Angular momentum and vortex formation in Bose-Einstein-condensed cold dark matter haloes

Abstract

Various extensions of the standard model of particle physics predict the existence of very light bosons, with masses ranging from about 10 −5 eV for the QCD axion down to 10 −33 eV for ultra-light particles. These particles could be responsible for all or part of the cold dark matter (CDM) in the Universe. For such particles to serve as CDM, their phase-space density must be high enough to form a Bose-Einstein condensate (BEC). The fluid-like nature of BEC-CDM dynamics differs from that of standard collisionless CDM, however, so different signature effects on galactic haloes may allow observations to distinguish them. Standard CDM has problems with galaxy observations on small scales; cuspy central density profiles of haloes and the overabundance of subhaloes seem to conflict with observations of dwarf galaxies. It has been suggested that BEC-CDM can overcome these shortcomings for a large range of particle mass m and self-interaction coupling strength g. For quantum coherence to influence structure on the scale of galactic haloes of radius R and mass M, either the de-Broglie wavelength λ deB R, which requires m m H ∼ = 10 −25 (R/100 kpc) −1/2 (M/10 12 M ) −1/2 eV, or else λ deB R but gravity is balanced by self-interaction, which requires m m H and g g H ∼ = 2 × 10 −64 (R/100 kpc)(M/10 12 M ) −1 eV cm 3 . Here we study the largely neglected effects of angular momentum on BEC haloes. Dimensionless spin parameters λ 0.05 are expected from tidal-torquing by large-scale structure formation, just as for standard CDM. Since laboratory BECs develop quantum vortices if rotated rapidly enough, we ask whether this amount of angular momentum is sufficient to form vortices in BEC haloes, which would affect their structure with potentially observable consequences. The minimum angular momentum required for a halo to sustain a vortex, L QM , corresponds to per particle, or M/m. For λ = 0.05, this requires m ≥ 9.5m H , close enough to the particle mass required to influence structure on galactic scales that BEC haloes may be subject to vortex formation. While this is a necessary condition, it is not sufficient. To determine if and when quantum vortices will form in BEC haloes with a given λ-value, we study the equilibrium of self-gravitating, rotating, virialized BEC haloes which satisfy the Gross-Pitaevskii-Poisson equations, and calculate under what conditions vortices are energetically favoured, in two limits: either just enough angular momentum for one vortex or a significant excess of angular momentum. For λ = 0.05, vortex formation is energetically favoured for L/L QM ≥ 1 as long as both m/m H ≥ 9.5 and g/g H ≥ 68.0. Hence, vortices are expected for a wide range of BEC parameters. However, vortices cannot form for vanishing self-interaction (i.e. when λ deB R), and a range of particle parameters also remain even for BEC haloes supported by self-interaction, for which vortices will not form. Such BEC haloes can be modelled by compressible, (n = 1)-polytropic, irrotational Riemann-S ellipsoids.

Constraints on anharmonic corrections of fuzzy dark matter

“…The additional source of pressure from the repulsive self-interactions helps to solve the 'corecusp' problem with larger masses [46]. Additionaly, unlike the axion case, it could explain the formation of vortices in galaxies [53].…”

Scalar field (wave) dark matter

“…There has been considerable work in finding numerical solutions to the noninteracting SFDM in the non-relativistic regime to model spherically symmetric haloes 3,8,25,26,31,72 , and also for the self-interacting SFDM 2,4,12,21,53,55 , it is worth noting that as mentioned in 26 for the weak field limit of the system that determines the evolution of a spherically symmetric scalar field, that is, the Einstein and KleinGordon equations, for a complex and a real scalar field the system reduces to the Schrödinger-Poisson (SP) equations 1 . The contraints reported in 37 , obtained by imposing that the SF behaves cosmologically as pressureless matter (dust), imply that the interacting parameter would be extremely small for the typical mass of ∼10 −22 eV/c 2 , therefore we expect that solutions to the SP system with no interactions would behave qualitatively similar to those when self-interactions are included, as supported by the similarity in the solutions of the non-iteracting case and those with a small self-coupling found in other works 2,10,12 .…”

Nonminimally coupled topological-defect boson stars: Static solutions

“…Motivated by their simplicity and stability, boson stars have been studied extensively as dark matter candidates [8][9][10], simplified models for compact objects such as neutron stars [11][12][13] and alternatives to black holes [1,[14][15][16]. Additionally, they have been considered in models where they are nonminimally coupled to gravity [1,17] and in conformal and scalar-tensor extensions to gravity [18].…”