The physics and phenomenology of wave dark matter appear to be related to 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, thus well described as a set of classical waves. The particle physics motivations for them are outlined, including the QCD axion as well as ultra-light axion-like-particles such as fuzzy dark matter. The wave nature of the dark matter implies a rich phenomenology:
- Wave interference gives rise to order unity density fluctuations on de Broglie scale in halos. One manifestation is vortices where the density vanishes and around which the velocity circulates. There is one vortex ring per de Broglie volume on average.
- For sufficiently low masses, soliton condensation occurs at centers of halos. The soliton oscillates and random walks, another manifestation of wave interference. The halo and subhalo abundance is expected to be suppressed at small masses, but the precise prediction from numerical wave simulations remains to be determined.
- 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.
- Axion detection experiments are sensitive to interference substructures for wave dark matter that is moderately light. The stochastic nature of the waves affects the interpretation of experimental constraints and motivates the measurement of correlation functions.
Dynamical measurements tell us the dark matter mass density in the solar neighborhood is about 0.4GeVcm . From this, one can deduce the average inter-particle separation, given a dark matter particle mass. We can compare it against the de Broglie wavelength of the particle:
2π 10−22 eV250km/s 10−6 eV250km/s λdB ≡ mv = 0.48 kpc m v = 1.49 km m v , where v is the velocity dispersion of the galactic halo, and m is the dark matter particle.
A range of local dark matter density values have been reported in the literature: e.g. 0.008 M⊙/pc3 = 0.3 GeV/cm3 (Bovy & Tremaine 2012), 0.0122 M⊙/pc3 = 0.46 GeV/cm3 (Siverts- son et al. 2018), 0.013 M⊙/pc3 = 0.49 GeV/cm3 (McKee et al. 2015).
In a Milky-Way-like environment, the average number of particles in a de Broglie volume λ3dB is:
Such a light dark matter particle is necessarily bosonic, for the Pauli exclusion principle** precludes multiple occupancies for fermions—this is the essence of the bound by Tremaine & Gunn (1979). For concreteness, we focus on a spin zero (scalar) particle, although much of the wave phenomenology applies to higher spin cases as well (Graham et al. 2016b, Kolb & Long 2020, Aoki & Mukohyama 2016). There is a long history of investigations of dark matter as a scalar field (e.g., Baldeschi et al. 1983, Turner 1983, Press et al. 1990, Sin 1994, Peebles 2000, Goodman 2000, Lesgourgues et al. 2002, Amendola & Barbieri 2006, Chavanis 2011, Suarez & Matos 2011, Rindler-Daller & Shapiro 2012, Berezhiani & Khoury 2015a, Fan 2016, Alexander & Cormack 2017).
Perhaps the most well motivated example is the Quantum Chromodynamics (QCD) axion (Peccei & Quinn 1977, Kim 1979, Weinberg 1978, Wilczek 1978, Shifman et al. 1980, Zhitnitsky 1980, Dine et al. 1981, Preskill et al. 1983, Abbott & Sikivie 1983, Dine & Fischler 1983).
Its possible the mass spans a large range— experimental detection has focused on masses around 10−6 eV, with newer experiments reaching down to much lower values. For recent reviews, see Graham et al. (2015), Marsh (2016), Sikivie (2020). String theory also predicts a large number of axion-like-particles (ALP), one or some of which could be dark matter (Svrcek & Witten 2006, Arvanitaki et al. 2010, Halverson et al. 2017, Bachlechner et al. 2019). At the extreme end of the spectrum
described by the classical electric and magnetic fields.
Classical physics, for large occupancy, implies negligible quantum fluctuations. The question of how the classical description relates to the underlying quantum one is a fascinating subject. We unfortunately do not have the space to explore it here (see Sikivie & Yang 2009, Guth et al. 2015, Dvali & Zell 2018, Lentz et al. 2020, Allali & Hertzberg 2020).
is the possibility of an ALP with mass around 10-22nd - 10-20th
that naturally matches the observed dark matter density. More generally, ultra-light dark matter in this mass range is often referred to as fuzzy dark matter (FDM).
