Effects of Neutrino Masses and Asymmetries on Dark Matter Halo Assembly

Massive cosmological neutrinos suppress the Large-Scale Structure (LSS) in the Universe by smoothing the cosmic over-densities, and hence structure formation is delayed relative to that in the standard Lambda-Cold Dark Matter ($\Lambda$CDM) model. We characterize the merger and mass accretion history of dark matter halos with the halo formation time $a_{1/2}$, tree entropy $s$ and halo leaf function $\ell(X)$ and measure them using neutrino-involved N-body simulations. We show that a non-zero sum of neutrino masses $M_\nu$ delays the $a_{1/2}$ for halos with virial mass between $10^{13} M_\odot$ and $3\times 10^{13} M_\odot$, whereas a non-zero neutrino asymmetry parameter $\eta^2$ has the opposite effect. While the mean tree entropy $\bar s$ does not depend significantly on either $M_\nu$ or $\eta^2$, the halo leaf function does. Furthermore, the dependencies of $\ell$ on $M_\nu$ and $\eta^2$ have significant evolution in redshift $z$, with the relative contributions of $M_\nu$ and $\eta^2$ showing a sigmoid-like transition as a function of $z$ around $z \approx 0.6$. Together with the matter power spectrum, these halo parameters allow us to break the parameter degeneracy between $M_\nu$ and $\eta^2$ so that they can both be constrained in principle.