The Splashback Mass Function in the Presence of Massive Neutrinos

We present a complementary methodology to constrain the total neutrino mass, $\sum m_ν$, based on the diffusion coefficient of the splashback mass function of dark matter halos. Analyzing the snapshot data from the Massive Neutrino Simulations, we numerically obtain the number densities of distinct halos identified via the SPARTA code as a function of their splashback masses at various redshifts for two different cases of $\sum m_ν=0.0$ eV and $0.1$ eV. Then, we fit the numerical results to the recently developed analytic formula characterized by the diffusion coefficient that quantifies the degree of ambiguity in the identification of the splashback boundaries. Our analysis confirms that the analytic formula works excellently even in the presence of neutrinos and that the decrement of its diffusion coefficient with redshift is well described by a linear fit, $B(z-z_{c})$, in the redshift range of $0.2\le z\le 2$. It turns out that the massive neutrino case yields significantly lower value of $B$ and substantially higher value of $z_{c}$ than the massless neutrino case, which indicates that the higher masses the neutrinos have, the more severely the splashback boundaries become disturbed by the surroundings. Given our result, we conclude that the total neutrino mass can in principle be constrained by measuring how rapidly the diffusion coefficient of the splashback mass function diminishes with redshifts at $z\ge 0.2$. We also discuss the anomalous behavior of the diffusion coefficient found at lower redshifts for both of the $\sum m_ν$ cases, and ascribe it to the fundamental limitation of the SPARTA code at $z\le 0.13$.