Testing deprojection algorithms on mock angular catalogues: evidence for a break in the power spectrum

Abstract

We produce mock angular catalogues from simulations with different initial power spectra to test methods that recover measures of clustering in three dimensions, such as the power spectrum, variance and higher order cumulants. We find that the statistical properties derived from the angular mock catalogues are in good agreement with the intrinsic clustering in the simulations. In particular, we concentrate on the detailed predictions for the shape of the power spectrum, $P(k)$. We find that there is good evidence for a break in the galaxy $P(k)$ at scales between $ 0.02 < k < 0.06 ~\impc$ using an inversion technique applied to the angular correlation function measured from the APM Galaxy Survey. For variants on the standard Cold Dark Matter model, a fit at the location of the break implies $\Omega h= 0.45 \pm 0.10$, where $\Omega$ is the ratio of the total matter density to the critical density and Hubble's constant is parameterised as $H_{0}= 100~hkm ~s^{-1}Mpc^{-1}$. On slightly smaller, though still quasi-linear scales, there is a feature in the APM power spectrum where the local slope changes appreciably, with the best match to CDM models obtained for $\Omega h \simeq 0.2$. Hence the location and narrowness of the break in the APM power spectrum combined with the rapid change in its slope on quasi-linear scales cannot be matched by any variant of CDM, including models that have a non-zero cosmological constant or a tilt to the slope of the primordial $P(k)$. These results are independent of the overall normalization of the CDM models or any simple bias that exists between the galaxy and mass distributions.