Mathematics – Logic
Scientific paper
Aug 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994apj...431..569p&link_type=abstract
The Astrophysical Journal, vol. 431, no. 2, pt. 1, p. 569-585
Mathematics
Logic
206
Dark Matter, Data Correlation, Galactic Clusters, Luminosity, Power Spectra, Red Shift, Computerized Simulation, Cosmology, Galactic Evolution, Many Body Problem, Normal Density Functions
Scientific paper
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 greater than 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 approximately 200 h-1 Mpc. The power spectrum has slope n approximately equal -2.1 on small scales (lambda less than or equal 25 h-1 Mpc) and n approximately -1.1 on scales 30 less than lambda less than 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, lambdazero = 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 lambda greater than 30 h-1 Mpc. Biased CDM with a normalization that matches the Cosmic Microwave Background (CMB) anisotropy (OMEGA h = 0.5, b = 1.4, sigma8 (mass) = 1) has too much power on small scales to match the observed galaxy power spectrum. This model with b = 1 matches both Cosmic Background Explorer Satellite (COBE) and the small-scale power spect rum but has insufficient power on scales lambda approximately 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 approximately 40% larger for the brightest 50% of galaxies in volume-limited samples that have Mlim greater than 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 less than M* = -19.2 + 5 log h) and fainter galaxies, but that voids preferentially harbor fainter galaxies (approximately 2 sigma significance level).
Geller Margaret J.
Huchra John P.
Park Changbom
Vogeley Michael S.
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