Precision reconstruction of the dark matter-neutrino relative velocity from N-body simulations
Discovering the mass of neutrinos is a principle goal in high energy physics and cosmology. In addition to cosmological measurements based on two-point statistics, the neutrino mass can also be estimated by observations of neutrino wakes resulting from the relative motion between dark matter and neutrinos. Such a detection relies on an accurate reconstruction of the dark matter-neutrino relative velocity which is affected by non-linear structure growth and galaxy bias. We investigate our ability to reconstruct this relative velocity using large N-body simulations where we evolve neutrinos as distinct particles alongside the dark matter. We find that the dark matter velocity power spectrum is overpredicted by linear theory whereas the neutrino velocity power spectrum is underpredicted. The magnitude of the relative velocity observed in the simulations is found to be lower than what is predicted in linear theory. Since neither the dark matter nor the neutrino velocity fields are directly observable from galaxy or 21 cm surveys, we test the accuracy of a reconstruction algorithm based on halo density fields and linear theory. Assuming prior knowledge of the halo bias, we find that the reconstructed relative velocities are highly correlated with the simulated ones with correlation coefficients of 0.94, 0.93, 0.91 and 0.88 for neutrinos of mass 0.05, 0.1, 0.2 and 0.4 eV. We confirm that the relative velocity field reconstructed from large scale structure observations such as galaxy or 21 cm surveys can be accurate in direction and, with appropriate scaling, magnitude.