Constraints on the mass and self-coupling of ultra-light scalar field dark matter using observational limits on galactic central mass

Abstract

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.

ULDM self-interactions, tidal effects and tunnelling out of satellite galaxies

“…In the non-relativistic limit, the real φ can be written in terms of a complex field, φ = ℏ m √ 2c e −imc 2 t/ℏ Ψ + c.c. , and by averaging out the rapidly oscillating modes and taking the weak-gravity limit, the scalar field can be described using the Gross-Pitaevskii-Poisson equations (see [15] for a detailed derivation),…”

“…To describe a different soliton, one can either numerically solve the system again for a different value of φ(0) or one can scale every variable in a manner that preserves the form of the system of equations (see e.g. [15] for details).…”

“…The above property is also called scaling symmetry [27][28][29] (see also [15]), and is able to characterize an entire family of solitons with different masses, sizes and central densities from a single numerical solution found for a fixed φ(0). For our numerical solutions, we fix φ(0) = 1, which from our normalization scheme in eqs.…”

“…Matter (ULDM) and if λ = 0, Fuzzy Dark Matter (FDM) [11][12][13]. In such scenarios, even very small values of self-coupling (λ ∼ 10 −96 for m ∼ 10 −22 eV [14,15]) can significantly impact the size and masses of stable configurations [16,17]. Note that self-interactions are extremely important in another model of dark matter as well viz., Self-Interacting Dark Matter (SIDM) (see [18] for a recent review).…”

“…Another way to see this is the following: we know that for a fixed soliton mass, central densities are higher for attractive self-interactions while lower for repulsive self-interactions (see figure 1 of [15]). We also know from [20][21][22] that the lifetime of a satellite with a fixed orbital frequency is longer (shorter) for a larger (smaller) central density (see section 3.3 for details).…”