THE TOPOLOGY OF THE IRAS POINT-SOURCE-CATALOG-REDSHIFT-SURVEY

We investigate the topology of the new Point Source Catalogue Redshift Survey (PSCz) of IRAS galaxies by means of the genus statistic. The s urvey maps the local Universe with approximately 15 000 galaxies over 84.1 per cent of the sky, and provides an unprecedented number of reso lution elements for the topological analysis. For comparison with the PSCz data we also examine the genus of large N-body simulations of fou r variants of the cold dark matter (CDM) cosmogony. The simulations ar e part of the Virgo project to simulate the formation of structure in the Universe. We assume that the statistical properties of the galaxy distribution can be identified with those of the dark matter particles in the simulations. We extend the standard genus analysis by examinin g the influence of sampling noise on the genus curve and introducing a statistic able to quantify the amount of phase correlation present in the density field, the amplitude drop of the genus compared to a Gaus sian field with identical power spectrum. The results for PSCz are con sistent with the hypothesis of random-phase initial conditions. In par ticular, no strong phase correlation is detected on scales ranging fro m 10 to 32 h(-1) Mpc, whereas there is a positive detection of phase c orrelation at smaller scales. Among the simulations, phase correlation s are detected in all models at small scales, albeit with different st rengths, When scaled to a common normalization, the amplitude drop dep ends primarily on the shape of the power spectrum. We find that the co nstant-bias standard CDM model can be ruled out at high significance, because the shape of its power spectrum is not consistent with PSCz. T he other CDM models with more large-scale power all fit the PSCz data almost equally well, with a slight preference for a high-density tau C DM model.