Role of self-gravity on the central halo structure of fuzzy dark matter

Fuzzy dark matter (FDM) is a dark matter model that is characterized by the ultralight masses around 10−22 eV. As FDM has the wave-like nature, the self-gravitating structure is described by the Schrödinger-Poisson equation. Previous simulations based on the Schrödinger-Poisson equation have demonstrated that soliton-like structure having a high-density flat core is formed at the central region of the FDM halos, and the size of such a core is typically determined by the de Broglie wavelength. Away from the central core, the density profile of the FDM halos resembles that of the cold dark matter halos on average, and is shown to be described by the Navarro-Frenk-White (NFW) profile. In this paper, we study the role of the self-gravity of the soliton core, and its relation to the bulk halo properties by solving the Schrödinger-Poisson equation in a simplified setup. The findings indicate that the contribution from the soliton self-gravity must dominate over the NFW potential in order to sustain the soliton.