It is well known that Ultra-Light Dark Matter (ULDM), usually scalar fields of mass m ∼ 10-22 eV, can solve some of the outstanding problems of the Cold Dark Matter (CDM) paradigm. Such a scalar field could have non-negligible self-coupling λ. In this work, using the known observational upper limit on the amount of centrally concentrated dark matter in a galaxy, we arrive at the observational constraints in the λ-m (self coupling-mass) parameter space. It is found that the observational limit on the mass m of the ULDM depends upon the sign and strength of the self-interactions. We demonstrate that, for m ∼ 10-22 eV, self-coupling values of 𝒪(10-96) (corresponding to a scattering length of as ∼ 10-82 m) can be probed using limits on the dark matter mass within 10 pc of the centre of M87 galaxy. Our analysis suggests that if Ultra Light Axion particles (ULAs) form all of dark matter, dark matter particle mass must be less than  ∼ 6 × 10-23 eV.

One of the most important unanswered 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 ∼ 10-22 eV. This kind of ultralight dark matter (ULDM) would form cored density profiles (called “solitons”) at the centres 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 eV, the requirement of satisfying both galactic rotation curves as well as SH relations can be fulfilled with repulsive self-coupling λ ∼ 𝒪(10-90).

It is well known that Ultra-Light Dark Matter (ULDM), usually scalar fields of mass m ∼ 10 −22 eV, can solve some of the outstanding problems of the Cold Dark Matter (CDM) paradigm. Such a scalar field could have non-negligible self-coupling λ. In this work, using the known observational upper limit on the amount of centrally concentrated dark matter in a galaxy, we arrive at the observational constraints in the λ − m (self coupling − mass) parameter space. It is found that the observational limit on the mass m of the ULDM depends upon the sign and strength of the self-interactions. We demonstrate that, for m ∼ 10 −22 eV, self-coupling values of O(10 −96 ) (corresponding to a scattering length of a s ∼ 10 −82 m) can be probed using limits on the dark matter mass within 10 pc of the centre of M87 galaxy. Our analysis suggests that if Ultra Light Axions (ULAs) form all of dark matter, its mass has to be less than ∼ 6 × 10 −23 eV.

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