Genus statistics of the Virgo N-body simulations and the 1.2-Jy redshift survey

We study the topology of the Virgo N-body simulations and compare it with the 1.2-Jy redshift survey of IRAS galaxies by means of the genus statistic. Four high-resolution simulations of variants of the CDM cosmology are considered: a flat standard model (SCDM), a variant of it with higher large-scale power (τCDM), and two low-density universes, one open (OCDM, Ω0 = 0.3) and one flat (ΛCDM, Ω0 = 0.3, Λ 0.7). In all cases, the initial fluctuation amplitudes are chosen so that the simulations approximately reproduce the observed abundance of rich clusters of galaxies at the present day. The fully sampled N-body simulations are examined down to strongly non-linear scales, both with spatially fixed smoothing and with an adaptive smoothing technique. While the τCDM, ΛCDM and OCDM simulations have very similar genus statistics in the regime accessible to fixed smoothing, they can be separated with adaptive smoothing at small mass scales. In order to compare the N-body models with the 1.2-Jy survey, we extract large ensembles of mock catalogues from the simulations. These mock surveys are used to test for various systematic effects in the genus analysis and to establish the distribution of errors of the genus curve. We find that a simple multivariate analysis of the genus measurements is compromised both by non-Gaussian distributed errors and by noise that dominates the covariance matrix. We therefore introduce a principal components analysis of the genus curve. With a likelihood ratio test we find that the 1.2-Jy data favour the ΛCDM, τCDM and OCDM models compared with SCDM. When genus measurements for different smoothing scales are combined, the SCDM model can be excluded at a 99 per cent confidence level, while the other three models fit the 1.2-Jy data well. These results are unlikely to be significantly modified if galaxies are biased tracers of the mass, provided that biasing preserves a monotonic relation between galaxy density and mass density.