Reconstructing the Spectrum of the Pregalactic Density Field from Astronomical Data

Open Access
Publisher Website
Google Scholar
Abstract
In this paper we evaluate the spectrum of the pregalactic density field on scales 1 h-1 Mpc < r < 100 h-1 Mpc from a variety of astronomical data. We start with the APM data on the projected angular correlation function, w(θ), in six narrow magnitude bins and check whether possible evolutionary effects can affect inversion of the w(θ) data in terms of the underlying power spectrum. This is done by normalizing to the angular correlation function on small scales where the underlying three-dimensional galaxy correlation function, ξ(r) is known. Using the Automatic Plate Measuring Facility (APM) data in narrow magnitude bins allows us to test the various fits to the APM data power spectrum more accurately. We find that for linear scales r > 10 h-1 Mpc, the Baugh & Efstathiou spectrum of galaxy distribution gives the best fit to the data at all depths. Fitting power spectra of cold dark matter (CDM) models to the data at all depths requires Ωh = 0.2 if the primordial index n = 1 and Ωh = 0.3 if the spectrum is tilted with n = 0.7. Next we compare the peculiar velocity field predicted by the APM spectrum of galaxy (light) distribution with the actual velocity data. The two fields are consistent, and the comparison suggests that the bias factor is scale independent with Ω0.6/b (0.2–0.4). These steps enable us to fix the pregalactic mass-density field on scales between 10 and ~100 h-1 Mpc. The next data set we use to determine the pregalactic density field comes from the cluster correlation data. We calculate in detail the amplification of the cluster correlation function due to gravitational clustering and use the data on both the slope of the cluster correlation function and its amplitude-richness dependence. Cluster masses are normalized using the Coma Cluster. We find that no CDM model can fit all three data sets: APM data on w(θ), the data on cluster correlation function, and the data on the latter's amplitude-richness dependence. Next we show that the data on the amplitude-richness dependence can be used directly to obtain the spectrum of the pregalactic density field. Applying the method to the data, we recover the density field on scales between 5 and 25 h-1 Mpc whose slope is in good agreement with the APM data on the same scales. Requiring the two amplitudes to coincide fixes the value of Ω to be 0.25–0.3 in agreement with observations of the dynamics of the Coma Cluster. We then use the data on high-z objects to constrain the small-part, (1–5) h-1 Mpc of the pregalactic density field. We argue that the data at high redshifts require more power than given by CDM models normalized to the APM and cluster data. Then we reconstruct the pregalactic density field out of which modern-day galaxies have formed. We use the data on blue absolute luminosities, the fundamental plane relations, and the latest X-ray data on the halo velocity dispersion. From this we recover the pregalactic density field on comoving scales between 1 and 5 h-1 Mpc, which is in reasonable agreement with the simple power-law extrapolation from the larger scales.