Dark matter flow data and manuscript: On the statistical theory of self-gravitating collisionless dark matter flow

Manuscript and data for Xu (2023), On the statistical theory of self-gravitating collisionless dark matter flow, Phys. Fluids 35, 077105 (doi:10.1063/5.0151129; arXiv:2202.00910). Using the Virgo SCDM N-body simulation (256^3 particles, box 239.5 Mpc/h, redshifts z = 10 to 0), the paper shows that dark matter flow is a constant-divergence flow inside haloes and an irrotational flow on large scales, and that the second-order velocity statistics follow analytic laws: an exponential transverse velocity correlation on large scales and a one-fourth power law for the longitudinal structure function on small scales. This deposit contains the revised manuscript (P20_revised.pdf, 23 pages, 28 figures) and 63 CSV files: every pair statistic at full resolution for redshifts z = 10 to 0 (statistics), the result tables (tables), and the plotted data of 26 of the 28 figures (figures; Figs. 1 and 2 have no CSV). The files use the format of the Dark matter flow dataset Parts I and II (doi:10.5281/zenodo.6541231 and doi:10.5281/zenodo.6757654). The analysis code is not part of this deposit. Text and data: CC BY 4.0. Major findings (Virgo SCDM N-body simulation, redshifts z = 10 to 0): Exact kinematic relations link the correlation, structure, dispersion and spectrum functions of three idealized flows: incompressible, constant-divergence and irrotational. Incompressible and constant-divergence flows share the same relations for even-order correlations. The peculiar velocity is a constant-divergence flow on small scales, where particle pairs sit in the same halo, and an irrotational flow on large scales, with the transition near rt ≈ 1.3 Mpc/h. Because the flow is collisionless, the longitudinal velocities of two particles at vanishing separation are only partly correlated: the limiting correlation coefficient is ρL = 1/2, compared with ρL = 1 for incompressible flow. On large scales the transverse velocity correlation is exponential, T2 ∝ e−r/r2, with a time-independent comoving scale r2 ≈ 23.1 Mpc/h that may be related to the horizon size at matter–radiation equality; all other velocity, density and potential statistics on these scales then follow analytically. On small scales the longitudinal structure function follows a one-fourth law, S2l ∝ r1/4, from which the remaining small-scale statistics follow. Vorticity is negatively correlated for separations between 1 and 7 Mpc/h, and divergence for r ≳ 33 Mpc/h, which produces a negative density correlation on those scales.