We illustrate the effect of boundary conditions on the evolution of structure in Fuzzy Dark Matter. Scenarios explored include the evolution of single, ground-state equilibrium solutions of the Schrödinger-Poisson system, the relaxation of a Gaussian density fluctuation, mergers of two equilibrium configurations, and the random merger of many solitons. For comparison, each scenario is evolved twice, with isolation boundary conditions and periodic boundary conditions, the two commonly used to simulate isolated systems and structure formation, respectively. Replacing isolation boundary conditions by periodic boundary conditions changes the domain topology and dynamics of each scenario, by affecting the outcome of gravitational cooling. With periodic boundary conditions, the ground-state equilibrium solution and Gaussian fluctuation each evolve toward the single equilibrium solitonic core of the isolated case, but surrounded by a tail, unlike the isolated versions. The case of head-on, binary mergers illustrates additional effects, caused by the pull suffered by the system due to the infinite network of periodic images along each direction of the domain. Binary merger with angular momentum is the first scenario we found in which the tail has a polynomial profile when using a periodic domain. Finally, the 3D merger of many, randomly-placed solitonic cores of different mass makes a solitonic core surrounded by a tail with power-law-like density profile, for periodic boundary conditions, while producing a core with a much sharper fall-off in the isolated case. This suggests that the conclusion of earlier work that the ground-state equilibrium solution is an attractor for the asymptotic state is true even in 3D and for general circumstances, but only if gravitational cooling is able to carry mass and energy off to infinity, which isolation boundary conditions allow, but periodic ones do not.
We present zoom-in simulations of fuzzy dark matter (FDM) halos including baryons and star-formation with sufficient resolution to follow the formation and evolution of central solitons. We find that their properties are determined by the local dark matter velocity dispersion in the combined dark matter-baryon gravitational potential. This motivates a simple prescription to estimate the radial density profiles of FDM cores in the presence of baryons. As cores become more massive and compact if baryons are included, galactic rotation curve measurements are likely harder to reconcile with FDM.
The distinctive effects of fuzzy dark matter are most visible at non-linear galactic scales. We present the first simulations of mixed fuzzy and cold dark matter, obtained with an extended version of the Nyx code. Fuzzy (or ultralight, or axion-like) dark matter dynamics are governed by the comoving Schrödinger-Poisson equation. This is evolved with a pseudospectral algorithm on the root grid, and with finite differencing at up to six levels of adaptive refinement. Cold dark matter is evolved with the existing N-body implementation in Nyx. We present the first investigations of spherical colla…
We perform a numerical comparison between the fuzzy dark matter model and the cold dark matter model, focusing on formation of satellite galaxy planes around massive galaxies. Such galactic dynamics with controlled initial subhalo configurations are investigated using GADGET2 for the cold dark matter and PyUltraLight for the fuzzy dark matter, respectively. We demonstrate that satellite galaxies in the fuzzy dark matter side have a tendency to form more flattened and corotating satellite systems than in the cold dark matter side mainly due to the dissipation by the gravitational cooling effect…
The electroweak axion is identified with the fuzzy dark matter of a mass $m\simeq 10^{-20}$--$10^{-19}\,{\rm eV}$. The model predicts two components of dark matter, one is ultralight and the other is WIMP-like. The Chern-Simons-type interaction between the fuzzy dark matter and photon and the $B+L$ breaking proton decays are predicted.
