Fuzzy Dark Matter Research Articles

Relaxation in a Fuzzy Dark Matter Halo. II. Self-consistent Kinetic Equations

Abstract Fuzzy dark matter (FDM) is composed of ultra-light bosons having a de Broglie wavelength that is comparable to the size of the stellar component of galaxies at typical galactic velocities. FDM behaves like cold dark matter on large scales. However, on the scale of the de Broglie wavelength, an FDM halo exhibits density fluctuations that lead to relaxation, a process similar to the two-body relaxation that occurs in classical gravitational N-body systems and is described by the Fokker–Planck equation. We derive the FDM analog of that kinetic equation, which describes the evolution of the velocity distribution in a spatially homogeneous FDM halo. We show that the evolution of the velocity distribution predicted by our kinetic equation matches numerical solutions of the coupled Schrödinger–Poisson equations. We also determine the dielectric function and the dispersion relation for linear waves in an FDM halo.

Structure formation in large-volume cosmological simulations of fuzzy dark matter: impact of the non-linear dynamics

ABSTRACT An ultralight bosonic particle of mass around $10^{-22}\, \mathrm{eV}/c^2$ is of special interest as a dark matter candidate, as it both has particle physics motivations, and may give rise to notable differences in the structures on highly non-linear scales due to the manifestation of quantum-physical wave effects on macroscopic scales, which could address a number of contentious small-scale tensions in the standard cosmological model, ΛCDM. Using a spectral technique, we here discuss simulations of such fuzzy dark matter (FDM), including the full non-linear wave dynamics, with a comparatively large dynamic range and for larger box sizes than considered previously. While the impact of suppressed small-scale power in the initial conditions associated with FDM has been studied before, the characteristic FDM dynamics are often neglected; in our simulations, we instead show the impact of the full non-linear dynamics on physical observables. We focus on the evolution of the matter power spectrum, give first results for the FDM halo mass function directly based on full FDM simulations, and discuss the computational challenges associated with the FDM equations. FDM shows a pronounced suppression of power on small scales relative to cold dark matter (CDM), which can be understood as a damping effect due to ‘quantum pressure’. In certain regimes, however, the FDM power can exceed that of CDM, which may be interpreted as a reflection of order-unity density fluctuations occurring in FDM. In the halo mass function, FDM shows a significant abundance reduction below a characteristic mass scale only. This could in principle alleviate the need to invoke very strong feedback processes in small galaxies to reconcile ΛCDM with the observed galaxy luminosity function, but detailed studies that also include baryons will be needed to ultimately judge the viability of FDM.

Dark matter from a dark connection

In the first part of this note, we observe that a non-Riemannian piece in the affine connection (a “dark connection”) leads to an algebraically determined, conserved, symmetric 2-tensor in the Einstein field equations that is a natural dark matter candidate. The only other effect it has, is through its coupling to standard model fermions via covariant derivatives. If the local dark matter density is the result of a background classical dark connection, these Yukawa-like mass corrections are minuscule ([Formula: see text] for terrestrial fermions) and none of the tests of general relativity or the equivalence principle are affected. In the second part of the note, we give dynamics to the dark connection and show how it can be re-interpreted in terms of conventional dark matter particles. The simplest way to do this is to treat it as a composite field involving scalars or vectors. The (pseudo-)scalar model naturally has a perturbative shift-symmetry and leads to versions of the Fuzzy Dark Matter (FDM) scenario that has recently become popular (e.g. arXiv:1610.08297) as an alternative to WIMPs. A vector model with a [Formula: see text]-parity falls into the Planckian Interacting Dark Matter (PIDM) paradigm, introduced in arXiv:1511.03278. It is possible to construct versions of these theories that yield the correct relic density, fit with inflation and are falsifiable in the next round of CMB experiments. Our work is an explicit demonstration that the meaningful distinction is not between gravity modification and dark matter, but between theories with extra fields and those without.

