An algorithm to build mock galaxy catalogues using MICE simulations

TL;DR

The paper introduces an economical hybrid approach that merges halo occupation distribution (HOD) and subhalo abundance matching (SHAM) to populate MICE halo catalogues with galaxies, producing mock catalogues that reproduce the SDSS luminosity function, colour distribution, and clustering as a function of luminosity and colour. Central galaxies are set by a simple HOD with one central per halo above $M_{min}$ and a Poisson-distributed satellite population with a mass-dependent mean $\langle N_{sat}\rangle = (M_h/M_1)^{\alpha}$, where $\alpha=1$ and $M_1$ depends smoothly on $M_{min}$ through a calibrated function $f_{M_1}$; SHAM then provides central luminosities via the $M_h$–$L_{gal}$ relation, while satellites are drawn from the satellite LF with additional scatter applied to the central luminosities to control large-scale clustering. Satellite positions are tuned using a concentrated NFW profile (and triaxial haloes) to match the one-halo term, and satellites/centrals are assigned colours through a three-Gaussian model (red/green/blue) with luminosity-dependent fractions to reproduce the observed CMD and colour-dependent clustering. The resulting MICECAT v1.0 mock catalogue accurately matches the observed LF, CMD, and clustering across luminosity and colour, providing a scalable tool for survey design and interpretation; the authors also outline future extensions to lightcones and further refinements.

Abstract

We present a method to build mock galaxy catalogues starting from a halo catalogue that uses halo occupation distribution (HOD) recipes as well as the subhalo abundance matching (SHAM) technique. Combining both prescriptions we are able to push the absolute magnitude of the resulting catalogue to fainter luminosities than using just the SHAM technique and can interpret our results in terms of the HOD modelling. We optimize the method by populating with galaxies friends-of-friends dark matter haloes extracted from the Marenostrum Institut de Ciències de l'Espai (MICE) dark matter simulations and comparing them to observational constraints. Our resulting mock galaxy catalogues manage to reproduce the observed local galaxy luminosity function and the colour-magnitude distribution as observed by the Sloan Digital Sky Survey. They also reproduce the observed galaxy clustering properties as a function of luminosity and colour. In order to achieve that, the algorithm also includes scatter in the halo mass - galaxy luminosity relation derived from direct SHAM and a modified NFW mass density profile to place satellite galaxies in their host dark matter haloes. Improving on general usage of the HOD that fits the clustering for given magnitude limited samples, our catalogues are constructed to fit observations at all luminosities considered and therefore for any luminosity subsample. Overall, our algorithm is an economic procedure of obtaining galaxy mock catalogues down to faint magnitudes that are necessary to understand and interpret galaxy surveys.

Figures (19)

• Figure 1: $M_{min}$ and $M_{1}$ HOD parameters as a function of the luminosity threshold of galaxy samples. The red solid line is the fit we set to model $M_{1}$ as a function of $M_{min}$. The blue squares and triangles are the HOD parameters found by Zehavi:05 while the green squares and triangles refer to the parameters found by Zehavi:11. The dashed blue line is the $M_{min}-M_{r}$ found by Zehavi:05 scaled by a factor of 23, and the dashed green one is the same relation found by Zehavi:11 but scaled by a factor of 17.
• Figure 2: Relation between central galaxy luminosities and their host halo mass showing the scatter applied in the halo mass-central luminosity relation. In the figure a sample of central and satellite galaxies from a simulation of box-size $L_{box}=307.2$ Mpc/h is shown. The scatter is applied for galaxies brighter than $M^{*}_{r}=-20.44$.
• Figure 3: Luminosity function of a $L=302.7$ Mpc/h sub-box of the mock galaxy catalogue. The blue solid line is the best-fitting Schechter function to the SDSS data shifted to z=0.1. The black, blue and red triangles are the luminosity function of total (central+satellite), central and satellite galaxies of the catalogue respectively. The error bars are derived as Poisson errors.
• Figure 4: Mean value of the real space 2-point correlation (top panels) and scale dependent linear halo bias (bottom panels). Different colours refer to seven different halo mass thresholds (left panels) and three halo mass bins (right panels). They have been computed using the $10^{3}$ volumes with box-size $L_{box}= 307.2$ Mpc/h. The error bars are the errors on the mean value between volumes. In the two top panels, the dashed black line is the 2-point correlation function of the linear MICE correlation function calculated as the FT of the linear MICE power spectrum, while the black dotted line is the non-linear MICE correlation function.
• Figure 5: Linear bias at large scales for the halo mass thresholds and halo mass bins using the value of the correlation function at $r = 16.9$ Mpc/h. The black solid line is the expression of the halo bias given by Manera:10 and using the parameters found by Crocce:10 for the MICE simulations. The blue solid line is the cumulative bias derived by integrating equation \ref{['eq:Warren bias']}.