We introduce a tool that solves the Schrödinger-Euler-Poisson system of equations and allows the study of the interaction between ultralight bosonic dark matter, whose dynamics is described with the Schrödinger-Poisson system and luminous matter which, as a first approximation, is modeled with a single component compressible ideal fluid. The two matter fields are coupled through the Poisson equation, whose source is the addition of both, dark matter and fluid densities. We describe the numerical methods used to solve the system of equations and present tests for each of the two components, tha…
In hierarchical models of structure formation, the first galaxies form in low-mass dark matter potential wells, probing the behavior of dark matter on kiloparsec (kpc) scales. Even though these objects are below the detection threshold of current telescopes, future missions will open an observational window into this emergent world. In this Letter we investigate how the first galaxies are assembled in a `fuzzy' dark matter (FDM) cosmology where dark matter is an ultralight $\sim 10^{-22}$~eV boson and the primordial stars are expected to form along dense dark matter filaments. Using a first-of…
We present the results of a full cosmological simulation with the new code SCALAR, where dark matter is in form of fuzzy dark matter, described by a light scalar field with a mass of $m_{\rm B} = 2.5 \times 10^{-22}$ eV and evolving according to the Schrödinger-Poisson system of equations. In comoving units, the simulation volume is $2.5 ~ h^{-1} {\rm Mpc}$ on a side, with a resolution of $20~h^{-1}{\rm pc}$ at the finest refinement level. We analyse the formation and the evolution of central solitonic cores, which are found to leave their imprints on dark matter density profiles, resulting in…
Axion-like particle (ALP) dark matter shows distinctive behavior on scales where wavelike effects dominate over self-gravity. Ultralight axions are candidates for fuzzy dark matter (FDM) whose de Broglie wavelength in virialized halos reaches scales of kiloparsecs. Important features of FDM scenarios are the formation of solitonic halo cores, suppressed small-scale perturbations, and enhanced gravitational relaxation. More massive ALPs, including the QCD axion, behave like CDM on galactic scales but may be clumped into axion miniclusters if they were produced after inflation. Just as FDM halos…
We numerically study the movement of two colliding fuzzy dark matter solitons without explicit self-interaction and find the effective cross section of dissipative change in velocity. The cross section turns out to be inversely proportional to the velocity cubed, and we present its analytic interpretation. Using the result we roughly estimate spatial offsets during head-on collisions of two fuzzy dark matter halos, which can be related to the spatial offsets between stars and dark matter in collisions of some galaxy clusters. We also show that the gravitational cooling plays an important role …
Scalar fields appear in many cosmological models, in particular in order to provide explanations for dark energy and inflation, but also to emulate dark matter. In this paper, we show that it is possible for a scalar field to replace simultaneously dark matter, dark energy and inflation by assuming the existence of a non-minimal coupling to gravity, a Mexican hat potential, and a spontaneous symmetry breaking before inflation. After inflation, the scalar field behaves like a dark fluid, mimicking dark energy and dark matter, and has a dark matter behaviour similar to fuzzy dark matter.
We study tidal stripping of fuzzy dark matter (FDM) subhalo cores using simulations of the Schrödinger-Poisson equations and analyze the dynamics of tidal disruption, highlighting the differences with standard cold dark matter. Mass loss outside of the tidal radius forces the core to relax into a less compact configuration, lowering the tidal radius. As the characteristic radius of a solitonic core scales inversely with its mass, tidal stripping results in a runaway effect and rapid tidal disruption of the core once its central density drops below $4.5$ times the average density of the host wi…
We derive the halo mass function (HMF) for fuzzy dark matter (FDM) by solving the excursion set problem explicitly with a mass-dependent barrier function, which has not been done before. We find that compared to the naive approach of the Sheth--Tormen HMF for FDM, our approach has a higher cut off mass and the cut off mass changes less strongly with redshifts. Using merger trees constructed with a modified version of the Lacey & Cole formalism that accounts for suppressed small scale power and the scale-dependent growth of FDM haloes and the semi-analytic GALACTICUS code, we study the statisti…
Fuzzy Dark Matter (FDM) is one of the recent models for dark matter. According to this model, dark matter is made of very light scalar particles with considerable quantum mechanical effects on the galactic scale, which solves many problems of the cold dark matter (CDM). Here we use the observed data from the rotation curve of the Milky Way (MW) Galaxy to compare the results from FDM and CDM models. We show FDM adds a local peak on the rotation curve close to the center of the bulge, where its position and amplitude depend on the mass of FDM particles. By fitting the observed rotation curve wit…
We present a novel method to constrain the mass of ultra-light bosons as the dark matter using stellar streams formed by disrupting Globular Clusters in the Milky Way. The turbulent density field of Fuzzy Dark Matter (FDM) haloes results in perturbations and dynamical heating of thin streams. Using numerical simulations based on an effective model, we explore the magnitude of this phenomenon and show that this is observable for the range of axion masses $m_a$ that is interesting for alleviating the `small-scale problems' of $Λ$CDM. We derive an analytical model for the thickening of thin stell…
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 …
Fuzzy Dark Matter (FDM), motivated by string theory, has recently become a hot candidate for dark matter. The rest mass of FDM is believed to be $\sim 10^{-22}$eV and the corresponding de-Broglie wave length is $\sim 1$kpc. Therefore, the quantum effect of FDM plays an important role in structure formation. In order to study the cosmological structure formation in FDM model, several simulation techniques have been introduced. We review the current status and challenges in the cosmological simulation for the FDM model in this paper.
