Testing the lognormality of the galaxy and weak lensing convergence distributions from Dark Energy Survey maps

TL;DR

This study investigates whether the probability distribution functions of galaxy density contrast and weak lensing convergence are lognormal, using Dark Energy Survey data, and finds that they are well modeled by lognormal distributions with some noise considerations.

Contribution

It provides the first empirical validation that the PDFs of weak lensing convergence are approximately lognormal at certain scales, extending the known lognormality of galaxy density contrasts.

Findings

Galaxy density contrast is well modeled by a lognormal PDF with Poisson noise.

Weak lensing convergence PDF is approximately lognormal at scales 10-20 arcmin.

Joint PDF of galaxy and convergence distributions is consistent with a bivariate lognormal model.

Abstract

It is well known that the probability distribution function (PDF) of galaxy density contrast is approximately lognormal; whether the PDF of mass fluctuations derived from weak lensing convergence (kappa_WL) is lognormal is less well established. We derive PDFs of the galaxy and projected matter density distributions via the Counts in Cells (CiC) method. We use maps of galaxies and weak lensing convergence produced from the Dark Energy Survey (DES) Science Verification data over 139 deg^2. We test whether the underlying density contrast is well described by a lognormal distribution for the galaxies, the convergence and their joint PDF. We confirm that the galaxy density contrast distribution is well modeled by a lognormal PDF convolved with Poisson noise at angular scales from 10-40 arcmin (corresponding to physical scales of 3-10 Mpc). We note that as kappa_WL is a weighted sum of the mass fluctuations along the line of sight, its PDF is expected to be only approximately lognormal. We find that the kappa_WL distribution is well modeled by a lognormal PDF convolved with Gaussian shape noise at scales between 10 and 20 arcmin, with a best-fit chi^2/DOF of 1.11 compared to 1.84 for a Gaussian model, corresponding to p-values 0.35 and 0.07 respectively, at a scale of 10 arcmin. Above 20 arcmin a simple Gaussian model is sufficient. The joint PDF is also reasonably fitted by a bivariate lognormal. As a consistency check we compare the variances derived from the lognormal modelling with those directly measured via CiC. Our methods are validated against maps from the MICE Grand Challenge N-body simulation.