Axial Anomaly in Galaxies and the Dark Universe

Motivated by the SU(2)CMB modification of the cosmological model ΛCDM, we consider isolated fuzzy-dark-matter lumps, made of ultralight axion particles whose masses arise due to distinct SU(2) Yang–Mills scales and the Planck mass MP. In contrast to SU(2)CMB, these Yang–Mills theories are in confining phases (zero temperature) throughout most of the Universe’s history and associate with the three lepton flavours of the Standard Model of particle physics. As the Universe expands, axionic fuzzy dark matter comprises a three-component fluid which undergoes certain depercolation transitions when dark energy (a global axion condensate) is converted into dark matter. We extract the lightest axion mass ma,e=0.675×10−23 eV from well motivated model fits to observed rotation curves in low-surface-brightness galaxies (SPARC catalogue). Since the virial mass of an isolated lump solely depends on MP and the associated Yang–Mills scale the properties of an e-lump predict those of μ- and τ-lumps. As a result, a typical e-lump virial mass ∼6.3×1010M⊙ suggests that massive compact objects in galactic centers such as Sagittarius A* in the Milky Way are (merged) μ- and τ-lumps. In addition, τ-lumps may constitute globular clusters. SU(2)CMB is always thermalised, and its axion condensate never has depercolated. If the axial anomaly indeed would link leptons with dark matter and the CMB with dark energy then this would demystify the dark Universe through a firmly established feature of particle physics.

Landau equation for self-gravitating classical and quantum particles: application to dark matter

We develop the kinetic theory of classical and quantum particles (fermions and bosons) in gravitational interaction. The kinetic theory of quantum particles may have applications in the context of dark matter. For simplicity, we consider an infinite and spatially homogeneous system (or make a local approximation) and neglect collective effects. This leads to the quantum Landau equation derived heuristically in (Physica A 332: 89, 2004). We establish its main properties: conservation laws, H-theorem, equilibrium state, relaxation time, quantum diffusion and friction coefficients, quantum Rosenbluth potentials, self-consistent evolution, (thermal) bath approximation, quantum Fokker–Planck equation, quantum King model $$\ldots $$ For bosonic particles, the Landau equation can describe the process of Bose–Einstein condensation. We discuss the relation of our study with the works of Levkov et al. (Phys Rev Lett 121: 151301, 2018) and Bar-Or et al. (Astrophys J 871: 28, 2019) on fuzzy dark matter halos and the formation of Bose stars and solitons.

Rapid onset of the 21-cm signal suggests a preferred mass range for dark matter particle

We are approaching a new era to probe the 21-cm neutral hydrogen signal from the period of cosmic dawn. This signal offers a unique window to the virgin Universe, e.g., to study dark matter models with different small-scale behaviours. The EDGES collaboration has recently published the first results of the global 21-cm spectrum. We demonstrate that such a signal can be used to set, unlike most observations concerning dark matter, both lower and upper limits for the mass of dark matter particles. We study the 21-cm signal resulting from a simple warm dark matter model with a sharp-$k$ window function calibrated for high redshifts. We tie the PopIII star formation to Lyman-alpha and radio background production. Using MCMC to sample the parameter space we find that to match the EDGES signal, a warm dark matter particle must have a mass of $7.3^{+1.6}_{-3.3}$ keV at 68\% confidence interval. This translates to $2.2^{+1.4}_{-1.7} \times 10^{-20}$ eV for fuzzy dark matter and $63^{+19}_{-35}$ keV for Dodelson-Widrow sterile neutrinos. Cold dark matter is unable to reproduce the signal due to its slow structure growth.

Soliton oscillations and revised constraints from Eridanus II of fuzzy dark matter

Fuzzy dark matter (FDM) has been a promising alternative to standard cold dark matter. The model consists of ultralight bosons with mass $m_b \sim 10^{-22}$ eV and features a quantum-pressure-supported solitonic core that oscillates. In this work, we show that the soliton density oscillations persist even after significant tidal stripping of the outer halo. We report two intrinsic yet distinct timescales associated, respectively, with the ground-state soliton wavefunction $\tau_{00}$ and the soliton density oscillations $\tau_\text{soliton}$, obeying $\tau_\text{soliton} /\tau_{00} \simeq 2.3$. The central star cluster (SC) in Eridanus II has a characteristic timescale $\tau_\text{soliton} / \tau_\text{SC} \sim 2$ to $3$ that deviates substantially from unity. As a result, we demonstrate, both analytically and numerically with three-dimensional self-consistent FDM simulations, that the gravitational heating of the SC owing to soliton density oscillations is negligible irrespective of $m_b$. We also show that the subhalo mass function to form Eridanus II does not place a strong constraint on $m_b$. These results are contrary to the previous findings by Marsh & Niemeyer (2019).

