Axion dark matter, solitons and the cusp–core problem

Self-gravitating bosonic fields can support stable and localized (solitonic) field configurations. Such solitons should be ubiquitous in models of axion dark matter, with their characteristic mass and size depending on some inverse power of the axion mass, m a. Using a scaling symmetry and the uncertainty principle, the soliton core size can be related to the central density and axion mass in a universal way. Solitons have a constant central density due to pressure support, unlike the cuspy profile of cold dark matter (CDM). Consequently, solitons composed of ultralight axions (ULAs) may resolve the ‘cusp–core’ problem of CDM. In dark matter (DM) haloes, thermodynamics will lead to a CDM-like Navarro–Frenk–White (NFW) profile at large radii, with a central soliton core at small radii. Using Monte Carlo techniques to explore the possible density profiles of this form, a fit to stellar kinematical data of dwarf spheroidal galaxies is performed. The data favour cores, and show no preference concerning the NFW part of the halo. In order for ULAs to resolve the cusp–core problem (without recourse to baryon feedback, or other astrophysical effects) the axion mass must satisfy m a