Generating log-normal mock catalog of galaxies in redshift space

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.

Comparing approximate methods for mock catalogues and covariance matrices – I. Correlation function

“…The log-normal mocks were produced using the public code presented in Agrawal et al (2017), which models the matter and halo density fields as log-normal fields, and generates the velocity field from the matter density field, using the linear continuity equation.…”

“…Also note, that because halos in this prescription correspond to just discrete points, we do not assign any mass to them. An effective bias relation can still be established using the cross-correlation between the halo and matter fields, or using the input clustering statistics (Agrawal et al (2017)).…”

The Impact of Line Misidentification on Cosmological Constraints from Euclid and Other Spectroscopic Galaxy Surveys

“…Comparison of variance of monopole power spectrum, C 00 for an [OIII] survey contaminated with Hα with fractional contamination fc = 0.2. Green crosses correspond to sample variance measured in bins of width ∆k = 0.005 h Mpc −1 from 500 log-normal simulations using code described by Agrawal et al (2017) with interlopers remapped by-hand as described in the text. Solid lines show results of analytic calculations (Section 2).…”

“…B. COMPARISON WITH LOG-NORMAL SIMULATIONS Here we provide some more details of the comparison with mock galaxy catalogs from log-normal simulations using publicly-available code 14 described by Agrawal et al (2017). The code generates catalogs of three-dimensional galaxy position and velocity vectors by Poisson sampling the density field given an input matter power spectrum, galaxy bias, mean ELG density, and choice of resolution scale, using Fast Fourier Transform (FFT).…”

“…Note that some coupling exists between multipoles of the power spectrum computed from the simulations, as described in Appendix D.2.3 of Agrawal et al (2017). Recovering an unbiased estimate for each multipole to compare with our analytic calculations then requires a deconvolution with a multipole mixing matrix.…”