*Summary:*

*Dmitriev and colleagues studied rotating Bose stars, i.e. gravitationally bound clumps of Bose–Einstein condensate composed of non-relativistic particles with nonzero angular momentum ‘l’.**They analytically proved that these objects are unstable, if particle self–interactions are attractive or negligibly small.**On the other hand, they numerically showed that in models with sufficiently strong repulsive self–interactions the Bose star is stable. But, although this Bose star becomes stable at sufficiently strong repulsive self–couplings, the fate of the higher ‘l’ objects is far less trivial.**They also computed the lifetimes of the unstable rotating stars and found that their lifetimes are always comparable to the inverse binding energies; hence, these objects cannot be considered long–living.*

Friends, every object in the Universe can rotate around its center of mass and carry angular momentum. There is, however, a unique substance — Bose–Einstein condensate of particles in a quantum state ψ(t, x) — that does not rotate easily, and if it does, it rotates in its own peculiar way. Indeed, the condensate velocity can be identified with the phase gradient divided by the particle mass:

*v = ∇ arg ψ(t, x)/m .*

This vector is explicitly irrotational at nonzero density: rot *v* = 0 at *ψ ≠ 0*. Hence, the only way to add rotation is to drill a hole through the condensate, i.e. introduce a vortex line *ψ* = 0 through its center in Fig. 1. And this costs energy! As a by–product, the angular momentum of the condensate is quantized with the number ‘*l’ *of vortex lines.

“One can rotate Bose star by driving a vortex through its center”— told Dmitriev, first author of the study

In the present–day Universe, the Bose–Einstein condensate of dark matter particles may exist in the form of gravitationally self–bound Bose stars. During decades, the studies of these objects were migrating from the periphery of scientific interest towards its focal point. Now, it is clear that the Bose stars may form abundantly by universal gravitational mechanisms in the mainstream models with light dark matter. If the latter consists of QCD axions, they nucleate inside the typical axion miniclusters — widespread smallest–scale structures conceived at the QCD phase transition. In the case of fuzzy dark matter, gigantic Bose stars (“solitonic cores”) appear in the centers of galaxies during structure formation. In both cases these objects cease growing beyond certain mass.

Rotating Bose stars, if stable, would be important for astrophysics and cosmology. Their centrifugal barriers can resist to bosenovas — collapses of overly massive stars due to attractive self–interactions of bosons. This means, in particular, that fast–rotating QCD axion stars would reach larger masses and densities which may be sufficient to ignite observable parametric radioemission. Besides, the angular momenta of the Bose stars are detectable in principle: directly by observing gravitational waves from their mergers or indirectly if they eventually collapse into spinning black holes which merge and emit gravitational waves.

Now, Dmitriev and colleagues studied rotating Bose stars, i.e. gravitationally bound clumps of Bose–Einstein condensate composed of non-relativistic particles with nonzero angular momentum *‘l’*. They analytically proved that these objects are unstable at arbitrary *l* ≠ 0 if particle self–interactions are attractive (λ < 0) or negligibly small (λ = 0). This result is applicable in the popular cases of fuzzy and QCD axion dark matter. On the other hand, they numerically showed that in models with sufficiently strong repulsive self–interactions (λ > 0) the Bose star with *l* = 1 is stable. But, although the *l* = 1 Bose star becomes stable at sufficiently strong repulsive self–couplings λ > λ_0, the fate of the higher ‘*l’* objects is far less trivial.

Their approach reveals the mechanism for the instability: it is caused by the pairwise transitions of the condensed particles from the original state with the angular momentum *l* to the *l + ∆l *and *l − ∆l* states, see Fig. 2 above. This process conserves the total spin and decreases the potential energy of the Bose star. Piling up due to Bose factors, the particle transitions lead to exponential growth of the axially asymmetric perturbations:

*δψ ∝ e^µt, *

where µ is the complex exponent and (Re µ)^−1 is the lifetime of the rotating configuration.

They also computed the lifetimes of the unstable rotating stars and found that their lifetimes are always comparable to the inverse binding energies; hence, these objects cannot be considered long–living. This observation has a number of phenomenological consequences.

First, the scenario with rotating axion stars reaching threshold for the explosive parametric radioemission cannot be realized. One still can consider emission during the intermediate stages when dense and short–living rotating configuration shakes off its angular momentum. But a specific formation scenario for the latter should be suggested in the first place.

Second, instability of rotating Bose stars provides a universal mechanism to destroy the angular momentum. One can imagine e.g. that a subset of dark matter Bose stars collapses gravitationally into black holes with suppressed spins. This is possible in models with positive self–coupling or in axionic models with near–Planckian decay constants. Formation of such non–spinning black holes may explain observational hints in GWTC-1, advanced LIGO & VIRGO etc.

**Reference***: A.S. Dmitriev, D.G. Levkov, A.G. Panin, E.K. Pushnaya, I.I. Tkachev, “Instability of rotating Bose stars”, ArXiv, pp. 1-18, 2 Apr, 2021. **https://arxiv.org/abs/2104.00962*

*Copyright of this article totally belongs to our author S. Aman. One is allowed to reuse it only by giving proper credit either to him or to us *