FILAMENT AND SHAPE STATISTICS - A QUANTITATIVE COMPARISON OF COLD PLUS HOT AND COLD DARK-MATTER COSMOLOGIES VERSUS CFA1 DATA

A new class of geometric statistics for analysing galaxy catalogues is presented. Filament statistics quantify filamentarity and planarity i n large-scale structure in a manner consistent with catalogue visualiz ations. These statistics are based on sequences of spatial links which follow local high-density structures. From these link sequences we co mpute the discrete curvature, planarity, and torsion. Filament statist ics are applied to cold dark matter (CDM) and cold+hot dark matter (CH DM) (Ohm(v) = 0.3) simulations of Klypin et al., the CfA1-like mock re dshift catalogues of Nolthenius, Klypin & Primack, and the CfA1 catalo gue. We also apply the moment-based shape statistics developed by Babu l & Starkman, Luo & Vishniac and Robinson & Albrecht to these same cat alogues, and compare their robustness and discriminatory power versus filament statistics. For 100-Mpc periodic simulation boxes (H-0 = 50 k m s(-1) Mpc(-1)), we find discrimination of similar to 4 sigma (where sigma represents resampling errors) between CHDM and CDM for selected filament statistics and shape statistics, including variations in the galaxy identification scheme. Comparing the CfA1 data versus the model s does not yield a conclusively favoured model; no model is excluded a t more than a similar to 2 sigma level for any statistic, not includin g cosmic variance which could further degrade the discriminatory power . We find that CfA1 discriminates poorly between models, mainly becaus e of its sparseness and small number of galaxies, not as a result of r edshift distortion, magnitude limiting or geometrical effects. We anti cipate that the proliferation of large redshift surveys and simulation s will enable the statistics presented here to provide robust discrimi nation between large-scale structure in various cosmological models.