# Generating Log-normal Mock Catalog of Galaxies in Redshift Space

## TL;DR

This paper introduces a public code for generating log-normal mock galaxy catalogs in redshift space, accurately reproducing key statistical properties and highlighting the importance of non-linear effects in redshift-space distortions.

## Contribution

The paper presents a novel method for creating log-normal mock galaxy catalogs that incorporate non-linear redshift-space distortions without relying on random velocities.

## Key findings

- The catalog's two-point correlation function and power spectrum match input data precisely.
- Linear bias in power spectrum does not imply linear bias in density contrasts.
- Non-linear Jacobian effects dominate small-scale redshift-space distortions.

## Abstract

We present a public code to generate a mock galaxy catalog in redshift space assuming a log-normal probability density function (PDF) of galaxy and matter density fields. We draw galaxies by Poisson-sampling the log-normal field, and calculate the velocity field from the linearised continuity equation of matter fields, assuming zero vorticity. This procedure yields a PDF of the pairwise velocity fields that is qualitatively similar to that of N-body simulations. We check fidelity of the catalog, showing that the measured two-point correlation function and power spectrum in real space agree with the input precisely. We find that a linear bias relation in the power spectrum does not guarantee a linear bias relation in the density contrasts, leading to a cross-correlation coefficient of matter and galaxies deviating from unity on small scales. We also find that linearising the Jacobian of the real-to-redshift space mapping provides a poor model for the two-point statistics in redshift space. That is, non-linear redshift-space distortion is dominated by non-linearity in the Jacobian. The power spectrum in redshift space shows a damping on small scales that is qualitatively similar to that of the well-known Fingers-of-God (FoG) effect due to random velocities, except that the log-normal mock does not include random velocities. This damping is a consequence of non-linearity in the Jacobian, and thus attributing the damping of the power spectrum solely to FoG, as commonly done in the literature, is misleading.