Evidence for Filamentarity in the Las Campanas Redshift Survey

We apply Shape—nders, statistical measures of ii shape ˇˇ constructed from two-dimensional partial Minkowski functionals, to study the degree of —lamentarity in the Las Campanas Redshift Survey (LCRS). In two dimensions, three Minkowski functionals characterize the morphology of an object; these are its perimeter (L ), area (S), and genus. Out of L and S a single dimensionless Shape—nder sta- tistic, F, can be constructed (0 "F " 1). The statistic F acquires extreme values on a circle (F \ 0) and a —lament (F \ 1). Using F, we quantify the extent of —lamentarity in the LCRS by comparing our results with a Poisson distribution having similar geometrical properties and the same selection function as the survey. Our results unambiguously demonstrate that the LCRS displays a high degree of —lamen- tarity in both the northern and southern Galactic sections, in general agreement with the visual appear- ance of the catalog. It is well known that gravitational clustering from Gaussian initial conditions gives rise to the development of non-Gaussianity, re—ected in the formation of a network-like —lamentary structure on supercluster scales. Consequently, the fact that the smoothed LCRS catalog shows proper- ties consistent with those of a Gaussian random —eld,whereas the unsmoothed catalog demonstrates the presence of —lamentarity, lends strong support to the conjecture that the large-scale clustering of galaxies is driven by gravitational instability. Subject headings: galaxies: clusters: generallarge-scale structure of universemethods: statistical ¨ surveys