Statistical and systematic errors in redshift-space distortion measurements from large surveys

TL;DR

This paper assesses the impact of statistical and systematic errors on redshift-space distortion measurements in large surveys, highlighting the importance of non-linear models and providing a practical error scaling formula.

Contribution

It introduces a new scaling formula for RSD error prediction that aligns with simulation results and improves upon Fisher matrix estimates by accounting for non-linear effects.

Findings

Redshift-space distortion measurements are underestimated by up to 10% using linear models.

Fisher matrix errors match simulation errors only on linear scales (k<0.2 h/Mpc).

A new error scaling formula accurately predicts RSD errors across survey regimes.

Abstract

We investigate the impact of statistical and systematic errors on measurements of linear redshift-space distortions (RSD) in future cosmological surveys, analyzing large catalogues of dark-matter halos from the BASICC simulation. These allow us to estimate the dependence of errors on typical survey properties, as volume, galaxy density and mass (i.e. bias factor) of the adopted tracer. We find that measures of the specific growth rate \beta=f/b using the Hamilton/Kaiser harmonic expansion of the redshift-space correlation function \xi(r_p,\pi) on scales larger than 3/h Mpc are typically under-estimated by up to 10% for galaxy sized halos. This is significantly larger than the corresponding statistical errors, which amount to a few percent, indicating the importance of non-linear improvements to the Kaiser model to obtain accurate measurements of the growth rate. We compare the statistical errors to predictions obtained with the Fisher information matrix, based on the usual FKP prescription for the errors on the power spectrum. We show that this produces parameter errors fairly similar to the standard deviations from the halo catalogues, but only if applied to strictly linear scales in Fourier space (k<0.2 h/Mpc). Finally, we present an accurate scaling formula describing the relative error on {\beta} as a function of the survey parameters, which closely matches the simulation results in all explored regimes. This provides a handy and plausibly more realistic alternative to the Fisher matrix approach, to quickly and accurately predict RSD statistical errors expected from future surveys.