Fuzzy Dark Matter was proposed by Hu, Barkana & Gruzinov (2000) to address small scale structure issues thought to be associated with conventional cold dark mater (CDM) (Spergel & Steinhardt 2000). It remains unclear whether the small scale structure issues point to novelty in the dark matter sector, or can be resolved by baryonic physics, once the complexities of galaxy formation are properly understood (for a recent review, see Weinberg et al. 2015).
For a further elucidation, see:
https://arxiv.org/pdf/2101.11735.pdf
* DeBroglie wavelength, also called matter wave, any aspect of the behaviour or properties of a material object that varies in time or space in conformity with the mathematical equations that describe waves. By
analogy with the
wave and particle behaviour of light that had already been established experimentally, the French physicist
Louis de Broglie suggested (1924) that particles might have wave properties in addition to particle properties.
Three years later the wave nature of electrons was detected experimentally. Objects of everyday experience, however, have a computed wavelength much smaller than that of electrons, so their wave properties have never been detected; familiar objects show only particle behaviour. De Broglie waves play an appreciable role, therefore, only in the realm of
subatomic particles.
De Broglie waves account for the appearance of subatomic particles at conventionally unexpected sites because their waves penetrate barriers much as sound passes through walls. Thus a heavy atomic nucleus occasionally can eject a piece of itself in a process called
alpha decay. The piece of nucleus (alpha particle) has insufficient energy as a particle to overcome the force barrier surrounding the nucleus; but as a wave it can leak through the barrier—that is, it has a
finite probability of being found outside the nucleus.
See:
https://www.britannica.com/science/de-Broglie-wave
** Pauli exclusion principle is the assertion that no two electrons in an
atom can be at the same time in the same state or
configuration, proposed (1925) by the Austrian physicist
Wolfgang Pauli to account for the observed patterns of light emission from atoms. The exclusion principle subsequently has been generalized to include a whole class of particles of which the
electron is only one member.
Subatomic particles fall into two classes, based on their statistical behaviour. Those particles to which the Pauli exclusion principle applies are called
fermions; those that do not obey this principle are called
bosons. When in a closed system, such as an atom for electrons or a nucleus for protons and neutrons, fermions are distributed so that a given state is occupied by only one at a time.
See:
https://www.britannica.com/science/Pauli-exclusion-principle
Particles obeying the exclusion principle have a
characteristic value of
spin, or
intrinsic angular momentum; their spin is always some odd whole-number multiple of one-half. In the modern view of atoms, the space surrounding the dense nucleus may be thought of as consisting of
orbitals, or regions, each of which
comprises only two distinct states. The Pauli exclusion principle indicates that, if one of these states is occupied by an electron of spin one-half, the other may be occupied only by an electron of opposite spin, or spin negative one-half. An orbital occupied by a pair of electrons of opposite spin is filled: no more electrons may enter it until one of the pair vacates the orbital. An
alternative version of the exclusion principle as applied to atomic electrons states that no two electrons can have the same values of all four
quantum numbers.
The dark matter sector could well be peppered with different kinds of particles. This has a certain plausibility in string theory, which generically predicts a variety of axions*. Most of them would be too massive to be a suitable dark matter candidate. But if one of them is light enough to be dark matter, perhaps there may be more .
Hartmann352
* Axions are hypothetical lightweight particles whose existence would resolve two major problems.
The first, fussed over since the 1960s, is the strong charge-parity (CP) problem, which asks why the quarks and gluons that make up protons and neutrons obey a certain symmetry. Axions would show that
an unseen field is responsible.
The second is dark matter. Axions “are excellent dark matter candidates,” said
Asimina Arvanitaki, a theoretical physicist at the Perimeter Institute for Theoretical Physics in Waterloo, Canada. Axions would clump together in exactly the ways we expect dark matter to, and they have just the right properties to explain why they’re so hard to find — namely, they’re extremely light and reluctant to interact with regular matter.
See:
https://www.quantamagazine.org/a-hint-of-dark-matter-sends-physicists-looking-to-the-skies-20211019/