arXiv subjects

E. Gaztanaga

Publications and source records attributed to E. Gaztanaga.

356 records · Page 20Linked to original sources

arXiv1999

The Projected Three-point Correlation Function: Theory and Observations

We report results for the angular three-point galaxy correlation function in the APM survey and compare them with theoretical expectations. For the first time, these measurements extend to sufficiently large scales to probe the weakly non-linear regime. On large scales, the results are in good agreement with the predictions of non-linear cosmological perturbation theory, for a model with initially Gaussian fluctuations and linear power spectrum $P(k)$ consistent with that inferred from the APM survey. These results reinforce the conclusion that large-scale structure is driven by non-linear gravitational instability and that APM galaxies are relatively unbiased tracers of the mass on large scales; they also provide stringent constraints upon models with non-Gaussian initial conditions and strongly exclude the standard cold dark matter model.

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arXiv1998

Data compression on board the PLANCK Satellite Low Frequency Instrument: optimal compression rate

Data on board the future PLANCK Low Frequency Instrument (LFI), to measure the Cosmic Microwave Background (CMB) anisotropies, consist of $N$ differential temperature measurements, expanding a range of values we shall call $R$. Preliminary studies and telemetry allocation indicate the need of compressing these data by a ratio of $c_r \simgt 10$. Here we present a study of entropy for (correlated multi-Gaussian discrete) noise, showing how the optimal compression $c_{r,opt}$, for a linearly discretized data set with $N_{bits}=\log_2{N_{max}}$ bits is given by: $c_r \simeq {N_{bits}/\log_2(\sqrt{2πe} ~σ_e/Δ)}$, where $σ_e\equiv (det C)^{1/2N}$ is some effective noise rms given by the covariance matrix $C$ and $Δ\equiv R / N_{max}$ is the digital resolution. This $Δ$ only needs to be as small as the instrumental white noise RMS: $Δ\simeq σ_T \simeq 2 mK$ (the nominal $μK$ pixel sensitivity will only be achieved after averaging). Within the currently proposed $N_{bits}=16$ representation, a linear analogue to digital converter (ADC) will allow the digital storage of a large dynamic range of differential temperature $R= N_{max} Δ$ accounting for possible instrument drifts and instabilities (which could be reduced by proper on-board calibration). A well calibrated signal will be dominated by thermal (white) noise in the instrument: $σ_e \simeq σ_T$, which could yield large compression rates $c_{r,opt} \simeq 8$. This is the maximum lossless compression possible. In practice, point sources and $1/f$ noise will produce $σ_e > σ_T$ and $c_{r,opt} < 8$. This strategy seems safer than non-linear ADC or data reduction schemes (which could also be used at some stage).

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arXiv1998

The implications of the large scale galaxy power spectrum for Cold Dark Matter

The APM Galaxy Survey maps the angular positions of more than one million galaxies to $b_{J} = 20$, covering a volume comparable to the forthcoming Sloan Digital Sky Survey. A numerical algorithm has been developed to estimate the power spectrum in three dimensions, using the angular clustering and a model for the redshift distribution of APM Galaxies. The power spectrum obtained is free from distortions of the pattern of clustering caused by the peculiar motions of galaxies. We discuss the uncertainties in the estimated power spectrum and describe tests of the algorithm using large numerical simulations. The APM Galaxy power spectrum shows an inflection at a wavenumber $k \sim 0.15 h/Mpc$, with evidence for a peak or turnover in the range $ k \sim 0.03-0.06 h/Mpc$. These features can place strong constraints on Cold Dark Matter models for structure formation.

