The Power Spectrum of Galaxy Clustering in the Las Campanas Redshift Survey

The Las Campanas Redshift Survey (LCRS) contains 23697 galaxies, with an average redshift $z=0.1$, distributed over six $1.5\text{arcdeg}$ by $80\text{arcdeg}$ slices in the North and South galactic caps. We have computed the power spectrum $P(k)$ for LCRS galaxies over wavelengths $\lambda = 2\pi / k = 5 - 400\ h^{-1}$Mpc\mathrm{.}TheLCRS$P(k)$maybeapproximatedas$\propto k^{-1.8 \pm 0.1}$forsmallscales$\lambda = 5 - 30\ h^{-1}$Mpc,changingto$\propto k^{1 \pm 1}$forlargescales$\lambda \approx 200 - 400\ h^{-1}$~Mpc. The overall amplitude corresponds to ${\sigma }_8=1.0\pm 0.1$ in redshift space. Comparisons to the power spectra of other redshift surveys will be presented; the LCRS results agree best with those from the combined Center for Astrophysics and Southern Sky redshift surveys. We find evidence for type- dependent clustering differences in the LCRS, such that galaxies brighter than about $M^{\ast }-1$ appear about 50% more strongly clustered than those fainter, and that a sample of emission galaxies shows 30% weaker clustering than the full LCRS sample. On large scales $\lambda \gtrsim 40h^{-1}$~Mpc, we have also fit the LCRS results to various linear CDM models, and find that a number of them could meet the constraints set by the LCRS power spectrum, the Hubble constant range $0.5\lesssim h\lesssim 0.8$, the abundance of galaxy clusters, and the reasonable assumption that LCRS galaxies are roughly unbiased tracers of the mass, relative to the normalization provided by the 4-year COBE DMR data. The possibilites include open CDM or flat non-zero cosmological-constant CDM models with ${\mathrm{\Omega }}_0\approx 0.4-0.6$ and shape parameter $\Gamma \approx 0.2-0.3$,aswellasflat$\Omega_0 = 1$modelswithmassiveneutrinodensity$\Omega_\nu \approx 0.2-0.3$oraspectraltilt$n \approx 0.7-0.8$. (abridged)