Dynamical evolution of primordial dark matter haloes through mergers

Primordial darkmatter (DM) haloes are the smallest gravitationally bound DM structures from which the first stars, black holes and galaxies form and grow in the early universe. However, their structures are sensitive to the free streaming scale of DM, which in turn depends on the nature of DM particles. In this work, we test the hypothesis that the slope of the central cusps in primordial DM haloes near the free streaming scale depends on the nature of merging process. By combining and analysing data from a cosmological simulation with the cutoff in the small-scale matter power spectrum as well as a suite of controlled, high-resolution simulations of binary mergers, we find that (1) the primordial DM haloes form preferentially through major mergers in radial orbits; (2) their central DM density profile is more susceptible to a merging process compared to that of galaxy-and cluster-sized DM haloes; (3) consecutive major mergers drive the central density slope to approach the universal form characterized by the Navarro-Frenk-White profile, which is shown to be robust to the impacts of mergers and serves an attractor solution for the density structure of DM haloes. Our work highlights the importance of dynamical processes on the structure formation during the Dark Ages.