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 shallower central densities, and on rotation curves, producing an additional circular velocity peak at small radii from the center. We find that the suppression of structures due to the quantum nature of the scalar field results in an shallower halo mass function in the low-mass end compared to the case of a $Λ$CDM simulation, in which dark matter is expected to cluster at all mass scales even if evolved with the same initial conditions used for fuzzy dark matter. Furthermore, we verify the scaling relations characterising the solution to the Schrödinger-Poisson system, for both isolated and merging halos, and we find that they are preserved by merging processes. We characterise each fuzzy dark matter halo in terms of the dimensionless quantity $Ξ\propto \left | E_{\rm halo} \right |/M_{\rm halo}^3$ and we show that the core mass is tightly linked to the halo mass by the core-halo mass relation $M_{\rm core}/M_{\rm halo} \propto Ξ^{1/3}$. We also show that the core surface density of the simulated fuzzy dark matter halos does not follow the scaling with the core radius as observed for dwarf galaxies, representing a big challenge for the fuzzy dark matter model as the sole explanation of core formation.
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.
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.
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) 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 $τ_{00}$ and the soliton density oscillations $τ_\text{soliton}$, obeying $τ_\text{soliton} /τ_{00} \simeq 2.3$. The centra…
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 …
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.
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…
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 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…
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.
We derive the non-relativistic limit of a massive vector field. We show that the Cartesian spatial components of the vector behave as three identical, non-interacting scalar fields. We find classes of spherical, cylindrical, and planar self-gravitating vector solitons in the Newtonian limit. The gravitational properties of the lowest-energy vector solitons$\mathrm{-}$the gravitational potential and density field$\mathrm{-}$depend only on the net mass of the soliton and the vector particle mass. In particular, these self-gravitating, ground-state vector solitons are independent of the distribut…
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…
The fuzzy dark matter model (FDM, also known as quantum wave dark matter model) argues that light bosons with a mass of $\sim10^{-22}{\;{\rm eV}}$ are a possible candidate for dark matter in the Universe. One of the most important predictions of FDM is the formation of a soliton core instead of a density cusp at the center of galaxies. If FDM is the correct theory of dark matter, then the predicted soliton core can help to form the Central Molecular Zone (CMZ) in the Milky Way. We present high-resolution hydrodynamical simulations of gas flow patterns to constrain the properties of the soliton…
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）
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…
Ultralight bosonic dark matter called fuzzy dark matter (FDM) has attracted much attention as an alternative to the cold dark matter. An intriguing feature of the FDM model is the presence of a soliton core, a stable dense core formed at the center of halos. In this paper, we analytically study the dependence of the soliton core properties on the halo characteristics by solving approximately the Schrödinger-Poisson equation. Focusing on the ground-state eigenfunction, we derive a key expression for the soliton core radius, from which we obtain the core-halo mass relations similar to those foun…
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 …
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…
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 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…
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…
We study the secular effects that an oscillating background ultralight (fuzzy) cosmological vector field has on the dynamics of binary systems; such effects appear when the field and the binary are in resonance. We first consider the gravitational interaction between the field and the systems, and quantify the main differences with an oscillating background scalar field. If the energy density of such a field is sufficiently large, as required if it is supposed to be all of the dark matter, we show that the secular effects could yield potentially observable signatures in high precision time of …
Dark matter models involving a very light bosonic particle, generally known as Fuzzy Dark Matter (FDM), have been recently attracting great interest in the cosmology community, as their wave-like phenomenology would simultaneously explain the longstanding mis-detection of a dark matter particle and help easing the small-scale issues related to the standard Cold Dark Matter (CDM) scenario. With the present work, we initiate a series of papers aiming at investigating the evolution of FDM structures in a cosmological framework performed with our N-body code AX-GADGET, detailing for the first time…
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…
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 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…
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…
