Approximating the peculiar velocity distribution of dark matter halos with Tsallis statistics

Abstract: Dark matter halos, which host galaxies and galaxy clusters, have peculiar velocities far from thermal equilibrium. Characterizing the nonlinear and non-Gaussian features of this velocity distribution improves our understanding of the gravitational evolution of the cosmic web and supports related cosmological applications. We endeavor to establish a connection between the peculiar velocity distribution of halos and nonequilibrium statistical mechanics, with the objective of obtaining a model that is both concise and accurate for practical applications. We extracted halo samples from large N-body simulations and performed maximum-likelihood fits to the peculiar velocity distributions using a two-parameter Tsallis model, derived from non-extensive statistical mechanics. On the theoretical side, we reformulated the halo distribution in the superstatistics framework by means of a generalized Gram-Charlier expansion based on the gamma distribution. For halo peculiar velocities below 1000 km/s, the Tsallis model achieves 5 percent accuracy over z=0-2, with performance improving toward lower redshifts. Our results show that the halo velocity distribution becomes increasingly non-Gaussian and departs further from equilibrium over time. The best-fit parameters depend only weakly on mass, though low-mass halos exhibit slightly stronger non-Gaussianity. The two parameters, especially the velocity dispersion, offer promising probes of cosmological parameters. Theoretically, we find that in general the halo peculiar velocity distribution function is expressible as a superposition of a series of Tsallis distribution functions, while simulation results demonstrate that the zeroth-order approximation, namely a single Tsallis function, already achieves sufficient accuracy.