Galaxy 2-Point Covariance Matrix Estimation for Next Generation Surveys

Abstract

We perform a detailed analysis of the covariance matrix of the spherically averaged galaxy power spectrum and present a new, practical method for estimating this within an arbitrary survey without the need for running mock galaxy simulations that cover the full survey volume. The method uses theoretical arguments to modify the covariance matrix measured from a set of small-volume cubic galaxy simulations, which are computationally cheap to produce compared to larger simulations and match the measured small-scale galaxy clustering more accurately than is possible using theoretical modelling. We include prescriptions to analytically account for the window function of the survey, which convolves the measured covariance matrix in a non-trivial way. We also present a new method to include the effects of supersample covariance and modes outside the small simulation volume which requires no additional simulations and still allows us to scale the covariance matrix. As validation, we compare the covariance matrix estimated using our new method to that from a brute force calculation using 500 simulations originally created for analysis of the Sloan Digital Sky Survey Main Galaxy Sample (SDSS-MGS). We find excellent agreement on all scales of interest for large scale structure analysis, including those dominated by the effects of the survey window, and on scales where theoretical models of the clustering normally break-down, but the new method produces a covariance matrix with significantly better signal-to-noise. Although only formally correct in real-space, we also discuss how our method can be extended to incorporate the effects of Redshift Space Distortions.

arXiv comment18 pages, 9 figures. Accepted for publication in MNRAS. Added new references to introduction and slightly updated text accordingly

References in corpus (68)

• The cosmological simulation code GADGET-2
• Efficient Computation of CMB anisotropies in closed FRW models
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample
• The 2dF Galaxy Redshift Survey: Spectra and redshifts
• The 2dF Galaxy Redshift Survey: Power-spectrum analysis of the final dataset and cosmological implications
• The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Baryon Acoustic Oscillations in the Data Release 10 and 11 galaxy samples
• The Clustering of the SDSS DR7 Main Galaxy Sample I: A 4 per cent Distance Measure at z=0.15
• Power Spectrum Analysis of Three-Dimensional Redshift Surveys
• Euclid Definition Study Report
• The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Baryon Acoustic Oscillations in the Data Release 9 Spectroscopic Galaxy Sample
• The 2dF Galaxy Redshift Survey: The power spectrum and the matter content of the universe
• CMB power spectrum parameter degeneracies in the era of precision cosmology
• Sample Variance Considerations for Cluster Surveys
• Measuring cosmological parameters with galaxy surveys
• The DESI Experiment, a whitepaper for Snowmass 2013
• The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: a large sample of mock galaxy catalogues
• Power Spectrum Super-Sample Covariance
• The Clustering of the SDSS Main Galaxy Sample II: Mock galaxy catalogues and a measurement of the growth of structure from Redshift Space Distortions at $z=0.15$
• Cosmology and the Bispectrum
• The Clustering of Galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Including covariance matrix errors
• Power Spectrum Correlations Induced by Non-Linear Clustering
• Fast Estimators for Redshift-Space Clustering
• The Effect of Covariance Estimator Error on Cosmological Parameter Constraints
• Putting the Precision in Precision Cosmology: How accurate should your data covariance matrix be?
• EZmocks: extending the Zel'dovich approximation to generate mock galaxy catalogues with accurate clustering statistics
• Super-Sample Covariance in Simulations
• PTHalos: A fast method for generating mock galaxy distributions
• Mock galaxy catalogs using the quick particle mesh method
• Simulations of Wide-Field Weak Lensing Surveys I: Basic Statistics and Non-Gaussian Effects
• The Impact of Non-Gaussian Errors on Weak Lensing Surveys
• Initial conditions to cosmological N-body simulations, or how to run an ensemble of simulations
• The Clustering of Galaxies in SDSS-III DR9 Baryon Oscillation Spectroscopic Survey: Constraints on Primordial Non-Gaussianity
• Measuring line-of-sight dependent Fourier-space clustering using FFTs
• On measuring the covariance matrix of the nonlinear power spectrum from simulations
• The Growth of Correlations in the Matter Power Spectrum
• An accurate tool for the fast generation of dark matter halo catalogs
• Simulations of Baryon Acoustic Oscillations II: Covariance matrix of the matter power spectrum
• Information content of weak lensing power spectrum and bispectrum: including the non-Gaussian error covariance matrix
• Probing dark energy with cluster counts and cosmic shear power spectra: including the full covariance
• Cosmological Structure Formation with Augmented Lagrangian Perturbation Theory
• Analytic model for the matter power spectrum, its covariance matrix, and baryonic effects
• Rapid modelling of the redshift-space power spectrum multipoles for a masked density field
• nIFTy Cosmology: Galaxy/halo mock catalogue comparison project on clustering statistics
• Super-Sample Signal
• Non-Gaussian Covariance of the Matter Power Spectrum in the Effective Field Theory of Large Scale Structure
• Information content of the non-linear power spectrum: the effect of beat-coupling to large scales
• Dark matter statistics for large galaxy catalogs: power spectra and covariance matrices
• Improving fast generation of halo catalogs with higher-order Lagrangian perturbation theory
• Thinking Outside the Box: Effects of Modes Larger than the Survey on Matter Power Spectrum Covariance
• The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: mock galaxy catalogues for the low-redshift sample
• Shrinkage Estimation of the Power Spectrum Covariance Matrix
• Perturbative approach to covariance matrix of the matter power spectrum
• Non-Gaussian Error Contribution to Likelihood Analysis of the Matter Power Spectrum
• Matter Power Spectrum Covariance Matrix from the DEUS-PUR ΛCDM simulations: Mass Resolution and non-Gaussian Errors
• Adding Long-Wavelength Power to N-body Simulations
• Improving the precision matrix for precision cosmology
• Large Covariance Matrices: Smooth Models from the 2-Point Correlation Function
• Fast generation of ensembles of cosmological N-body simulations via mode-resampling
• Estimating the power spectrum covariance matrix with fewer mock samples
• sCOLA: The N-body COLA Method Extended to the Spatial Domain
• On the information content of the matter power spectrum
• Estimating sparse precision matrices
• An optimal survey geometry of weak lensing survey: minimizing super-sample covariance
• Removable Matter-Power-Spectrum Covariance from Bias Fluctuations
• Cosmological parameter inference from galaxy clustering: The effect of the posterior distribution of the power spectrum
• Jackknife resampling technique on mocks: an alternative method for covariance matrix estimation
• Toward optimal cluster power spectrum analysis
• Approximate methods for the generation of dark matter halo catalogs in the age of precision cosmology

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