The MUSE-Faint survey. II. The dark matter-density profile of the ultra-faint dwarf galaxy Eridanus 2

Aims. We use stellar line-of-sight velocities to constrain the dark-matter density profile of Eridanus 2, an ultra-faint dwarf galaxy with an absolute V-band magnitude MV = −7.1 that corresponds to a stellar mass M* ≈ 9 × 104 M⊙. We furthermore derive constraints on fundamental properties of self-interacting and fuzzy dark matter scenarios. Methods. We present new observations of Eridanus 2 from MUSE-Faint, a survey of ultra-faint dwarf galaxies with the Multi Unit Spectroscopic Explorer on the Very Large Telescope, and determine line-of-sight velocities for stars inside the half-light radius. Combined with literature data, we have 92 stellar tracers out to twice the half-light radius. With these tracers we constrain models of cold dark matter, self-interacting dark matter, and fuzzy dark matter, using CJAM and pyGravSphere for the dynamical analysis. The models of self-interacting and fuzzy dark matter relate the density profile to the self-interaction coefficient and the dark-matter particle mass, respectively. Results. We find substantial evidence (Bayes factor ∼10−0.6) for cold dark matter (a cuspy halo) over self-interacting dark matter (a cored halo) and weak evidence (Bayes factor ∼10−0.4) for fuzzy dark matter over cold dark matter. We find a virial mass M200 ∼ 108 M⊙ and astrophysical factors J(αcJ) ~ 1011 M⊙2 kpc−5 and D(αcD) ~ 102 − 102.5 M⊙ kpc−2 (proportional to dark-matter annihilation and decay signals, respectively), the exact values of which depend on the density profile model. The mass-to-light ratio within the half-light radius is consistent with the literature. We do not resolve a core (rc < 47 pc, 68% confidence level) or a soliton (rsol < 7.2 pc, 68% confidence level). These limits are equivalent to an effective self-interaction coefficient fΓ < 2.2 × 10−29 cm3 s−1 eV−1 c2 and a fuzzy-dark-matter particle mass ma > 4.0 × 10−20 eV c−2. The constraint on self-interaction is complementary to those from gamma-ray searches. The constraint on fuzzy-dark-matter particle mass is inconsistent with those obtained for larger dwarf galaxies, suggesting that the flattened density profiles of those galaxies are not caused by fuzzy dark matter.

Angular momentum and the absence of vortices in the cores of fuzzy dark matter haloes

ABSTRACT Scalar field dark matter (SFDM), comprised of ultralight (≳ 10−22 eV) bosons, is distinguished from massive (≳GeV), collisionless cold dark matter (CDM) by its novel structure-formation dynamics as Bose–Einstein condensate (BEC) and quantum superfluid with wave-like properties, described by the Gross-Pitaevskii and Poisson (GPP) equations. In the free-field (‘fuzzy’) limit of SFDM (FDM), structure is inhibited below the de Broglie wavelength λdeB, but resembles CDM on larger scales. Virialized haloes have ‘solitonic’ cores of radius ∼λdeB that follow the ground-state attractor solution of GPP, surrounded by CDM-like envelopes. As superfluid, SFDM is irrotational (vorticity-free) but can be unstable to vortex formation. We previously showed this can happen in halo cores, from angular momentum arising during structure formation, when repulsive self-interaction (SI) is present to support them out to a second length scale λSI with λSI > λdeB (the Thomas–Fermi regime), but only if SI is strong enough. This suggested FDM cores ($ {\rm without}$ SI) would not form vortices. FDM simulations later found vortices, but only outside halo cores, consistent with our previous suggestion based upon TF-regime analysis. We extend that analysis now to FDM, to show explicitly that vortices should not arise in solitonic cores from angular momentum, modelling them as either Gaussian spheres, or ( n = 2)-polytropic, irrotational Riemann-S ellipsoids. We find that, for typical halo spin parameters, angular momentum per particle is below ℏ, the minimum required even for one singly-quantized vortex in the centre. Even for higher angular momentum, however, vortex formation is not energetically favoured.