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arXiv1998

Cosmological Perturbation Theory and the Spherical Collapse Model - I. Gaussian Initial Conditions

We present a simple and intuitive approximation for solving perturbation theory (PT) of small cosmic fluctuations. We consider only the spherically symmetric or monopole contribution to the PT integrals, which yields the exact result for tree-graphs (i.e. at leading order). We find that the non-linear evolution in Lagrangian space is then given by a simple {\it local} transformation over the initial conditions, although it is not local in Euler space. This transformation is found to be described the spherical collapse (SC) dynamics, as it is the exact solution in the shearless (and therefore local) approximation in Lagrangian space. Taking advantage of this property, it is straightforward to derive the one-point cumulants, $ξ_J$, for both the unsmoothed and smoothed density fields to {\it arbitrary} order in the perturbative regime. To leading order this reproduces, and provides with a simple explanation for, the exact results obtained by Bernardeau (1992, 1994). We then show that the SC model leads to accurate estimates for the next corrective terms when compared to the results derived in the exact perturbation theory making use of the loop calculations (Scoccimarro & Frieman 1996). The agreement is within a few per cent for the hierarchical ratios $S_J= ξ_J/ξ_2^{J-1}$. We compare our analytic results to N-body simulations, which turn out to be in very good agreement up to scales where $σ\approx 1$. A similar treatment is presented to estimate higher order corrections in the Zel'dovich approximation. These results represent a powerful and readily usable tool to produce analytical predictions to describe the gravitational clustering of large scale structure in the weakly non-linear regime.

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arXiv1998

Cosmological Perturbation Theory and the Spherical Collapse model - III. The Velocity divergence field and the $Ω$ dependence

Cosmological Perturbation Theory (PT) is a useful tool to study the cumulants of the density and velocity fields in the large scale structure of the Universe. In Papers I & II of this series we saw that the Spherical Collapse (SC) model provides with the exact solution to PT at tree-level and gives a good approximation to the loop corrections (next to leading orders), indicating negligible tidal effects. Here, we derive predictions for the (smoothed) cumulants of the velocity divergence field $θ\equiv \nabla\cdot\vv$ for an irrotational fluid in the SC model. By comparing with the exact analytic results by Scoccimarro & Frieman (1996), it is shown that, at least for the unsmoothed case, the loop corrections to the cumulants of $θ$ are dominated by tidal effects. However, most of the tidal contribution seems to cancel out when computing the hierarchical ratios, $T_J = {<θ^J> / <θ^2>^{J-1}}$. We also extend the work presented in Papers I & II to give predictions for the cumulants of the density and velocity divergence fields in non-flat spaces. In particular, we show the equivalence between the spherically symmetric solution to the equations of motion in the SC model (given in terms of the density) and that of the Lagrangian PT approach (in terms of the displacement field). It is shown that the $Ω$-dependence is very weak for both cosmic fields even at one-loop (a 10% effect at most), except for the overall factor $f(Ω)$ that couples to the velocity divergence.

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arXiv1998

Non-Gaussian bounds in the variance from small scale CMB observations

We compare the latest results from CMB experiments at scales around $l_e \sim 150$ over different parts of the sky to test the hypothesis that they are drawn from a Gaussian distribution, as is usually assumed. Using both the diagonal and the full covariance $χ^2$ test, we compare the data with different sets of strategies and find in all cases incompatibility with the Gaussian hypothesis above the one-sigma level. We next show how to include a generic non-Gaussian signal in the data analysis. Results from CMB observations can be made compatible with each other by assuming a non-Gaussian distribution for the signal, with a kurtosis at a level $B_4 = <{δ_T^4}>_c /{<{δ_T^2}>_c}^2 \simeq 90$. A possible interpretation for this result is that the initial fluctuations at the surface of last scattering are strongly non-Gaussian. Another interpretation is that the systematic errors have been understimated in all observations by a factor of two. Other explanations include foreground contamination, non-linear effects or a combination of them.

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arXiv1997

Testing deprojection algorithms on mock angular catalogues: Evidence for a break in the power spectrum

