An accurate tool for the fast generation of dark matter halo catalogues.

We present a new parallel implementation of the PINpointing Orbit Crossing-Collapsed HIerarchical Objects (PINOCCHIO) algorithm, a quick tool, based on Lagrangian Perturbation Theory, for the hierarchical build-up of dark matter (DM) haloes in cosmological volumes. To assess its ability to predict halo correlations on large scales, we compare its results with those of an N-body simulation of a 3 h−1 Gpc box sampled with 20483 particles taken from the MICE suite, matching the same seeds for the initial conditions. Thanks to the Fastest Fourier Transforms in the West (FFTW) libraries and to the relatively simple design, the code shows very good scaling properties. The CPU time required by PINOCCHIO is a tiny fraction (∼1/2000) of that required by the MICE simulation. Varying some of PINOCCHIO numerical parameters allows one to produce a universal mass function that lies in the range allowed by published fits, although it underestimates the MICE mass function of Friends-of-Friends (FoF) haloes in the high-mass tail. We compare the matter–halo and the halo–halo power spectra with those of the MICE simulation and find that these two-point statistics are well recovered on large scales. In particular, when catalogues are matched in number density, agreement within 10 per cent is achieved for the halo power spectrum. At scales k > 0.1 h Mpc−1, the inaccuracy of the Zel’dovich approximation in locating halo positions causes an underestimate of the power spectrum that can be modelled as a Gaussian factor with a damping scale of d = 3 h−1 Mpc at z = 0, decreasing at higher redshift. Finally, a remarkable match is obtained for the reduced halo bispectrum, showing a good description of non-linear halo bias. Our results demonstrate the potential of PINOCCHIO as an accurate and flexible tool for generating large ensembles of mock galaxy surveys, with interesting applications for the analysis of large galaxy redshift surveys.