Genus statistics for structure formation with topological defects

Abstract

We study the efficiency of genus statistics in differentiating between different models of structure formation. Simple models which reproduce the salient features of the structure seeded by topological defects are examined. We consider accretion onto static point masses, modeling slow-moving cosmic string loops or other primordial point-like sources. Filamentary structures and wakes are considered as models of the structures seeded by slow and fast moving string, respectively. Comparison is made with predictions of genus statistics for Gaussian fluctuations and with genus curves obtained by the CfA survey. A generic class of density models with wakes and filaments is found to provide results comparable or better than Gaussian models for this suite of tests.