Constraints on the fuzzy dark matter mass using globular clusters in dwarf galaxies from Euclid ERO data
LIRA, Observatoire de Paris, Université PSL, Sorbonne Université, Université Paris Cité, CY Cergy Paris Université, CNRS（巴黎天文台 LIRA 实验室，PSL 大学，索邦大学，巴黎西岱大学，CY 塞吉-蓬图瓦兹大学，法国国家科学研究中心）；Université de Strasbourg, CNRS, Observatoire astronomique de Strasbourg, UMR 7550（斯特拉斯堡大学，法国国家科学研究中心，斯特拉斯堡天文台）；Kavli IPMU (WPI), UTIAS, The University of Tokyo（东京大学 Kavli 宇宙物理学与数学起源研究所（WPI），UTIAS）；Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona（巴塞罗那大学宇宙科学研究所）
Fuzzy dark matter (FDM) or wave dark matter is an alternative theory designed to solve the small-scale problems faced by the standard cold dark matter proposal for the primary material component of the universe. It is made up of ultra-light axions having mass $\sim 10^{-22}$ eV that typically have de Broglie wavelength of several kpc, alleviating some of the apparent small-scale discrepancies faced by the standard $Λ$CDM paradigm. In this paper, we calculate the halo mass function for the fuzzy dark matter using a sharp-k window function and compare it with one calculated using numerical simul…
Equations of motion for excited states of weakly self-interacting bosons forming fuzzy dark matter are solved using the WKB approximation. The contribution of self-interactions are neglected in the equations of motion. Wave functions of excited states are expressed in terms of a yet undetermined gravitational potential. At equilibrium, the contributions of states to the density distribution are summed using Bose-Einstein statistics. Combined with the Poisson equation, a differential equation is obtained for the gravitational potential, which has physically acceptable solutions only if the ener…
We explore the effect of a supermassive black hole (SMBH) on the density profile of a fuzzy dark matter (FDM) soliton core at the centre of a dark matter halo. We numerically solve the Schrödinger-Poisson equations, treating the black hole as a gravitational point mass, and demonstrate that this additional perturbing term has a `squeezing' effect on the soliton density profile, decreasing the core radius and increasing the central density. In the limit of large black hole mass, the solution approaches one akin to the hydrogen atom, with radius inversely proportional to the black hole mass. By …
Whereas cold dark matter (CDM) simulations predict central dark matter cusps with densities that diverge as $ρ$(r)$\sim$ 1/r observations often indicate constant density cores with finite central densities $ρ_0$ and a flat density distribution within a core radius r$_0$. This paper investigates whether this core-cusp problem can be solved by fuzzy dark matter (FDM), a hypothetical particle with a mass of order m$\approx$10$^{-22}$eV and a corresponding de Broglie wavelength on astrophysical scales. We show that galaxies with CDM halo virial masses M$_{vir} \leq 10^{11}$M$_{\odot}$ follow two c…
Institute of Astrophysics, National Taiwan University（台湾大学天文研究所）；Department of Physics, National Taiwan University（台湾大学物理系）；Center for Theoretical Physics, National Taiwan University（台湾大学理论物理中心）；National Center for Theoretical Sciences（国家理论科学中心）
We find that a fuzzy dark matter background and the mG scale magnetic field in the galactic center can give rise to a radiation with a very large energy release. The frequency of the radiation field is the same as the frequency of the oscillating axion-like background field. We show that there is an energy transfer between the fuzzy dark matter sector and the electromagnetic sector because of the presence of the generated radiation field and the galactic magnetic field. The energy release rate of radiation is found to be very slow in comparison with the energy of fuzzy dark matter but could be…
Aims. We use stellar line-of-sight velocities to constrain the dark matter-density profile of Eridanus 2, an ultra-faint dwarf galaxy ($M_\mathrm{V} = -7.1$, $M_* \approx 9 \times 10^4\,M_\odot$). 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 MUSE 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 …
One of the challenging questions in cosmology is the nature of dark matter particles. Fuzzy Dark Matter (FDM) is one of the candidates which is made of very light ($m_{FDM}\simeq 10^{-22}-10^{-21}$ eV) bosonic particles with no self-interaction. It is introduced by the motivation to solve the core-cusp problem in the galactic halos. In this work, we investigate the observational features from FDM halo collisions. Taking into account the quantum wave-length of the condensed bosonic structure, we determine the interference of the wave function of cores after collision. The fringe formation in th…
We investigate cosmological structure formation in Fuzzy Dark Matter (FDM) with an attractive self-interaction (SI) with numerical simulations. Such a SI would arise if the FDM boson were an ultra-light axion, which has a strong CP symmetry-breaking scale (decay constant). Although weak, the attractive SI may be strong enough to counteract the quantum 'pressure' and alter structure formation. We find in our simulations that the SI can enhance small-scale structure formation, and soliton cores above a critical mass undergo a phase transition, transforming from dilute to dense solitons.
