Evidence for Filamentarity in the Las Campanas Redshift Survey
We apply Shapefinders, statistical measures of “shape" constructed from two-dimensional partial Minkowski functionals, to study the degree of flamentarity 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 Shapefinder statistic, F, can be constructed (0¹ F ¹ 1). The statistic F acquires extreme values on a circle (F \ 0) and a filament (F \ 1). Using F, we quantify the extent of filamentarity 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 filamentarity in both the northern and southern Galactic sections, in general agreement with the visual appearance of the catalog. It is well known that gravitational clustering from Gaussian initial conditions gives rise to the development of non-Gaussianity, reflected in the formation of a network-like filamentary structure on supercluster scales. Consequently, the fact that the smoothed LCRS catalog shows properties consistent with those of a Gaussian random field,whereas the unsmoothed catalog demonstrates the presence of filamentarity, lends strong support to the conjecture that the large-scale clustering of galaxies is driven by gravitational instability.
Astrophysical Journal, Vol. 528, No. 21, January 2000, 21-29.