We produce mock angular catalogues from simulations with different initial power spectra to test methods that recover measures of clustering in three dimensions, such as the power spectrum, variance and higher order cumulants. We find that the statistical properties derived from the angular mock catalogues are in good agreement with the intrinsic clustering in the simulations. In particular, we concentrate on the detailed predictions for the shape of the power spectrum, $P(k)$. We find that there is good evidence for a break in the galaxy $P(k)$ at scales between $ 0.02 < k < 0.06 ~\impc$ using an inversion technique applied to the angular correlation function measured from the APM Galaxy Survey. For variants on the standard Cold Dark Matter model, a fit at the location of the break implies $Ωh= 0.45 \pm 0.10$, where $Ω$ is the ratio of the total matter density to the critical density and Hubble's constant is parameterised as $H_{0}= 100~hkm ~s^{-1}Mpc^{-1}$. On slightly smaller, though still quasi-linear scales, there is a feature in the APM power spectrum where the local slope changes appreciably, with the best match to CDM models obtained for $Ωh \simeq 0.2$. Hence the location and narrowness of the break in the APM power spectrum combined with the rapid change in its slope on quasi-linear scales cannot be matched by any variant of CDM, including models that have a non-zero cosmological constant or a tilt to the slope of the primordial $P(k)$. These results are independent of the overall normalization of the CDM models or any simple bias that exists between the galaxy and mass distributions.

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arXiv1997

The skewness and kurtosis of the projected density distribution function: validity of perturbation theory

We study the domain of validity of Perturbation Theory (PT), by comparing its predictions for the reduced skewness, s_3, and kurtosis, s_4, of the projected cosmological density field, with the results of N-body simulations. We investigate models with different linear power spectra and consider as physical applications both angular galaxy catalogues and weak lensing surveys. We first find that the small-angle approximation for the predicted skewness provides a good match to the exact numerical PT results. On the other hand, results from non-linear simulated catalogues agree well with PT results on quasi-linear angular scales, which correspond to scales larger than about 1 degree in the applications we have considered. We also point out that, on smaller scale, the projection effects tend to attenuate the effects of the strong nonlinearities in the angular skewness and kurtosis.

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arXiv1996

Reconstruction of cosmological density and velocity fields in the Lagrangian Zel'dovich Approximation

We present a method for reconstructing cosmological densityn for and velocity fields using the Lagrangian Zel'dovich formalism. . The method involves finding the least action solution for straight line particle paths in an evolving density field. Our starting point is the final, evolved density , so that we are in effect carrying out the standard Zel'dovich Approximation based process in reverse. Using a simple numerical algorithm we are able to minimise the action for the trajectories of several million particles. We apply our method to the evolved density taken from N-body simulations of different cold dark matter dominated universes, testing both the prediction for the present day velocity field and for the initial density field. The method is easy to apply, reproduces the accuracy of the forward Zel'dovich Approximation, and also works directly in redshift space with minimal modification.

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arXiv1996

Testing ansatze for Quasi-nonlinear Clustering: the linear APM power spectrum

We compare the accuracy of published formulae that transform the linear perturbation theory power spectrum into the nonlinear regime against the results of an ensemble of large N-body simulations. We find that the modified transformation given by Jain, Mo and White (1995) performs well for initial fluctuations that have a power law power spectrum, but is less succesful for scale dependent spectra. The inverse transformation to obtain the linear power spectrum is applied to the APM Galaxy Survey power spectrum measured by Baugh \& Efstathiou (1993). The resulting linear spectrum is used to generate the initial density fluctuations in an N-body simulation, which is evolved to match the measured APM amplitude on large scales. We find very good agreement between the final power spectrum of the simulation and the measured APM power spectrum. However, the higher moments for the particle distribution only match the ones recovered from the APM Survey on large scales, $R \simgt 10 \mpc$. On small scales, $R \simlt 10 \mpc$, the APM estimations give smaller amplitudes, indicating that non-gravitational effects, such as biasing, are important on those scales. Our approach can be used to constrain a model of how light from galaxies traces the underlying mass distribution.

