Simulations of deep pencil-beam redshift surveys

We create mock pencil-beam redshift surveys from very large cosmological N -body simulations of two cold dark matter (CDM) cosmogonies, an Einstein–de Sitter model ( τ CDM) and a flat model with Ω₀=0.3 and a cosmological constant (ΛCDM). We use these to assess the significance of the apparent periodicity discovered by Broadhurst et al. Simulation particles are tagged as 'galaxies' so as to reproduce observed present-day correlations. They are then identified along the past light-cones of hypothetical observers to create mock catalogues with the geometry and the distance distribution of the Broadhurst et al. data. We produce 1936 (2625) quasi-independent catalogues from our τ CDM (ΛCDM) simulation. A couple of large clumps in a catalogue can produce a high peak at low wavenumbers in the corresponding one-dimensional power spectrum, without any apparent large-scale periodicity in the original redshift histogram. Although the simulated redshift histograms frequently display regularly spaced clumps, the spacing of these clumps varies between catalogues and there is no 'preferred' period over our many realizations. We find only a 0.72 (0.49) per cent chance that the highest peak in the power spectrum of a τ CDM (ΛCDM) catalogue has a peak-to-noise ratio higher than that in the Broadhurst et al. data. None of the simulated catalogues with such high peaks shows coherently spaced clumps with a significance as high as that of the real data. We conclude that in CDM universes, the regularity on a scale of ～130  h ^?1 Mpc observed by Broadhurst et al. has a priori probability well below 10^?3.