An attractive model: simulating fuzzy dark matter with attractive self-interactions

Fuzzy Dark Matter (FDM) comprised of ultralight ($m \sim 10^{-22}~\rm{eV}$) boson particles has received significant attention as a viable alternative to Cold Dark Matter (CDM), as it approximates CDM on large scales ($\gtrsim 1$ Mpc) while potentially resolving some of its small-scale problems via kiloparsec-scale quantum interference. However, the most basic FDM model, with one free parameter (the boson mass), is subject to a tension: small boson masses yield the desired cores of dwarf galaxies but underpredict structure in the Lyman-$\alpha$ forest, while large boson masses render FDM effectively identical to CDM. This Catch-22 problem may be alleviated by considering an axion-like particle with attractive particle self-interactions. We simulate an idealized FDM halo with self-interactions parameterized by an energy decay constant $f \sim 10^{15}~\rm{GeV}$ related to the axion symmetry-breaking conjectured to solve the strong-CP problem in particle physics. We observe solitons, a hallmark of FDM, condensing within a broader halo envelope, and find that the density profile and soliton mass depend on self-interaction strength. We propose generalized formulae to extend those from previous works to include self-interactions. We also investigate a critical mass threshold predicted for strong interactions at which the soliton collapses into a compact, unresolved state. We find that the collapse happens quickly and its effects are initially contained to the central region of the halo.