The scaling of the redshift power spectrum: observations from the Las Campanas redshift survey

In a recent paper we have studied the redshift power spectrum P^S(k,μ) in three cold dark matter (CDM) models with the help of high-resolution simulations. Here we apply the method to the largest available redshift survey, the Las Campanas Redshift Survey (LCRS). The basic model is to express P^S(k,μ) as a product of three factors P^S(k,μ)=P^R(k)(1+βμ²)² D(k,μ). Here μ is the cosine of the angle between the wave vector and the line of sight. The damping function D for the range of scales accessible for an accurate analysis of the LCRS is well approximated by the Lorentz factor D=[1+1/2(kμσ₁₂) ²]^-1. We have investigated different values for β (i.e. β=0.4, 0.5, 0.6), and measured the real-space power spectrum P^R(k) and the pairwise velocity dispersion σ₁₂(k) from P^S(k,μ) for different values of μ. The velocity dispersion σ₁₂(k) is nearly a constant from k=0.5-3hMpc^-1. The average value for this range is 510+/-70kms^-1. The power spectrum P^R(k) decreases with k approximately, with k^-1.7 for k between 0.1 and 4hMpc^-1. The statistical significance of the results, and the error bars, are found with the help of mock samples constructed from a large set of high-resolution simulations. A flat, low-density (Ω₀=0.2) CDM model can give a good fit to the data, if a scale-dependent special bias scheme is used which we have called the cluster-underweighted bias (Jing, Mo & Börner).