MEASUREMENT OF LARGE-SCALE AND SUPERLARGE-SCALE STRUCTURES OF THE UNIVERSE

Gravitational instability theory provides our physical understanding of how structure forms in the universe. The growth of the velocity held leads to the formation of filaments or chains of galaxies, which we shall term large-scale structure (LSS). As galaxies are not continuous tracers of structure, this leads us to introduce the concept of a ''broken network structure'' as a model of LSS. Furthermore, modulation by the gravitational potential results in ''voids'' containing regions of positive potential with boundaries of sheets or ''walls'' of rich filaments, which we shall identify as superlarge-scale structure (SLSS), with then a ''broken cellular structure'' as a model of SLSS. Observationally, large galaxy redshift surveys corroborate the theory by their striking visual evidence for such a structure. Thus, it would seem that the most basic physical measures of structure in the universe are simply the surface density of filaments, that is, the number intersecting unit area, and the size of ''cells.'' We introduce here a new simple method of analysis to measure these directly. As this present method deals with pencil beam surveys, instead of attempting to measure the cell size we measure the linear density of ''sheets,'' that is, the number intersecting a line of unit length. As the more frequent elements of SLSS are probably superclusters and rich filaments of galaxies, we shall simply term an element of SLSS a ''supercluster''; to a pencil beam survey such elements appear sheetlike. We test out the method using simple numerical simulations of such structure, as well as on simulations of Poisson and the geometric Soneira-Peebles hierarchical models, which clearly have no such structure. In an exploratory investigation of the method with real data, we apply it to the presently available deep pencil beam galaxy redshift surveys. We find for the mean surface density of filaments sigma(f) approximate to 0.45 x 10(-2) h(2) Mpc(-2), which corresponds to a mean separation of D-f approximate to 14 h(-1) Mpc, and for the mean linear density of ''sheets'' (superclusters) sigma(s) approximate to 0.02 h Mpc(-1), corresponding to a mean distance between superclusters of D-s approximate to 50 h(-1) Mpc. For the very deep surveys, we find instead D-s((2)) approximate to 130 h(-1) Mpc. If we take into account the low probability of approximate to 0.4 for a ''sheet'' to be detected in these surveys, the result also corresponds to a supercluster scale of approximate to 50 h(-1) Mpc. Finally, we consider the theoretical interpretation of these scales and discuss some of the possible observational problems and their future resolution.