Extending the halo mass resolution of N-body simulations

Abstract

We present a scheme to extend the halo mass resolution of N -body simulations of the hierarchical clustering of dark matter. The method uses the density field of the simulation to predict the number of sub-resolution dark matter haloes expected in different regions. The technique requires as input the abundance of haloes of a given mass and their average clustering, as expressed through the linear and higher order bias factors. These quantities can be computed analytically or, more accurately, derived from a higher resolution simulation as done here. Our method can recover the abundance and clustering in real-and redshift-space of haloes with mass below ∼ 7.5 × 10 13 h −1 M ⊙ at z = 0 to better than 10%. We demonstrate the technique by applying it to an ensemble of 50 low resolution, largevolume N -body simulations to compute the correlation function and covariance matrix of luminous red galaxies (LRGs). The limited resolution of the original simulations results in them resolving just two thirds of the LRG population. We extend the resolution of the simulations by a factor of 30 in halo mass in order to recover all LRGs. With existing simulations it is possible to generate a halo catalogue equivalent to that which would be obtained from a N -body simulation using more than 20 trillion particles; a direct simulation of this size is likely to remain unachievable for many years. Using our method it is now feasible to build the large numbers of high-resolution large volume mock galaxy catalogues required to compute the covariance matrices necessary to analyse upcoming galaxy surveys designed to probe dark energy.

A lightcone catalogue from the Millennium-XXL simulation

“…Other methods for augmenting the halo catalogue exist (e.g. de la Torre & Peacock 2013; Angulo et al 2014;Benson et al 2016), but we find that this simple method is able to bring the dN/dz of galaxies in the catalogue into better agreement with the measured dN/dz from GAMA, while only having a very small effect on the measured clustering.…”

“…However, there are approaches which can augment the resolution of the simulation merger trees (e.g. de la Torre & Peacock 2013;Angulo et al 2014;Benson et al 2016). The SHAM prescription assigns galaxies to subhaloes, requiring a complete subhalo catalogue.…”

The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: mock galaxy catalogues for the BOSS Final Data Release

“…A new generation of methods that can meet these high requirements have been developed during the past two years, in particular, PATCHY (Kitaura, Yepes & Prada 2014), QPM (White et al 2014), and EZMOCKS (Chuang et al 2015a). The key concept exploited by these methods is to rely only on the large-scale density field obtained from approximate gravity solvers and use biasing prescriptions to populate it with mock galaxies, in a similar way to the methods proposed to augment the resolution of N-body simulations (de la Torre & Peacock 2013;de la Torre et al 2013;Angulo et al 2014;Ahn et al 2015). One should however be careful, as computing an accurate dark matter field is a necessary, but not sufficient condition to reproduce the correct halo/galaxy three-point statistics.…”

Photon number conservation and the large-scale 21 cm power spectrum in semi-numerical models of reionization

“…Ideally, one would use a calibration of the conditional mass function needed above directly from high-resolution N -body simulations (Angulo et al 2014). In this work, we use the approximation discussed by Seehars et al (2016) which uses the conditional mass function obtained from the ellipsoidal collapse model (Sheth & Tormen 2002).…”