Filamentary structure from Gaussian fluctuations using the adhesion approximation

We use the Shandarin-Zel'dovich adhesion formalism to study the origin of large-scale filamentary structure in Gaussian realizations of various fluctuation power spectra. Artificial viscosity is used to halt the transverse motion of particles in filaments. Time evolution is simulated using the explicit solution of the Burgers equation at each time step. This amplifies the filaments and helps the comparison between the models. The filamentary structure is quantified using the measure of Vishniac. We test in two dimensions the power laws P ∝ k^m, m = -2, -1, 0, 1 and the spectra of neutrino and cold dark matter models. Our results confirm earlier claims by Shandarin and Zel'dovich that filaments form on scales well above any initial coherence length for m = -1 and even for m = 0 (equivalent to n = -2 and n = -1 in three dimensions) from high σ, large-scale waves. The filaments are not an artifact of poor representation in k-space. It remains to be seen, following Peebles, whether these filaments survive the nonlinear effects of gravity on small scales.