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arXiv1996

Large scale clustering from Non-Gaussian texture models

A basic ingredient to understand large scale fluctuations in our present day Universe is the initial conditions. Using N-body simulations, we compare the clustering that arises from Gaussian and non-Gaussian initial conditions. The latter is motivated by a global texture model which has initial $J$-order correlations $\xibar_J$ close to the strongly non-Gaussian regime $\xibar_J \simeq \xibar_2^{J/2}$. The final amplitudes $S_J \equiv \xibar_J/\xibar_2^{J-1}$ in the non-Gaussian (texture) model evolves slowly towards the (Gaussian) gravitational predictions but, even at $σ_8=1$, are still significantly larger, showing a characteristic minimum with a sharp increase in $S_J$ with increasing scales. This minimum, which is between $10$ and $15 \Mpc$, depending on the normalization, separates the regime where gravity starts dominating the evolution from the one in which the initial conditions are the dominant effect. In comparing this results with galaxy clustering observations, one has to take into account {\it biasing}, i.e. how galaxy fluctuations trace matter fluctuations. Although biasing could change the amplitudes, we show that the possible distortions to the shape of $S_J$ are typically small. In contrast to the non-Gaussian (texture) predictions, we find no significant minimum or rise in $S_J$ obtained from the APM Galaxy Survey.

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arXiv1994

Hierarchical correlations in models of galaxy clustering

We present a comparison of the predictions of perturbation theory for the hierarchical J-order correlation amplitudes $S_J=\xibar_J/\xibar_2^{J-1}$, $J=3-10$, with the results of large numerical simulations of gravitational clustering. We consider two different initial power spectra of density fluctuations, one being flatter than the other. The clustering amplitudes $S_J$ measured in these models are different at all scales. In each case, the perturbation theory predictions give an excellent agreement with the simulations on scales for which the variance is approximately linear, i.e. for scales on which $\xibar_2 \simlt 1$. For cells of radius $R \simgt 30 \Mpc$, the sampling variance arising from the finite size of our simulations dominates the results. We also find that $S_J$ are roughly independent of time, $Ω$, or $λ$, as expected. On comparing with the observations, one can use these results to discriminate between models for structure formation.

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arXiv1994

A comparison of the evolution of the density field in perturbation theory and numerical simulations - II Counts in cells analysis

We present a detailed comparison of the predictions of perturbation theory for the averaged J-point correlation functions, $\xibar_J$, with the results of numerical simulations of gravitational clustering. We have carried out a systematic analysis of this method using ensembles of simulations with different numbers of particles, different box sizes and using different particle arrangements and clustering amplitudes in the initial conditions. We estimate $\xibar_J$, for $J=2-10$, from moments of counts-in-cells. We find significant non-linear effects in the variance, $J=2$, even at scales as large as $R \sim 30 \Mpc$. Perturbation theory gives remarkable agreement at large scales, where $\xibar_2 \simlt 1$, with the measured hierarchical amplitudes $S_J=\xibar_J/\xibar_2^{J-1}$. We have followed the evolution of $\xibar_J$ in time and find that for a change in the effective redshift of at least $Δz \simeq 2$ the amplitudes $S_J$ remain unchanged, despite the fact that the $\xibar_J$ have evolved by large factors, $\simeq 10^{J-1}$. We illustrate how these results can be applied to interpret the clustering in galaxy surveys and conclude that the observed hierarchical pattern in the APM is compatible with gravitational evolution in unbiased, initially Gaussian, models.

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arXiv1994

Bias and high-order galaxy correlation functions in the APM Galaxy Survey

On large scales, the higher order moments of the mass distribution, $S_J=\xibar_J/\xibar_2^{J-1}$, e.g., the skewness $S_3$ and kurtosis $S_4$, can be predicted using non-linear perturbation theory. Comparison of these predictions with moments of the observed galaxy distribution probes the bias between galaxies and mass. Applying this method to models with initially Gaussian fluctuations and power spectra $P(k)$ similar to that of galaxies in the APM survey, we find that the predicted higher order moments $S_J(R)$ are in good agreement with those directly inferred from the APM survey {\it in the absence of bias}. We use this result to place limits on the linear and non-linear bias parameters. Models in which the extra power observed on large scales (with respect to standard CDM) is produced by scale-dependent bias match the APM higher order amplitudes only if non-linear bias (rather than non-linear gravity) generates the observed higher order moments. When normalized to COBE DMR, these models are significantly ruled out by the $S_3$ observations. The cold plus hot dark matter model normalized to COBE can reproduce the APM higher order correlations if one introduces non-linear bias terms, while the low-density CDM model with a cosmological constant does not require any bias to fit the large-scale amplitudes.

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