CONTROLLED EXPERIMENTS IN COSMOLOGICAL GRAVITATIONAL CLUSTERING

We systematically study gravitational instability in three dimensions from power-law initial spectra (n = +1, 0, -1, -2, -3) with and withou t spectral cutoffs. We emphasize the study of nonlinear effects and me asures of nonlinearity, separating those effects that result from shor t and long waves in the initial conditions. We confirm the existence o f second-generation pancakes, which form near the onset of nonlinearit y on a given scale k(nl). Although inhomogeneous, they create a strong visual signal of filamentarity and correspond to the location of Zel' dovich pancakes when models with spectra truncated at k(nl) have colla psed. We verify by cross correlation that there is a continuous transi tion from hierarchial to pancake models as power on large scales becom es relatively more important (going from n = +1 to -3). This is a natu ral explanation for the appearance of filamentary structure in models such as cold dark matter, since the spectrum in this model has negativ e slope in the range of interest. When there is a high-k cutoff at k(c ) in the primordial power spectrum, the existence of this cutoff is al most undetectable in the correlation function by the time clustering h as grown so that k(nl) < 0.5k(c), although the difference is still vis ually apparent; it therefore depends on phase correlations. We test an d show that parameters which identify the nonlinear scale in the mass distributions such as R(G) (sigma(rho) = 1 in a Gaussian window) or R( T) (sigma(rho) = 1 in a top-hat window) or the correlation length R(c) [xi(R(c)) = 1] are in a unique relationship with each other, independe ntly of the power index and of the scale of the cutoff R(T) almost-equ al-to 2R(G) almost-equal-to 4/3R(c). All of them scale quite well with the theoretical scale 1/k(nl) in the n = +1, 0, and -1 models but do not in the n = -2 and -3 models. By explicit comparison of smoothed in itial conditions with smoothed envelope models, we reconfirm that to e xtrapolate directly by linear theory from Gaussian initial conditions one must smooth over a scale considerably larger than any nonlinearity (R(G), R(T), R(c) or 1/k(nl)). If one demands a modest 25% correspond ence between the smoothed nonlinear and initial linear density fields the scale of smoothing R25 must exceed R(G) at least 5 times if the in itial slope is n = -1. We found that R25 scales very poorly with both 1/k(nl) and R(G) (or R(T) or R(c)) instead it scales very well with th e rms displacement of particles from unperturbed positions d(rms) = [( r(i)-q(i)BAR)2]1/2:R25 almost-equal-to 1.65d(rms).