Systematic Effects on Determination of the Growth Factor from Redshift-space Distortions

TL;DR

This study examines how systematic effects, such as halo mass and scale dependence, influence the measurement of the growth factor from redshift-space distortions using N-body simulations, highlighting implications for dark energy and gravity theories.

Contribution

It reveals the scale and mass dependence of the redshift distortion parameter beta and assesses the reliability of different galaxy samples for measuring the growth factor.

Findings

Beta depends on scale even on large scales, especially for smaller halos.

Massive halos with bias > 1.5 show beta approaching linear theory predictions.

Reconstruction of beta in Fourier space is more accurate than in configuration space.

Abstract

The linear growth factor of density perturbations is believed to be a powerful observable of future redshift surveys to probe physical properties of dark energy and to distinguish among gravity theories. We investigate systematic effects on determination of the growth factor f from a measurement of redshift-space distortions. Using N-body simulations we identify dark matter halos over a broad mass range. We compute the power spectra and correlation functions for the halos and then examine how well the redshift distortion parameter beta=f/b can be reconstructed as a function of halo mass. We find that beta measured for a fixed halo mass is generally a function of scale even on large scales, in contrast with the common expectation that beta approaches a constant described by Kaiser's formula on such scales. The scale dependence depends on the halo mass, being stronger for smaller halos. It also cannot be easily explained with the well-known distribution function of the halo peculiar velocities. We demonstrate that the biasing for smaller halos has larger nonlinearity and stochasticity, thus the linear bias assumption becomes worse for smaller halos. Only for massive halos with b>1.5, beta approaches the linear theory prediction on scales of r or pi/k>30Mpc/h. Luminous red galaxies (LRG), targeted by the SDSS-III's BOSS survey, tend to reside in very massive halos. Our results indicate that if the LRG is used for the measurement of redshift distortions, f can be measured unbiasedly. On the other hand, if one considers to use emission line galaxies, which are targeted by the BigBOSS survey and inhabited in halos of a broad mass range, the scale dependence of beta must be taken into account carefully; otherwise one might give incorrect constraints on dark energy or modified gravity theories. We also find that beta reconstructed in Fourier space behaves better than that in configuration space.