Fuzzy Dark Matter and the 21 cm Power Spectrum

Abstract We model the 21 cm power spectrum across the Cosmic Dawn and the Epoch of Reionization (EoR) in fuzzy dark matter (FDM) cosmologies. The suppression of low-mass halos in FDM models leads to a delay in the onset redshift of these epochs relative to cold dark matter (CDM) scenarios. This strongly impacts the 21 cm power spectrum and its redshift evolution. The 21 cm power spectrum at a given stage—i.e., compared at fixed average brightness temperature but varying redshift—of the EoR/Cosmic Dawn process is also modified: in general, the amplitude of 21 cm fluctuations is boosted by the enhanced bias factor of galaxy-hosting halos in FDM. We forecast the prospects for discriminating between CDM and FDM with upcoming power spectrum measurements from HERA, accounting for degeneracies between astrophysical parameters and dark matter properties. If FDM constitutes the entirety of the dark matter and the FDM particle mass is 10−21 eV, HERA can determine the mass to within 20% at 2σ confidence.

Narrowing the Mass Range of Fuzzy Dark Matter with Ultrafaint Dwarfs

Abstract Fuzzy dark matter (FDM) is an attractive dark matter candidate motivated by small-scale problems in astrophysics and with a rich phenomenology on those scales. We scrutinize the FDM model, more specifically the mass of the FDM particle, through a dynamical analysis for the Galactic ultrafaint dwarf (UFD) galaxies. We use a sample of 18 UFDs to place the strongest constraints to date on the mass of the FDM particle, updating on previous bounds using a subset of the sample used here. We find that most of the sample UFDs prefer an FDM particle mass heavier than 10−21 eV. In particular, Segue 1 provides the strongest constraint, with m ψ = 1.1 − 0.7 + 8.3 × 10 − 19 eV . The constraints found here are the first that are compatible with various other independent cosmological and astrophysical bounds found in the literature, in particular with the latest bounds using the Lyα forest. We also find that the constraints obtained in this work are not compatible with the bounds from luminous dwarf galaxies, as already pointed out in the previous work using UFDs. This could indicate that although a viable dark matter model, it might be challenging for the FDM model to solve the small-scale problems.

One-dimensional fuzzy dark matter models: Structure growth and asymptotic dynamics

This paper investigates the feasibility of simulating Fuzzy Dark Matter (FDM) with a reduced number of spatial dimensions. Our aim is to set up a realistic, yet numerically inexpensive, toy model in $(1+1)$-dimensional space time, that - under well controlled system conditions - is capable of realizing important aspects of the full-fledged $(3+1)$-FDM phenomenology by means of one-dimensional analogues. Based on the coupled, nonlinear and nonlocal $(3+1)$-Schr\"odinger-Poisson equation under periodic boundary conditions, we derive two distinct one-dimensional models that differ in their transversal matter distribution and consequently in their nonlocal interaction along the single dimension of interest. We show that these discrepancies change the relaxation process of initial states as well as the asymptotic, i.e., thermalized and virialized, equilibrium state. Our investigation includes the dynamical evolution of artificial initial conditions for non-expanding space, as well as cosmological initial conditions in expanding space. The findings of this work are relevant for the interpretation of numerical simulation data modelling nonrelativistic fuzzy cold dark matter in reduced dimensions, in the quest for testing such models and for possible laboratory implementations of them.

Constraints on long range force from perihelion precession of planets in a gauged L_e-L_{mu ,tau } scenario

