Improving lognormal models for cosmological fields

Abstract

It is common practice in cosmology to model large-scale structure observables as lognormal random fields, and this approach has been successfully applied in the past to the matter density and weak lensing convergence fields separately. We argue that this approach has fundamental limitations which prevent its use for jointly modelling these two fields since the lognormal distribution's shape can prevent certain correlations to be attainable. Given the need of ongoing and future large-scale structure surveys for fast joint simulations of clustering and weak lensing, we propose two ways of overcoming these limitations. The first approach slightly distorts the power spectra of the fields using one of two algorithms that minimises either the absolute or the fractional distortions. The second one is by obtaining more accurate convergence marginal distributions, for which we provide a fitting function, by integrating the lognormal density along the line of sight. The latter approach also provides a way to determine directly from theory the skewness of the convergence distribution and, therefore, the parameters for a lognormal fit. We present the public code Full-sky Lognormal Astro-fields Simulation Kit (FLASK) which can make tomographic realisations on the sphere of an arbitrary number of correlated lognormal or Gaussian random fields by applying either of the two proposed solutions, and show that it can create joint simulations of clustering and lensing with sub-per-cent accuracy over relevant angular scales and redshift ranges.

Density split statistics: Cosmological constraints from counts and lensing in cells in DES Y1 and SDSS data

“…As pointed out by, e.g., Xavier et al [49], 2D projections of the 3D density contrast such as δ m;T and κ θ are not well described by a joint log-normal distribution if the kernels of their projection have a very different width along the line-of-sight. In our situation, the lensing kernel W s ðwÞ is significantly broader than the distribution in co-moving distance of our tracer galaxies.…”

“…We want to stress, that this does not mean that we employ a log-normal approximation for the joint PDF of δ m;T and κ <θ . E.g., Xavier et al [49] have shown that such an approximation can be inaccurate if the lensing kernel W s ðχÞ and the lineof-sight distribution of tracers q l ðχÞ have strongly different widths in co-moving distance. Rather, we model the convergence field as a sum of two fields, one of which is a log-normal random field and one of which is Gaussian and uncorrelated to δ m;T .…”

“…On the scales we care about in this work, we can measure the sum of both contributions to the covariance, to good approximation, from log-normal simulations of the related matter and convergence fields and Poissonian realizations of the tracer galaxy catalog. We do this by generating a large number of realizations of these fields and catalogs with FLASK [49].…”

Dark Energy Survey Year 1 results: Cosmological constraints from cosmic shear

“…We use the publicly available code FLASK 12 [88], which generates consistent density and convergence fields, to produce 150 mock full-sky shear maps that reproduce a set of input power spectra that fit a fiducial cosmology 13 and the actual redshift distribution of sources in our data. These maps are produced on a HEALPIX grid with resolution set by an N side parameter of 4096.…”

Dark Energy Survey year 1 results: Galaxy-galaxy lensing

“…We use the publicly available code FLASK 1 [58], to generate galaxy position and convergence fields consistent with our lens and source samples, and produce 150 full-sky shear and density mock catalogs. The maps are pixelated on a HEALPIX grid with resolution set by an N side parameter of 4096.…”