Second-order Lagrangian perturbation theory initial conditions for resimulations

We describe and test a new method for creating initial conditions for cosmological N-body dark matter simulations based on second-order Lagrangian perturbation theory (2lpt). The method can be applied to multimass particle distributions making it suitable for creating resimulation, or 'zoom' initial conditions. By testing against an analytic solution, we show that the method works well for a spherically symmetric perturbation with radial features ranging over more than three orders of magnitude in linear scale and 11 orders of magnitude in particle mass. We apply the method and repeat resimulations of the rapid formation of a high-mass halo at redshift similar to 50 and the formation of a Milky Way mass dark matter halo at redshift zero. In both cases, we find that many properties of the final halo show a much smaller sensitivity to the start redshift with the 2lpt initial conditions than simulations started from Zel'dovich initial conditions. For spherical overdense regions, structure formation is erroneously delayed in simulations starting from Zel'dovich initial conditions, and we demonstrate for the case of the formation of the high-redshift halo that this delay can be accounted for using the spherical collapse model. In addition to being more accurate, 2lpt initial conditions allow simulations to start later, saving computer time.