Filament and shape statistics: a quantitative comparison of cold + hot

A new class of geometric statistics for analyzing galaxy catalogs ispresented. Filament statistics quantify filamentarity and planarity in largescale structure in a manner consistent with catalog visualizations. Thesestatistics are based on sequences of spatial links which follow localhigh-density structures. From these link sequences we compute the discretecurvature, planarity, and torsion. Filament statistics are applied to CDM andCHDM ($\Omega_\nu = 0.3$) simulations of Klypin \etal (1996), the CfA1-likemock redshift catalogs of Nolthenius, Klypin and Primack (1994, 1996), and theCfA1 catalog. We also apply the moment-based shape statistics developed byBabul \& Starkman (1992), Luo \& Vishniac (1995), and Robinson \& Albrecht(1996) to these same catalogs, and compare their robustness and discriminatorypower versus filament statistics. For 100 Mpc periodic simulation boxes ($H_0 =50$ km s$^{-1}$ Mpc$^{-1}$), we find discrimination of $\sim 4\sigma$ (where$\sigma$ represents resampling errors) between CHDM and CDM for selectedfilament statistics and shape statistics, including variations in the galaxyidentification scheme. Comparing the CfA1 data versus the models does not yielda conclusively favored model; no model is excluded at more than a $\sim2\sigma$ level for any statistic, not including cosmic variance which couldfurther degrade the discriminatory power. We find that CfA1 discriminatesbetween models poorly mainly due to its sparseness and small number ofgalaxies, not due to redshift distortion, magnitude limiting, or geometricaleffects. We anticipate that the proliferation of large redshift surveys andsimulations will enable the statistics presented here to provide robustdiscrimination between large-scale structure in various cosmological models.Comment: 17 pages, 12 figures, LaTex (uses mn.sty). Accepted by MNRA