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 $P^S(k,\mu)$ in three 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 $P^S(k,\mu)$ as a product of three factors P^S(k,\mu)=P^R(k)(1+\beta\mu^2)^2 D(k,\mu). Here $\mu$ 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 to an accurate analysis of the LCRS is well approximated by the Lorentz factor D=[1+{1\over 2}(k\mu\sigma_{12})^2]^{-1}. We have investigated different values for $\beta$ ($\beta=0.4$, 0.5, 0.6), and measured $P^R(k)$ and $\sigma_{12}(k)$ from $P^S(k,\mu)$ for different values of $\mu$. The velocity dispersion $\sigma_{12}(k)$ is nearly a constant from $k=0.5$ to 3 $\mpci$. The average value for this range is $510\pm 70 \kms$. The power spectrum $P^R(k)$ decreases with $k$ approximately with $k^{-1.7}$ for $k$ between 0.1 and 4 $\mpci$. 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 ($\Omega_0=0.2$) 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-under-weighted bias (Jing et al.).