A QUANTITATIVE MEASURE OF STRUCTURE IN THE 3-DIMENSIONAL GALAXY DISTRIBUTION - SHEETS AND FILAMENTS

We introduce a set of structure functions, constructed to quantify the relative prevalence of filamentary, sheetlike and clumplike structures in a three-dimensional particle distribution. The functions are weighted averages of appropriately chosen combinations of the principal moments of inertia of the distribution within randomly placed spherical windows. To illustrate their response, the structure functions are applied to numerous idealized point distributions. We also demonstrate the response of the structure functions when applied to several simulations where structure arises from gravitational clustering of initial Gaussian random density fluctuations, characterized by power-law power spectra. The results illustrate, in a very preliminary way, the efficacy of our measures in detecting the morphology of large-scale structures in realistic galaxy distributions. We also discuss the use of density thresholds in order to amplify the signal of structures embedded in noisy environments.