An excursion set model of the cosmic web : The abundance of sheets , filaments and halos

We discuss an analytic approach for modeling structure formation in sheets, filaments and knots. This is accomplished by combining models of triaxial collapse with the excursion set approach: sheets are defined as objects which have collapsed along only one axis, filaments have collapsed along two axes, and halos are objects in which triaxial collapse is complete. In the simplest version of this approach, which we develop here, large scale structure shows a clear hierarchy of morphologies: the mass in large-scale sheets is partitioned up among lower mass filaments, which themselves are made-up of still lower mass halos. Our approach provides analytic estimates of the mass fraction in sheets, filaments and halos, and its evolution, for any background cosmological model and any initial fluctuation spectrum. In the currently popular ΛCDM model, our analysis suggests that more than 99% of the cosmic mass is in sheets, and 72% in filaments, with mass larger than 10M⊙ at the present time. For halos, this number is only 46%. Our approach also provides analytic estimates of how halo abundances at any given time correlate with the morphology of the surrounding large-scale structure, and how halo evolution correlates with the morphology of large scale structure. Subject headings: structure formation: ellipsoidal collapse – mass functions: sheets, filaments, halos