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We review the physics and phenomenology of wave dark matter: a bosonic dark matter candidate lighter than about 30 eV. Such particles have a de Broglie wavelength exceeding the average inter-particle separation in a galaxy like the Milky Way, and are well described as classical waves. We outline the particle physics motivations for them, including the QCD axion and ultra-light axion-like-particles such as fuzzy dark matter. The wave nature of the dark matter implies a rich phenomenology: (1) Wave interference leads to order unity density fluctuations on de Broglie scale. A manifestation is vortices where the density vanishes and around which the velocity circulates. There is one vortex ring per de Broglie volume on average. (2) For sufficiently low masses, soliton condensation occurs at centers of halos. The soliton oscillates and random walks, another manifestation of wave interference. The halo/subhalo abundance is suppressed at small masses, but the precise prediction from numerical wave simulations remains to be determined. (3) For ultra-light ~$10^{-22}$ eV dark matter, the wave interference substructures can be probed by tidal streams/gravitational lensing. The signal can be distinguished from that due to subhalos by the dependence on stream orbital radius/image separation. (4) Axion detection experiments are sensitive to interference substructures for moderately light masses. The stochastic nature of the waves affects the interpretation of experiments and motivates the measurement of correlation functions. Current constraints and open questions, covering detection experiments and cosmological/galactic/black-hole observations, are discussed.
The black hole merging rates inferred after the gravitational-wave detection by Advanced LIGO/VIRGO and the relatively high mass of the progenitors are consistent with models of dark matter made of massive primordial black holes (PBH). PBH binaries e
We present a wave generalization of the classic Schwarzschild method for constructing self-consistent halos -- such a halo consists of a suitable superposition of waves instead of particle orbits, chosen to yield a desired mean density profile. As an
We consider a dark matter halo (DMH) of a spherical galaxy as a Bose-Einstein condensate of the ultra-light axions interacting with the baryonic matter. In the mean-field limit, we have derived the integro-differential equation of the Hartree-Fock ty
In a galactic halo like the Milky Way, bosonic dark matter particles lighter than about $30$ eV have a de Broglie wavelength larger than the average inter-particle separation and are therefore well described as a set of classical waves. This applies
Seven observations point towards the existence of primordial black holes (PBH), constituting the whole or an important fraction of the dark matter in the Universe: the mass and spin of black holes detected by Advanced LIGO/VIRGO, the detection of mic