A Minimal Model for Massive Neutrinos in Newtonian N-body Simulations

We present a novel method for including the impact of massive neutrinos in cold dark matter N-body simulations. Our approach is compatible with widely employed Newtonian N-body codes and relies on only three simple modifications. First, we use commonly employed backscaling initial conditions, based on the cold dark matter plus baryon power spectrum instead of the total matter power spectrum. Second, the accurate Hubble rate is employed in both the backscaling and the evolution of particles in the N-body code. Finally, we shift the final particle positions in a post-processing step to account for the integrated effect of neutrinos on the particles in the simulation. However, we show that the first two modifications already capture most of the relevant neutrino physics for a large range of observationally interesting redshifts and scales. The output of the simulations are the cold dark matter and baryon distributions and can be analysed using standard methods. All modifications are simple to implement and do not generate any computational overhead. By implementing our methods in the N-body codes GADGET and gevolution, we show that any state-of-the-art Newtonian N-body code can be utilised out of the box. Our method is also compatible with higher order Lagrangian perturbation theory initial conditions and accurate for combined neutrino masses of up to at least 0.3 eV. Being formulated in relativistic gauge theory, in addition to including the impact of massive neutrinos, our method further includes relativistic corrections relevant on the large scales for free.