The standard model leptons can be gauged in an anomaly free way by three possible gauge symmetries namely {L_e-L_mu }, {L_e-L_tau }, and {L_mu -L_tau }. Of these, {L_e-L_mu } and {L_e-L_tau } forces can mediate between the Sun and the planets and change the perihelion precession of planetary orbits. It is well known that a deviation from the 1/r^2 Newtonian force can give rise to a perihelion advancement in the planetary orbit, for instance, as in the well known case of Einstein’s gravity (GR) which was tested from the observation of the perihelion advancement of the Mercury. We consider the long range Yukawa potential which arises between the Sun and the planets if the mass of the gauge boson is M_{Z^{prime }}le mathcal {O}(10^{-19})mathrm {eV}. We derive the formula of perihelion advancement for Yukawa type fifth force due to the mediation of such U(1)_{L_e-L_{mu ,tau }} gauge bosons. The perihelion advancement for Yukawa potential is proportional to the square of the semi major axis of the orbit for small M_{Z^{prime }}, unlike GR where it is largest for the nearest planet. For higher values of M_{Z^{prime }}, an exponential suppression of the perihelion advancement occurs. We take the observational limits for all planets for which the perihelion advancement is measured and we obtain the upper bound on the gauge boson coupling g for all the planets. The Mars gives the stronger bound on g for the mass range le 10^{-19}mathrm {eV} and we obtain the exclusion plot. This mass range of gauge boson can be a possible candidate of fuzzy dark matter whose effect can therefore be observed in the precession measurement of the planetary orbits.

Evolving ultralight scalars into non-linearity with Lagrangian perturbation theory

ABSTRACT Many models of high energy physics suggest that the cosmological dark sector consists of not just one, but a spectrum of ultralight scalar particles with logarithmically distributed masses. To study the potential signatures of low concentrations of ultralight axion (also known as fuzzy) dark matter, we modify Lagrangian perturbation theory (LPT) by distinguishing between trajectories of different dark matter species. We further adapt LPT to include the effects of a quantum potential, which is necessary to generate correct initial conditions for ultralight axion simulations. Based on LPT, our modified scheme is extremely efficient on large scales and it can be extended to an arbitrary number of particle species at very little computational cost. This allows for computation of self-consistent initial conditions in mixed dark matter models. Additionally, we find that shell-crossing is delayed for ultralight particles and that the deformation tensor extracted from LPT can be used to identify the range of redshifts and scales for which the Madelung formalism of fuzzy dark matter can lead to divergences.

Don't cross the streams: caustics from fuzzy dark matter

We study how tidal streams from globular clusters may be used to constrain the mass of ultra-light dark matter particles, called `fuzzy' dark matter (FDM). A general feature of FDM models is the presence of ubiquitous density fluctuations in bound, virialized dark matter structures, on the scale of the de Broglie wavelength, arising from wave interference in the evolving dark matter distribution. These time-varying fluctuations can disturb the motions of stars, leading to potentially observable signatures in cold thin tidal streams in our own Galaxy. The study of this effect has been hindered by the difficulty in simulating the FDM wavefunction in Milky Way-sized systems. We present a simple method to evolve realistic wavefunctions in nearly static potentials, that should provide an accurate estimate of this granulation effect. We quantify the impact of FDM perturbations on tidal streams, and show that initially, while stream perturbations are small in amplitude, their power spectra exhibit a sharp cutoff corresponding to the de Broglie wavelength of the FDM potential fluctuations. Eventually, when stream perturbations become nonlinear, fold caustics generically arise that lead to density fluctuations with universal behavior. This erases the signature of the de Broglie wavelength in the stream density power spectrum, but we show that it will still be possible to determine the FDM mass in this regime, by considering the fluctuations in quantities like angular momenta or actions.

Constraints on Dark Matter Properties from Observations of Milky Way Satellite Galaxies

We perform a comprehensive study of Milky Way (MW) satellite galaxies to constrain the fundamental properties of dark matter (DM). This analysis fully incorporates inhomogeneities in the spatial distribution and detectability of MW satellites and marginalizes over uncertainties in the mapping between galaxies and DM halos, the properties of the MW system, and the disruption of subhalos by the MW disk. Our results are consistent with the cold, collisionless DM paradigm and yield the strongest cosmological constraints to date on particle models of warm, interacting, and fuzzy dark matter. At 95% confidence, we report limits on (i) the mass of thermal relic warm DM, mWDM>6.5 keV (free-streaming length, λfs≲10h−1 kpc), (ii) the velocity-independent DM-proton scattering cross section, σ0<8.8×10−29 cm2 for a 100 MeV DM particle mass [DM-proton coupling, cp≲(0.3 GeV)−2], and (iii) the mass of fuzzy DM, mϕ>2.9×10−21 eV (de Broglie wavelength, λdB≲0.5 kpc). These constraints are complementary to other observational and laboratory constraints on DM properties.Received 30 July 2020Revised 12 December 2020Accepted 27 January 2021DOI:https://doi.org/10.1103/PhysRevLett.126.091101© 2021 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasDark matterParticle dark matterPhysical SystemsGalactic halosGravitation, Cosmology & Astrophysics

