the cell size increases. The Gaussian approximation is valid only in the weakly non-linear regime, otherwise it severely underestimates the true errors. We study the concept of ``number of statistically independent cells'' This number is found to depend highly on the statistical object under study and is generally quite different from the number of cells needed to cover the survey volume. In light of these findings, we advocate high oversampling for measurements of counts in cells.

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arXiv1995

Effects of Sampling on Measuring Galaxy Count Probabilities

We investigate in detail the effects of sampling on our ability to accurately reconstruct the distribution of galaxies from galaxy surveys. We use a simple probability theory approach, Bayesian classifier theory and Bayesian transition probabilities. We find the best Bayesian estimator for the case of low sampling rates, and show that even in the optimal case certain higher order characteristics of the distribution are irretrievably washed out by sparse sampling: we illustrate this by a simple model for cluster selection. We show that even choosing an optimal threshold, there are nonzero numbers for both misidentified clusters and true clusters missed. The introduction of sampling has an effect on the distribution function that is similar to convolution. Deconvolution is possible and given in the paper, although it might become unstable as sampling rates become low. These findings have important consequences on planning and strategies of future galaxy surveys.

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