AN ALTERNATIVE APPROACH TO THE FINGER OF GOD IN LARGE SCALE STRUCTURES

Abstract

It is generally accepted that linear theory of growth of structure under gravity produces a squashed structure in the two-point correlation function (2PCF) along the line of sight (LoS). The observed radial spread out structure known as Finger of God (FoG) is attributed to non-linear effects. We argue that the squashed structure associated with the redshift-space (s−) linear theory 2PCF is obtained only when this function is displayed in real-space (r−), or when the mapping from r − to s−space is approximated. We solve for the mapping function s(r) that allows us to display thes −space 2PCF in a grid in s−space, by using plane of the sky projections of the r − and s − 2PCFs. Even in the simplest case of a linear Kaiser spectrum with a conservative power-law r−space 2PCF, a structure quite similar to the FoG is observed in the small scale region, while in the large scale the expected squashed structure is obtained. This structure depends on only three parameters.