The oscillating behavior of the pair correlation function in galaxies

The pair correlation function (PCF) for galaxies presents typical oscillations in the range 20-200 Mpc/h which are named baryon acoustic oscillation (BAO). We first review and test the oscillations of the PCF when the 2D/3D vertexes of the Poissonian Voronoi Tessellation (PVT) are considered. We then model the behavior of the PCF at a small scale in the presence of an auto gravitating medium having a line/plane of symmetry in 2D/3D. The analysis of the PCF in an astrophysical context was split into two, adopting a non-Poissonian Voronoi Tessellation (NPVT). We first analyzed the case of a 2D cut which covers few voids and a 2D cut which covers approximately 50 voids. The obtained PCF in the case of many voids was then discussed in comparison to the bootstrap predictions for a PVT process and the observed PCF for an astronomical catalog. An approximated formula which connects the averaged radius of the cosmic voids to the first minimum of the PCF is given.