Accurate initial conditions in mixed dark matter-baryon simulations

We quantify the error in the results of mixed baryon-dark-matter hydrodynamic simulations, stemming from outdated approximations for the generation of initial conditions. The error at redshift 0 in contemporary large simulations is of the order of few to 10 per cent in the power spectra of baryons and dark matter, and their combined total-matter power spectrum. After describing how to properly assign initial displacements and peculiar velocities to multiple species, we review several approximations: (1) using the total-matter power spectrum to compute displacements and peculiar velocities of both fluids, (2) scaling the linear redshift-zero power spectrum back to the initial power spectrum using the Newtonian growth factor ignoring homogeneous radiation, (3) using a mix of general-relativistic gauges so as to approximate Newtonian gravity, namely longitudinal-gauge velocities with synchronous-gauge densities and (4) ignoring the phase-difference in the Fourier modes for the offset baryon grid, relative to the dark-matter grid. Three of these approximations do not take into account that dark matter and baryons experience a scale-dependent growth after photon decoupling, which results in directions of velocity that are not the same as their direction of displacement. We compare the outcome of hydrodynamic simulations with these four approximations to our reference simulation, all setup with the same random seed and simulated using GADGET-III.