## Wavelet analysis of baryon acoustic structures in the galaxy distribution

 Authors: P. Arnalte-Mur, A. Labatie, N. Clerc, V. J. Martínez, J.-L. Starck, et al. Journal: A&A Year: 2012 Download: ADS | arXiv

## Abstract

Baryon Acoustic Oscillations (BAO) are a feature imprinted in the density field by acoustic waves travelling in the plasma of the early universe. Their fixed scale can be used as a standard ruler to study the geometry of the universe. BAO have been previously detected using correlation functions and power spectra of the galaxy distribution. In this work, we present a new method for the detection of the real-space structures associated with this feature. These baryon acoustic structures are spherical shells with a relatively small density contrast, surrounding high density central regions. We design a specific wavelet adapted to the search for shells, and exploit the physics of the process by making use of two different mass tracers, introducing a specific statistic to detect the BAO features. We show the effect of the BAO signal in this new statistic when applied to the Lambda - Cold Dark Matter (LCDM) model, using an analytical approximation to the transfer function. We confirm the reliability and stability of our method by using cosmological N-body simulations from the MareNostrum Institut de Ci\encies de l'Espai (MICE). We apply our method to the detection of BAO in a galaxy sample drawn from the Sloan Digital Sky Survey (SDSS). We use the Main' catalogue to trace the shells, and the Luminous Red Galaxies (LRG) as tracers of the high density central regions. Using this new method, we detect, with a high significance, that the LRGs in our sample are preferentially located close to the centres of shell-like structures in the density field, with characteristics similar to those expected from BAOs. We show that stacking selected shells, we can find their characteristic density profile. We have delineated a new feature of the cosmic web, the BAO shells. As these are real spatial structures, the BAO phenomenon can be studied in detail by examining those shells.

## Summary

We have designed a specific wavelet adapted to search for shells, and exploit the physics of the process by making use of two different mass tracers, introducing a specific statistic to detect the BAO features. We have applied our method to the detection of BAO in a galaxy sample drawn from the Sloan Digital Sky Survey (SDSS). We have used the "main" catalogue to trace the shells, and the luminous red galaxies (LRG) as tracers of the high density central regions. Using this new method, we detect, with a high significance, that the LRG in our sample are preferentially located close to the centers of shell-like structures in the density field, with characteristics similar to those expected from BAO (Arnalte-Mur, Labatie, Clerc, Martínez,  Starck et al, A&A, 2012). Then we have studied the classical method for detecting BAOs and the assumptions that the method requires. We have also found that the approximation of a constant covariance matrix in the classical BAO analysis method can affect non negligibly both the BAO detection and cosmological parameter constraints (Labatie, Starck, Lachieze-Rey, ApJ,2012a) (Labatie, Starck, Lachieze-Rey, ApJ,2012b).

## Galaxy clustering in the CFHTLS-Wide: the changing relationship between galaxies and haloes since z ~ 1.2

 Authors: J. Coupon, M. Kilbinger, H. J. McCracken, et al. Journal: A&A Year: 2012 Download: ADS | arXiv

## Abstract

We present a detailed investigation of the changing relationship between galaxies and the dark matter haloes they inhabit from z~1.2 to the present day. We do this by comparing precise galaxy clustering measurements over 133 deg2 of the "Wide" component of the CFHT Legacy Survey (CFHTLS) with predictions of an analytic HOD model where the number of galaxies in each halo depends only on the halo mass. Starting from a parent catalogue of ~ 3x10^6 galaxies at i'_AB < 22.5 we use accurate photometric redshifts calibrated using ~ 10^4 spectroscopic redshifts to create a series of type-selected volume-limited samples covering 0.2 < z < 1.2. Our principal result, based on clustering measurements in these samples, is a robust determination of the luminosity-to-halo mass ratio and its dependence on redshift and galaxy type. For the full sample, this reaches a peak at low redshifts of Mh,peak = 4.5x10^11 h^-1 M_sun and moves towards higher halo masses at higher redshifts. For redder galaxies the peak is at higher halo masses and does not evolve significantly over the entire redshift range of our survey. We also consider the evolution of bias, average halo mass and the fraction of satellites as a function of redshift and luminosity. Our observed growth of a factor of ~ 2 in satellite fraction between z~1 and z~0 is testament to the limited role that galaxy merging plays in galaxy evolution for ~ 10^12 h^-1 M_sun mass haloes at z<1. Qualitatively, our observations are consistent with a picture in which red galaxies in massive haloes have already accumulated most of their stellar mass by z~1 and subsequently undergo little evolution until the present day. The observed movement of the peak location for the full galaxy population is consistent with the bulk of star-formation activity migrating from higher mass haloes at high redshifts to lower mass haloes at lower redshifts.

## Summary

We measured the galaxy spatial correlation function in multi-band optical data over 133 square degree in the CFHTLS-Wide survey, from z=0.2 to 1.2 (Coupon, Kilbinger et al., A&A, 2012). Comparing these observations to a semi-analytical model of the matter distribution in the Universe, including a prescription how galaxies populate halos, a so-called halo occupation distribution (HOD) model, we determine the evolution of the luminosity-to-mass (L/M) ratios for stellar-mass selected galaxy samples. A maximum L/M is reached at halo masses of 6.3 × 1011 at low redshift. This mass increases with redshift, indicating “anti-hierarchical” evolution or “down-sizing”, where galaxies formed more efficiently in larger halos in the past.

