ICE-COLA: Towards fast and accurate synthetic galaxy catalogues optimizing a quasi $N$-body method

Next generation galaxy surveys demand the development of massive ensembles of galaxy mocks to model the observables and their covariances, what is computationally prohibitive using $N$-body simulations. COLA is a novel method designed to make this feasible by following an approximate dynamics but with up to 3 orders of magnitude speed-ups when compared to an exact $N$-body. In this paper we investigate the optimization of the code parameters in the compromise between computational cost and recovered accuracy in observables such as two-point clustering and halo abundance. We benchmark those observables with a state-of-the-art $N$-body run, the MICE Grand Challenge simulation (MICE-GC). We find that using 40 time steps linearly spaced since $z_i \sim 20$, and a force mesh resolution three times finer than that of the number of particles, yields a matter power spectrum within $1\%$ for $k \lesssim 1\,h {\rm Mpc}^{-1}$ and a halo mass function within $5\%$ of those in the $N$-body. In turn the halo bias is accurate within $2\%$ for $k \lesssim 0.7\,h {\rm Mpc}^{-1}$ whereas, in redshift space, the halo monopole and quadrupole are within $4\%$ for $k \lesssim 0.4\,h {\rm Mpc}^{-1}$. These results hold for a broad range in redshift ($0 < z < 1$) and for all halo mass bins investigated ($M > 10^{12.5} \, h^{-1} \, {\rm M_{\odot}}$). To bring accuracy in clustering to one percent level we study various methods that re-calibrate halo masses and/or velocities. We thus propose an optimized choice of COLA code parameters as a powerful tool to optimally exploit future galaxy surveys.