Numerical simulations of the Lyman α forest – a comparison of gadget-2 and enzo

We compare simulations of the Lyman α forest performed with two different hydrodynamical codes, gadget-2 and enzo . A comparison of the dark matter power spectrum for simulations run with identical initial conditions show differences of 1–3 per cent at the scales relevant for quantitative studies of the Lyman α forest. This allows a meaningful comparison of the effect of the different implementations of the hydrodynamic part of the two codes. Using the same cooling and heating algorithm in both codes, the differences in the temperature and the density probability distribution function are of the order of 10 per cent. The differences are comparable to the effects of box size and resolution on these statistics. When self-converged results for each code are taken into account, the differences in the flux power spectrum – the statistics most widely used for estimating the matter power spectrum and cosmological parameters from Lyman α forest data – are about 5 per cent. This is again comparable to the effects of box size and resolution. Numerical uncertainties due to a particular implementation of solving the hydrodynamic or gravitational equations appear therefore to contribute only moderately to the error budget in estimates of the flux power spectrum from numerical simulations. We further find that the differences in the flux power spectrum for enzo simulations run with and without adaptive mesh refinement are also of the order of 5 per cent or smaller. The latter require 10 times less CPU time making the CPU time requirement similar to that of a version of gadget-2 that is optimized for Lyman α forest simulations.     

Modelling galaxy clustering by colour

We extend the mass-halo formalism for analytically generating power spectra to allow for the different clustering behaviour observed in galaxy subpopulations. Although applicable to other separations, we concentrate our methods on a simple separation by rest-frame colour into 'red' and 'blue' subpopulations through modifications to the 〈 N 〉( M ) relations and halo distribution functions for each of the subpopulations. This sort of separation is within the capabilities of the current generations of simulations as well as galaxy surveys, suggesting a potentially powerful observational constraint for current and future simulations. In anticipation of this, we demonstrate the sensitivity of the resulting power spectra to the choice of model parameters.     

The three-point function in large-scale structure – I. The weakly non-linear regime in N-body simulations

This paper presents a comparison of the predictions for the two- and three-point correlation functions of density fluctuations, ξ and ζ , in gravitational perturbation theory (PT) against large cold dark matter (CDM) simulations. This comparison is made possible for the first time on large weakly non-linear scales (>10  h ⁻¹ Mpc) thanks to the development of a new algorithm for estimating correlation functions for millions of points in only a few minutes. Previous studies in the literature comparing the PT predictions of the three-point statistics with simulations have focused mostly on Fourier space, angular space or smoothed fields. Results in configuration space, such as those presented here, were limited to small scales where leading-order PT gives a poor approximation. Here we also propose and apply a method for separating the first-order and subsequent contributions to PT by combining different output times from the evolved simulations. We find that in all cases there is a regime where simulations do reproduce the leading-order (tree-level) predictions of PT for the reduced three-point function   Q ₃∼ ζ / ξ ²  . For steeply decreasing correlations (such as the standard CDM model) deviations from the tree-level results are important even at relatively large scales, ≃20 Mpc  h ⁻¹. On larger scales ξ goes to zero and the results are dominated by sampling errors. In more realistic models (such as the ΛCDM cosmology) deviations from the leading-order PT become important at smaller scales   r ≃10 Mpc  h ^-1  , although this depends on the particular three-point configuration. We characterize the range of validity of this agreement and show the behaviour of the next-order (one-loop) corrections.