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 w ith the 1.2-Jy redshift survey of IRAS galaxies by means of the genus statistic. Four high-resolution simulations of variants of the CDM cos mology are considered: a flat standard model (SCDM), a variant of it w ith higher large-scale power ( tau CDM), and two low-density universes , one open (OCDM, Omega(0) = 0.3) and one flat (Lambda CDM, Omega(0) = 0.3, Lambda = 0.7). In all cases, the initial fluctuation amplitudes are chosen so that the simulations approximately reproduce the observe d abundance of rich clusters of galaxies at the present day. The fully sampled N-body simulations are examined down to strongly non-linear s cales, both with spatially fixed smoothing and with an adaptive smooth ing technique. While the tau CDM, Lambda CDM and OCDM simulations have very similar genus statistics in the regime accessible to fixed smoot hing, they can be separated with adaptive smoothing at small mass scal es. In order to compare the N-body models with the 1.2-Jy survey, we e xtract large ensembles of mock catalogues from the simulations. These mock surveys are used to test for various systematic effects in the ge nus analysis and to establish the distribution of errors of the genus curve. We find that a simple multivariate analysis of the genus measur ements is compromised both by non-Gaussian distributed errors and by n oise that dominates the covariance matrix. We therefore introduce a pr incipal components analysis of the genus curve. With a likelihood rati o test we find that the 1.2-Jy data favour the Lambda CDM, tau CDM 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-J y data well. These results are unlikely to be significantly modified i f galaxies are biased tracers of the mass, provided that biasing prese rves a monotonic relation between galaxy density and mass density.