Genus statistics of the Virgo N-body simulations and the 1.2-Jy redshift survey
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abstract
We study the topology of the Virgo N-body simulations and compare it to 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 more large-scale power (tCDM),
and two low density universes, one open (OCDM) and one flat (LCDM). The fully
sampled N-body simulations are examined down to strongly nonlinear scales, both
with spatially fixed smoothing, and with an adaptive smoothing technique. While
the tCDM, LCDM, 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 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
favours the LCDM, tCDM and OCDM models compared to SCDM. When genus
measurements for different smoothing scales are combined, the SCDM model can be
excluded at a 99% confidence level, while the other three models fit the 1.2-Jy
data well. (abridged)