A Cuspy Dark Matter Halo

Abstract The cusp–core problem is one of the main challenges of the cold dark matter paradigm on small scales; the density of a dark matter halo is predicted to rise rapidly toward the center as ρ(r) ∝ r α with α between −1 and −1.5, while such a cuspy profile has not been clearly observed. We have carried out the spatially resolved mapping of gas dynamics toward a nearby ultradiffuse galaxy (UDG), AGC 242019. The derived rotation curve of dark matter is well fitted by the cuspy profile as described by the Navarro–Frenk–White model, while the cored profiles including both the pseudo-isothermal and Burkert models are excluded. The halo has α = −(0.90 ± 0.08) at the innermost radius of 0.67 kpc, M halo = (3.5 ± 1.2) × 1010 M ⊙, and a small concentration of 2.0 ± 0.36. The UDG AGC 242019 challenges alternatives of cold dark matter by constraining the particle mass of fuzzy dark matter to be &lt;0.11 × 10−22 or &gt;3.3 × 10−22 eV, the cross section of self-interacting dark matter to be &lt;1.63 cm2 g−1, and the particle mass of warm dark matter to be &gt;0.23 keV, all of which are in tension with other constraints. The modified Newtonian dynamics is also inconsistent with a shallow radial acceleration relationship of AGC 242019. For the feedback scenario that transforms a cusp to a core, AGC 242019 disagrees with the stellar-to-halo mass ratio dependent model but agrees with the star formation threshold dependent model. As a UDG, AGC 242019 is in a dwarf-sized halo with weak stellar feedback, late formation time, normal baryonic spin, and low star formation efficiency (SFR/gas).

Galaxies with fuzzy dark matter

This is a brief review on some properties of galaxies in the fuzzy dark matter model, where dark matter is an ultra-light scalar particle with mass $m = O(10^{-22})eV$. From quantum pressure, dark matter has a halo length scale which can solve the small scale issues of the cold dark matter model, such as the core-cusp problem, and explain many other observed mysteries of galaxies.

Oscillations and random walk of the soliton core in a fuzzy dark matter halo

A Fuzzy Dark Matter (FDM) halo consists of a soliton core close to the center and an NFW-like density profile in the outer region. Previous investigations found that the soliton core exhibits temporal oscillations and random walk excursions around the halo center. Analyzing a set of numerical simulations, we show that both phenomena can be understood as the results of wave interference -- a suitable superposition of the ground (solitonic) state and excited states in a fixed potential suffices to account for the main features of these phenomena. Such an eigenmode analysis can shed light on the evolution of a satellite halo undergoing tidal disruption. As the outer halo is stripped away, reducing the amplitudes of the excited states, the ground state evolves adiabatically. This suggests diminished soliton oscillations and random walk excursions, an effect to consider in deducing constraints from stellar heating.

Ultralight DM bosons with an axion-like potential: scale-dependent constraints revisited

A scalar field ϕ endowed with a trigonometric potential has been proposed to play the role of Dark Matter. A deep study of the cosmological evolution of linear perturbations, and its comparison to the Cold Dark Matter (CDM) and Fuzzy Dark Matter (FDM) cases (scalar field with quadratic potential), reveals an enhancement in the amplitude of the mass power spectrum for large wave numbers due to the non-linearity of the axion-like potential. For the first time, we study the scale-dependence on physical quantities such as the growth factor Dk, the velocity growth factor fk, and fk σ8. We found that for z<10, all these quantities recover the CDM evolution, whereas for high redshift there is a clear distinction between each model (FDM case, and axion-like potential) depending on the wavenumber k and on the decay parameter of the axion-like potential as well. A semi-analytical Halo Mass Function is also revisited, finding a suppression of the number of low mass halos, as in the FDM case, but with a small increment in the amplitude of the variance and halo mass function due to the non-linearity of the axion-like potential. Finally, we present constraints on the axion mass and the axion decay parameter by using data of the Planck Collaboration 2018 and Lyman-α forest.