Power spectrum, correlation function, and tests for luminosity bias in the CfA redshift survey

We describe and apply a method for directly computing the power spectrum for the galaxy distribution in the extension of the Center for Astrophysics Redshift Survey. Tests show that our technique accurately reproduces the true power spectrum for k > 0.03 h Mpc^-1^. The dense sampling and large spatial coverage of this survey allow accurate measurement of the redshift-space power spectrum on scales from 5 to ~200 h^-1^ Mpc. The power spectrum has slope n ~ -2.1 on small scales (λ<= 25 h^-1^ Mpc) and n ~ -1.1 on scales 30 < λ < 120 h^- 1^ Mpc. On larger scales the power spectrum flattens somewhat, but we do not detect a turnover. Comparison with N-body simulations of cosmological models shows that an unbiased, open universe CDM model ({OMEGA}h = 0.2) and a nonzero cosmological constant CDM model ({OMEGA}h = 0.24, λ_0_ = 0.6, b = 1.3) match the CfA power spectrum over the wavelength range we explore. The standard biased CDM model ({OMEGA}h = 0.5, b = 1.5) fails (99% significance level) because it has insufficient power on scales λ > 30 h^-1^ Mpc. Biased CDM with a normalization that matches the CMB anisotropy [{OMEGA}h = 0.5, b = 1.4, σ_8_(mass) = 1] has too much power on small scales to match the observed galaxy power spectrum. This model with b = 1 matches both COBE and the small-scale power spectrum but has insufficient power on scales λ ~ 100 h^-1^ Mpc. We derive a formula for the effect of small-scale peculiar velocities on the power spectrum and combine this formula with the linear-regime amplification described by Kaiser to compute an estimate of the real- space power spectrum. Two tests reveal luminosity bias in the galaxy distribution: First, the amplitude of the power spectrum is ~40% larger for the brightest 50% of galaxies in volume-limited samples that have M_lim_ > M^*^. This bias in the power spectrum is independent of scale, consistent with the peaks- bias paradigm for galaxy formation. Second, the distribution of local density around galaxies shows that regions of moderate and high density contain both very bright (M < M^*^ = - 19.2 + 5 log h) and fainter galaxies, but that voids preferentially harbor fainter galaxies (~2 σ significance level).