How to add massive neutrinos to your $Λ$CDM simulation -- extending cosmology rescaling algorithms

Abstract: Providing accurate predictions for the spatial distribution of matter and luminous tracers in the presence of massive neutrinos is an important task, given the imminent arrival of highly accurate large-scale structure observations. In this work, we address this challenge by extending cosmology-rescaling algorithms to massive neutrino cosmologies. In this way, a $\Lambda$CDM simulation can be modified to provide nonlinear structure formation predictions in the presence a hot component of arbitrary mass, and, if desired, to include non-gravitational modifications to the clustering of matter on large scales. We test the accuracy of the method by comparing its predictions to a suite of simulations carried out explicitly including a neutrino component in its evolution equations. We find that, for neutrino masses in the range $M_\nu \in [0.06, 0.3] ~ \mathrm{eV}$ the matter power spectrum is recovered to better than $1\%$ on all scales $k<2~h~\mathrm{Mpc}^{-1}$. Similarly, the halo mass function is predicted at a few percent level over the range $M_{\rm halo} \in [10^{12}, 10^{15}] ~ h^{-1} ~ \mathrm{M}{\odot}$, and so do also the multipoles of the galaxy 2-point correlation function in redshift space over $r \in [0.1, 200] ~ h^{-1} ~ \mathrm{Mpc}$. We provide parametric forms for the necessary transformations, as a function of $\Omega{\rm m}$ and $\Omega_{\nu}$ for various target redshifts.