SYSTEMATIC EFFECTS ON DETERMINATION OF THE GROWTH FACTOR FROM REDSHIFT-SPACE DISTORTIONS

The linear growth factor of density perturbations is generally believed to be a powerful observable quantity of future large redshift surveys to probe physical properties of dark energy and to distinguish among various gravity theories. We investigate systematic effects on determination of the linear growth factor f from a measurement of redshift-space distortions. Using a large set of high-resolution 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 investigate how well the redshift distortion parameter β ≡ f/b can be reconstructed as a function of halo mass both in Fourier and in configuration space, where b is the bias parameter. We find that the β value thus measured for a fixed halo mass generally is a function of scale for k>0.02 h Mpc−1 in Fourier space or r < 80 h−1 Mpc in configuration space, in contrast with the common expectation that β approaches a constant described by Kaiser's formula on the large scales. The scale dependence depends on the halo mass, being stronger for smaller halos. It is complex and cannot be easily explained with the exponential distribution function in configuration space or with the Lorentz function in Fourier space of the halo peculiar velocities. We demonstrate that the biasing for smaller halos has larger nonlinearity and stochasticity, thus the linear bias assumption adopted in Kaiser's derivation becomes worse for smaller halos. Only for massive halos with the bias parameter b ⩾ 1.5 does the β value approach the constant predicted by the linear theory on scales of k < 0.08 h Mpc−1 or r>30 h−1 Mpc. Luminous red galaxies (LRGs), targeted by the Sloan Digital Sky Survey (SDSS) and the SDSS-III's Baryon Oscillation Spectroscopic Survey (BOSS), tend to reside in very massive halos. Our results indicate that if the central LRG sample is used for the measurement of redshift-space distortions, the linear growth factor can fortunately be measured unbiasedly. On the other hand, emission-line galaxies, targeted by some future redshift surveys such as the BigBOSS survey, are inhabited in halos of a broad mass range. If one considers using such galaxies, the scale dependence of β must be taken into account carefully; otherwise, one might give incorrect constraints on dark energy or modified gravity theories. We also find that the β reconstructed in Fourier space behaves fairly better than that in configuration space when compared with the linear theory prediction.