Self-interactions of ULDM to the rescue?

One of the most important questions in cosmology is concerning the fundamental nature of dark matter (DM). DM could consist of spinless particles of very small mass i.e. $m \sim 10^{-22}\ \text{eV}$. This kind of ultralight dark matter (ULDM) would form cored density profiles (called "solitons") at the centre of galaxies. In this context, recently it has been argued that (a) there exists a power law relation between the mass of the soliton and mass of the surrounding halo called the Soliton-Halo (SH) relation, and, (b) the requirement of satisfying observed galactic rotation curves as well as SH relations is so stringent that ULDM is disfavoured from comprising $100\%$ of the total cosmological dark matter. In this work, we revisit these constraints for ULDM particles with non-negligible quartic self-interactions. Using a recently obtained soliton-halo relation which takes into account the effect of self-interactions, we present evidence which suggests that, for $m = 10^{-22}\ \text{eV}$, the requirement of satisfying both galactic rotation curves as well as SH relations can be fulfilled with repulsive self-coupling $\lambda \sim \mathcal{O}(10^{-90})$.