EZmocks: extending the Zel'dovich approximation to generate mock galaxy catalogues with accurate clustering statistics

TL;DR

EZmocks addresses the need for massive mock galaxy catalogues with accurate clustering statistics without resorting to computationally expensive N-body runs. By combining the Zel'dovich approximation with PDF mapping, scatter, density thresholding, BAO enhancement, small-scale power boosts, velocity modelling, and mass assignment, the method reproduces one-, two-, and three-point statistics with high fidelity ($\lesssim 1\%$ for the power spectrum up to $k\approx0.55\,h\mathrm{Mpc}^{-1}$ and $\lesssim10\,h^{-1}\mathrm{Mpc}$ for the real-space correlation function; bispectrum within ~20%). The approach achieves this with substantial speed: a single EZmock on a $960^3$ grid takes under 5 minutes on one node, enabling generation of thousands of mocks for covariance estimation and survey forecasting. EZmocks thus offer a practical, scalable alternative to full N-body simulations, providing accurate clustering statistics at a fraction of the computational cost while remaining complementary to gravity-based methods. The framework is validated against a high-resolution reference (BigMD) and demonstrates smooth mass-bias behavior, making it suitable for large-scale structure analyses and cosmological parameter inference.

Abstract

We present a new methodology to generate mock halo or galaxy catalogues, which have accurate clustering properties, nearly indistinguishable from full $N$-body solutions, in terms of the one-point, two-point, and three-point statistics. In particular, the agreement is remarkable, within $1\%$ up to $k=0.55$ $h$Mpc$^{-1}$ and down to $r=10$ $h^{-1}$Mpc, for the power spectrum and two-point correlation function respectively, while the bispectrum agrees in general within $20\%$ for different scales and shapes. Our approach is based on the Zel'dovich approximation, however, effectively including with the simple prescriptions the missing physical ingredients, and stochastic scale-dependent, non-local and nonlinear biasing contributions. The computing time and memory required to produce one mock is similar to that using the log-normal model. With high accuracy and efficiency, the effective Zel'dovich approximation mocks (EZmocks) provide a reliable and practical method to produce massive mock galaxy catalogues for the analysis of large-scale structure measurements.

Figures (6)

• Figure 1: The probability of each halo in the BigMD catalogue to be collected by one of the five sub-catalogues, represented by different colours. $M_{halo}$ is the halo mass in units of solar mass. These sub-catalogues are prepared to construct the EZmock including masses. The divisions are chosen, so that the sub-catalogues have a comparable number of haloes.
• Figure 2: Halo probability distribution functions for EZmock (solid red line) and BigMD (dashed black line). The PDFs are computed using nearest-grid-point (NGP) with a grid of $960^3$.
• Figure 3: Left panel: monopole of the power spectrum in real space. Right panel: monopole and quadrupole of the power spectrum in redshift-space.
• Figure 4: Left panel: monopole of the two-point correlation function in real space. Right panel: monopole and quadrupole of the two-point correlation function in redshift-space.
• Figure 5: Bispectrum in real and redshift-space. The configurations including $k_2=2k_1=0.1$, $k_2=2k_1=0.2$, $k_2=2k_1=0.3$, and $k_2=2k_1=0.4$$\,h\,{\rm Mpc}^{-1}$ are denoted in the panels.