We present an in-depth exploration of the phenomenon of dynamical friction in a universe where the dark matter is composed entirely of so-called Fuzzy Dark Matter (FDM), ultralight bosons of mass $m\sim\mathcal{O}(10^{-22})\,$eV. We review the classical treatment of dynamical friction before presenting analytic results in the case of FDM for point masses, extended mass distributions, and FDM backgrounds with finite velocity dispersion. We then test these results against a large suite of fully non-linear simulations that allow us to assess the regime of applicability of the analytic results. We…
In the fuzzy dark matter (FDM) model, gravitationally collapsed objects always consist of a solitonic core located within a virialised halo. Although various numerical simulations have confirmed that the collapsed structure can be described by a cored NFW like density profile, there is still disagreement about the relation between the core mass and the halo mass. To fully understand this relation, we have assembled a large sample of cored haloes based on both idealised soliton mergers and cosmological simulations with various box sizes. We find that there exists a sizeable dispersion in the co…
Fuzzy dark matter (FDM) is a proposed modification for the standard cold dark matter (CDM) model motivated by small-scale discrepancies in low-mass galaxies. Composed of ultra-light (mass $\sim 10^{-22}$ eV) axions with kpc-scale de Broglie wavelengths, this is one of a class of candidates that predicts that the first collapsed objects form in relatively massive dark matter halos. This implies that the formation history of the first stars and galaxies would be very different, potentially placing strong constraints on such models. Here we numerically simulate the formation of the first stars in…
We use observations of ultra-faint dwarf (UFD) galaxies to constrain the particle mass of ultra-light dark matter. Potential fluctuations created by wave interference in virialized "fuzzy" dark matter (FDM) halos dynamically heat stellar orbits in UFDs, some of which exhibit velocity dispersions of $\lesssim$ 3 km/s and sizes $\lesssim$ 40 pc. Using simulations of FDM halos, and existing measurements of sizes and stellar radial velocities in Segue 1 and Segue 2 UFDs, we derive a lower limit on the dark matter particle mass of $m_{fdm} > 3\times 10^{-19}$ eV at 99% confidence, marginalized over…
We model the 21cm power spectrum across the Cosmic Dawn and the Epoch of Reionization (EoR) in fuzzy dark matter (FDM) cosmologies. The suppression of small 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 21cm power spectrum and its redshift evolution. The 21cm power spectrum at a given stage of the EoR/Cosmic Dawn process is also modified: in general, the amplitude of 21cm fluctuations is boosted by the enhanced bias factor of galaxy hosting halos in FDM. We forecast the prospects for discr…
String theory has been claimed to give rise to natural fuzzy dark matter candidates in the form of ultralight axions. In this paper we revisit this claim by a detailed study of how moduli stabilisation affects the masses and decay constants of different axion fields which arise in type IIB flux compactifications. We find that obtaining a considerable contribution to the observed dark matter abundance without tuning the axion initial misalignment angle is not a generic feature of 4D string models since it requires a mild violation of the $S f\lesssim M_P$ bound, where $S$ is the instanton actio…
