The light and fuzzy side of dark matter

December 01, 2020

Dark matter is the most abundant matter component in the universe. But while it influences all structure in the universe, its nature is still unknown. Among the many candidates is ultra-light dark matter, the lightest possible candidate for dark matter, which been receiving a lot of attention recently, as this might be probed by current and future experiments. MPA researchers have written a review on the current status of these models and their search for observational markers, introducing a division into three classes and showing how the rich phenomenology of this leading candidate for dark matter could help answer the question of what dark matter really is.

The nature of dark matter is one of the biggest mysteries in physics. This component is the most abundant matter component in our universe, responsible for all the structures we see in the universe. Evidence for its existence comes from observations on a wide range of scales, from galactic scales to galaxy clusters, going up to the large-scale structure of our universe. Its properties, as measured by the large cosmological observations, are that it needs to clump together, in order to form structures, that it does not interact (or interacts very weakly) with visible matter, and that it dominates the matter content of the universe, accounting for approximately 85% of all matter. In the standard model of cosmology, this is then called “cold dark matter” (CDM).

Figure 1: Sketch (not to scale) of the huge range of possible DM models that have been proposed. They span many orders of magnitude in mass (bottom) or energy (top), with DM represented by very distinct phenomena. On the far left is shown the scale for Dark Energy, followed by Ultra-Light Dark Matter (ULDM) – the main focus of this work – and Light Dark Matter. Other candidates include also Weakly Interacting Massive Particles (WIMPs), Composite Dark Matter or even Primordial Black Holes from the early universe.

Until now, dark matter has only been probed through its gravitational interaction with visible matter in the Universe. There has been no direct, indirect or particle collider evidence of a particle that could be the dark matter. The mystery of its nature is therefore one of the most important questions in modern physics. A huge variety of models has been created to explain the nature of dark matter, ranging from new elementary particles to large astrophysical objects like black holes (see Fig. 1). In the past few years, a new and appealing class of alternative models of dark matter has emerged as a leading candidate for dark matter, the ultra-light dark matter (ULDM) models. This class consists of the lightest possible particles that could explain the dark matter observations, with masses many orders of magnitude lighter than the mass of the electron.

Such light particles show a very interesting behaviour: They behave as a wave, with its characteristic wavelength inversely proportional to the ULDM mass. This means that in the mass range where ULDM behaves as dark matter, this length is similar to the size of galaxies. Inside galaxies, the wave nature of this DM candidate therefore is manifest and the galaxy is “fuzzy”, presenting dynamics that depart from standard CDM. On the outskirts and outside of galaxies, on larger distances, the ULDM can effectively be treated as a particle, recovering the observational successes of CDM.

Figure 2: Illustration of the behaviour of ULDM in galaxies: A condensate core is expected to form in the inner parts of the galaxy, where the wavelength of the ULDM is smaller than the mean separation of the particles, while the Dark Matter behaves more “normal” and as individual particles in the outskirts or outside of galaxies.

The wave nature of ULDM on small scales might lead to many effects on observables. On Galactic scales, the ULDM waves interfere and superpose, forming a collective macroscopic wave inside the galaxy. In this regime, the pressure exerted by the ULDM avoids clumping of dark matter in the interior of galaxies, instead forming a core (Fig. 2). These less dense, cored galaxies are indeed what is preferred by observations. This pressure on small scales has also an impact on the structure formation in our universe, since it counteracts clumping and suppresses the formation of the structures on those scales. This leads to a universe where small DM halos are not present, different from what is expected from CDM.

The wave nature of the ULDM models might also lead to interesting wave-like phenomena like interference. This pattern has already been seen in simulations and would represent a smoking gun signature of ULDM models if actually measured. In the interior of galaxies, where this superposition of ULDM waves takes place, the ULDM forms a Bose-Einstein condensate (BEC) or superfluid. These are some of the most exciting phenomena in quantum mechanics and very well-known and studied in the laboratory. A Bose-Einstein condensate forms, when a gas of light particles is in thermal equilibrium and cools down to temperatures where all particles have the lowest possible energy. In this regime, instead of behaving like individual waves, the waves overlap and create a unique macroscopic wave that now describes the system – the particles behave as a collective. And this is exactly what happens to ULDM in the interior of galaxies.

Figure 3: Summary of the constraints on the mass of the fuzzy dark matter particle to date. The horizontal shaded regions give excluded regions from a range of observations assuming that this form of DM dominates in the universe. The vertical bar shows the masses that originally motivated the creation of the fuzzy dark matter model; this mass range is almost excluded by the present bounds.

The presence of this condensate core formed in galaxies is a prediction of this class of models, and ULDM can be divided into three classes according to the properties of the cores and structures they form inside galaxies, and their resulting observational consequences. The simplest of these models is the fuzzy dark matter (FDM) with a very light ULDM particle, which is only influenced by gravity. This class of models includes the famous axion, a new elementary particle postulated to solve other problems in particle physics, but that can also behave like dark matter. The second class is the self-interacting fuzzy dark matter, with some level of interaction between the ULDM particles. The third class is the superfluid dark matter, a model where the ULDM condenses into a superfluid in the interior of galaxies. This class of models has a very different dynamics on small scales, reproducing the empirical behaviour of modified theories of gravity that claim to explain how galaxies rotate more precisely than using the classical Newtonian laws. Each of these models presents different properties and leads to distinct observational effects that can be probed by current and future cosmological and astrophysical measurements.

The most tested and well-known class of models is the fuzzy dark matter model. Using its effects on the dynamics and structures of galaxies and other astrophysical observables, a variety of small- and large-scale observations have put stringent bounds on the mass of this class of dark matter particles in the past few years (Fig. 3). While the preferred mass for the fuzzy dark matter is almost excluded by current bounds, this particle can still be heavier than first anticipated, representing a dark matter candidate that behaves more closely to CDM. These bounds still need to be confirmed, but this analysis already gives an indication of the exciting times ahead where effects on such small scales can be probed to answer questions about the nature of dark matter. In addition, the other classes of ULDM models are almost unconstrained, providing us with the opportunity to explore the possibility of these models to describe dark matter.

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