RECOVERING THE REAL DENSITY FIELD OF GALAXIES FROM REDSHIFT SPACE

This paper proposes a number of methods for recovering the true, real- space large-scale density distributions from redshift data sets. On th e largest scales, the effects of peculiar velocities is to compress th e galaxy clustering along the line of sight and consequently the densi ty gradient in the radial direction is enhanced in comparison with the density gradient perpendicular to the line of sight. We calculate the relation between the density gradients in real and redshift space in the linear regime and show that it is a simple function of the density parameter, Omega By considering the anisotropy of density gradients i n redshift space it is possible, in principle, to obtain information a bout the value of Omega. Using N-body simulations we examine different methods for correcting the effects of large-scale velocities to obtai n the true density distributions. We derive the peculiar velocity fiel d from the redshift data and iterate to place each galaxy at a distanc e consistent with its measured redshift and its derived velocity. Line ar theory, as well as second-order solutions for the peculiar velocity field are tested. The density distributions in low-density regions pr edicted by both linear theory and second-order theory are similar, and in good agreement with the true density field in the simulation. The use of the second-order corrections improves the prediction of the den sity field in high-density regions.