Neutrinos, among the most abundant particles in the Universe, influence cosmic structure formation through their mass (Mnu) and possible chemical potential (xi3). Their free-streaming suppresses clustering on small scales, leaving measurable imprints on galaxy motions.
We use the mean pairwise peculiar velocity of galaxies, a statistic quantifying the relative motion of galaxy pairs under gravity and cosmic expansion, as a probe of neutrino properties. To validate our approach, we develop a pipeline to extract pairwise velocity from both simulations and observations, obtaining Hubble constant (H0 = 75.5 ± 1.4 km/s/Mpc) and total matter density (Om = 0.311 +0.029/-0.028).
Applying this pipeline to neutrino-involved N-body simulations, we study the impact of neutrino mass and degeneracy parameter on pairwise velocity. Comparing simulated halo-halo velocities with observed galaxy-galaxy velocities, we derive constraints of Mnu = 0.26 +0.33/-0.19 eV and xi3 = 1.221 +0.081/-0.093 for the CMB framework, and Mnu = 0.36 +0.32/-0.25 eV and xi3 = 1.41 +0.46/-0.60 for the local framework.