HIGH-RESOLUTION SIMULATION OF DEEP PENCIL BEAM SURVEYS - ANALYSIS OF QUASI-PERIODICITY

We carry out pencil beam constructions in a high-resolution simulation of the large-scale structure of galaxies. The initial density fluctuations are taken to have a truncated power spectrum. All the models have OMEGA = 1. As an example we present the results for the case of ''Hot-Dark-Matter'' (HDM) initial conditions with scale-free n = 1 power index on large scales as a representative of models with sufficient large-scale power. We use an analytic approximation for particle trajectories of a self-gravitating dust continuum and apply a local dynamical biasing of volume elements to identify luminous matter in the model. Using this method, we are able to resolve formally a simulation box of 1200h-1Mpc (e.g. for HDM initial conditions) down to the scale of galactic halos using 2160 3 particles. We consider this as the minimal resolution necessary for a sensible simulation of deep pencil beam data. Pencil beam probes are taken for a given epoch using the parameters of observed beams. In particular, our analysis concentrates on the detection of a quasi-periodicity in the beam probes using several different methods. The resulting beam ensembles are analyzed statistically using number distributions, pair-count histograms, unnormalized pair-counts, power spectrum analysis and trial-period folding. Periodicities are classified according to their significance level in the power spectrum of the beams. The simulation is designed for application to parameter studies which prepare future observational projects. We find that a large percentage of the beams show quasi-periodicities with periods which cluster at a certain length scale. The periods found range between one and eight times the cutoff length in the initial fluctuation spectrum. At significance levels similar to those of the data of Broadhurst et al. (1990), we find about 15% of the pencil beams to show periodicities, about 30% of which are around the mean separation of rich clusters, while the distribution of scales reaches values of more than 200h-1Mpc. The detection of periodicities larger than the typical void size must not be due to missing of ''walls'' (like the so called ''Great Wall'' seen in the CfA catalogue of galaxies), but can be due to different clustering properties of galaxies along the beams.