## Detecting Baryon Acoustic Oscillations

 Authors: A. Labatie, J.-L. Starck, M. Lachièze-Rey Journal: ApJ Year: 2012 Download: ADS | arXiv

## Abstract

Baryon Acoustic Oscillations are a feature imprinted in the galaxy distribution by acoustic waves traveling in the plasma of the early universe. Their detection at the expected scale in large-scale structures strongly supports current cosmological models with a nearly linear evolution from redshift approximately 1000, and the existence of dark energy. Besides, BAOs provide a standard ruler for studying cosmic expansion. In this paper we focus on methods for BAO detection using the correlation function measurement. For each method, we want to understand the tested hypothesis (the hypothesis H0 to be rejected) and the underlying assumptions. We first present wavelet methods which are mildly model-dependent and mostly sensitive to the BAO feature. Then we turn to fully model-dependent methods. We present the most often used method based on the chi^2 statistic, but we find it has limitations. In general the assumptions of the chi^2 method are not verified, and it only gives a rough estimate of the significance. The estimate can become very wrong when considering more realistic hypotheses, where the covariance matrix of the measurement depends on cosmological parameters. Instead we propose to use a new method based on two modifications: we modify the procedure for computing the significance and make it rigorous, and we modify the statistic to obtain better results in the case of varying covariance matrix. We verify with simulations that correct significances are different from the ones obtained using the classical chi^2 procedure. We also test a simple example of varying covariance matrix. In this case we find that our modified statistic outperforms the classical chi^2 statistic when both significances are correctly computed. Finally we find that taking into account variations of the covariance matrix can change both BAO detection levels and cosmological parameter constraints.

## Summary

We have designed a specific wavelet adapted to search for shells, and exploit the physics of the process by making use of two different mass tracers, introducing a specific statistic to detect the BAO features. We have applied our method to the detection of BAO in a galaxy sample drawn from the Sloan Digital Sky Survey (SDSS). We have used the "main" catalogue to trace the shells, and the luminous red galaxies (LRG) as tracers of the high density central regions. Using this new method, we detect, with a high significance, that the LRG in our sample are preferentially located close to the centers of shell-like structures in the density field, with characteristics similar to those expected from BAO (Arnalte-Mur, Labatie, Clerc, Martínez,  Starck et al, A&A, 2012). Then we have studied the classical method for detecting BAOs and the assumptions that the method requires. We have also found that the approximation of a constant covariance matrix in the classical BAO analysis method can affect non negligibly both the BAO detection and cosmological parameter constraints (Labatie, Starck, Lachieze-Rey, ApJ,2012a) (Labatie, Starck, Lachieze-Rey, ApJ,2012b).

## Uncertainty in 2-point correlation function estimators and BAO detection in SDSS DR7

 Authors: A. Labatie, J-L. Starck, M. Lachièze-Rey, P. Arnalte-Mur Journal: arXiv Year: 2010 Download: ADS | arXiv

## Abstract

We study the uncertainty in different two-point correlation function (2PCF) estimators in currently available galaxy surveys. This is motivated by the active subject of using the baryon acoustic oscillations (BAOs) feature in the correlation function as a tool to constrain cosmological parameters, which requires a fine analysis of the statistical significance. We discuss how estimators are affected by both the uncertainty in the mean density n¯ and the integral constraint 1V2V2ξ̂ (r)d3r=0 which necessarily causes a bias. We quantify both effects for currently available galaxy samples using simulated mock catalogues of the Sloan Digital Sky Survey (SDSS) following a lognormal model, with a Lambda-Cold Dark Matter (ΛCDM) correlation function and similar properties as the samples (number density, mean redshift for the ΛCDMcorrelation function, survey geometry, mass-luminosity bias). Because we need extensive simulations to quantify small statistical effects, we cannot use realistic N-body simulations and some physical effects are neglected. Our simulations still enable a comparison of the different estimators by looking at their biases and variances. We also test the reliability of the BAO detection in the SDSS samples and study the compatibility of the data results with our ΛCDM simulations.

## Summary

We have investigated whether Labini's group claim, that the 2PCF at large scales behavior in galaxy surveys (BAO, Universe homogenization) cannot be trusted due to the limited volume effect, is correct. We have demonstrated that all 2PCF estimators verifies a relation called integral constraint, which is not necessary by the real 2PCF, which biases correlation function estimators. But we showed using simulations of the Sloan Digital Sky Survey Data Release 7 (SDSS DR7) that the effect of the constraint is very small for current galaxy surveys (Labatie, Starck, Lachieze-Rey, Statistical Methodology, 2011).

## Multi-scale morphology of the galaxy distribution

 Authors: E. Saar, V. J. Martinez, J-L. Starck, D. L. Donoho Journal: MNRAS Year: 2007 Download: ADS | arXiv

## Abstract

Many statistical methods have been proposed in the last years for analyzing the spatial distribution of galaxies. Very few of them, however, can handle properly the border effects of complex observational sample volumes. In this paper, we first show how to calculate the Minkowski Functionals (MF) taking into account these border effects. Then we present a multiscale extension of the MF which gives us more information about how the galaxies are spatially distributed. A range of examples using Gaussian random fields illustrate the results. Finally we have applied the Multiscale Minkowski Functionals (MMF) to the 2dF Galaxy Redshift Survey data. The MMF clearly indicates an evolution of morphology with scale. We also compare the 2dF real catalog with mock catalogs and found that Lambda-CDM simulations roughly fit the data, except at the finest scale.

## Summary

We have shown how to calculate the Minkowski Functionals (MFs) taking into account border effects of complex observational sample volumes. We have proposed a multi-scale extension of the MF, which gives us more information about how the galaxies are spatially distributed. This method has been applied to the 2dF Galaxy Redshift Survey data. The MMF clearly indicates an evolution of morphology with scale. We also compare the 2dF real catalogue with mock catalogues and found that Λ cold dark matter simulations roughly fit the data, except at the finest scale (Saar, Martinez, Starck and Donoho, MNRAS, 2007).