Ultra-Light Axion Dark Matter and its impacts on dark halo structure in $N$-body simulation

Abstract: The Ultra-Light Axion (ULA) is a dark matter candidate with mass $\mathcal{O}(10^{-22})$eV and de Broglie wavelength of order kpc. Such an axion, also called the Fuzzy Dark Matter (FDM), thermalizes via the gravitational force and forms a Bose-Einstein condensate. Recent studies suggested that the quantum pressure from the FDM can significantly affect the structure formation in small scales, thus alleviating the so-called "small-scale crisis". In this paper, we develop a new technique to discretize the quantum pressure and illustrate the interactions among FDM particles in the $N$-body simulation, which accurately simulates the formation of the dark-matter halo and its inner structure in the region outside the softening length. In a self-gravitationally-bound virialized halo, we find a constant density, solitonic core, which is consistent with the theoretical prediction. The existence of the solitonic core reveals the non-linear effect of quantum pressure and impacts the structure formation in the FDM model.