Relativistic Axions from Collapsing Bose Stars

Self-Similar Growth of Bose Stars

We analytically solve the problem of Bose star growth in the bath of gravitationally interacting particles. We find that after nucleation of this object, the bath is described by a self-similar solution of the kinetic equation. Together with the conservation laws, this fixes mass evolution of the Bose star. Our theory explains, in particular, the slowdown of the star growth at a certain "core-halo" mass, but also predicts formation of heavier and lighter objects in magistral dark matter models. The developed "adiabatic" approach to self-similarity may be of interest for kinetic theory in general.

Axion Stars

The dark matter particle can be a QCD axion or axion-like particle. A locally over-densed distribution of axions can condense into a bound Bose–Einstein condensate called an axion star, which can be bound by self-gravity or bound by self-interactions. It is possible that a significant fraction of the dark matter axion is in the form of axion stars. This would make some efforts searching for the axion as the dark matter particle more challenging, but at the same time it would also open up new possibilities. Some of the properties of axion stars, including their emission rates and their interactions with other astrophysical objects, are not yet completely understood.

Balancing long-range interactions and quantum pressure: Solitons in the Hamiltonian mean-field model

The Hamiltonian mean-field (HMF) model describes particles on a ring interacting via a cosine interaction, or equivalently, rotors coupled by infinite-range XY interactions. Conceived as a generic statistical mechanical model for long-range interactions such as gravity (of which the cosine is the first Fourier component), it has recently been used to account for self-organization in experiments on cold atoms with long-range optically mediated interactions. The significance of the HMF model lies in its ability to capture the universal effects of long-range interactions and yet be exactly solvable in the canonical ensemble. In this work we consider the quantum version of the HMF model in one dimension and provide a classification of all possible stationary solutions of its generalized Gross-Pitaevskii equation (GGPE), which is both nonlinear and nonlocal. The exact solutions are Mathieu functions that obey a nonlinear relation between the wave function and the depth of the mean-field potential, and we identify them as bright solitons. Using a Galilean transformation these solutions can be boosted to finite velocity and are increasingly localized as the mean-field potential becomes deeper. In contrast to the usual local GPE, the HMF case features a tower of solitons, each with a different number of nodes. Our results suggest that long-range interactions support solitary waves in a novel manner relative to the short-range case.

Gravitational Bose-Einstein Condensation in the Kinetic Regime

We study Bose-Einstein condensation and the formation of Bose stars in virialized dark matter halos and miniclusters by universal gravitational interactions. We prove that this phenomenon does occur and it is described by a kinetic equation. We give an expression for the condensation time. Our results suggest that Bose stars may form kinetically in mainstream dark matter models such as invisible QCD axions and fuzzy dark matter.

Vortex lattice in the crossover of a Bose gas from weak coupling to unitarity

The formation of a regular lattice of quantized vortices in a fluid under rotation is a smoking-gun signature of its superfluid nature. Here we study the vortex lattice in a dilute superfluid gas of bosonic atoms at zero temperature along the crossover from the weak-coupling regime, where the inter-atomic scattering length is very small compared to the average distance between atoms, to the unitarity regime, where the inter-atomic scattering length diverges. This study is based on high-performance numerical simulations of the time-dependent nonlinear Schrödinger equation for the superfluid order parameter in three spatial dimensions, using a realistic analytical expression for the bulk equation of state of the system along the crossover from weak-coupling to unitarity. This equation of state has the correct weak-coupling and unitarity limits and faithfully reproduces the results of an accurate multi-orbital microscopic calculation. Our numerical predictions of the number of vortices and root-mean-square sizes are important benchmarks for future experiments.