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.
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 …
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…
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 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.
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…
Simulations of ultralight, $\sim 10^{-22}\,\rm eV$, bosonic dark matter exhibit rich wave-like structure, including a soliton core within a surrounding halo that continuously self-interferes on the de Broglie scale. We show here that as an inherent consequence, the soliton undergoes a confined random walk at the base of the halo potential. This is significant for the fate of the ancient central star cluster in Eridanus II, as the agitated soliton gravitationally shakes the star cluster in and out of the soliton on a time scale of $\sim 100\,\rm Myr$, so complete tidal disruption of the star cl…
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…
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…
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…
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…
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 …
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…
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…
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…
Confronting fuzzy dark matter with the rotation curves of nearby dwarf irregular galaxies
Instituto de Astrofísica de Canarias（加那利群岛天体物理研究所）；Universidad de La Laguna（拉奥罗哈大学）；Università di Padova（帕多瓦大学）；INFN-Padova（意大利国家核物理研究所帕多瓦分部）；INAF-Padova（意大利国家天体物理研究所帕多瓦分部）
Scalar Field Dark Matter (SFDM), comprised of ultralight ($\gtrsim 10^{-22}$ eV) bosons, is distinguished from massive ($\gtrsim$ 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-Pitaevski and Poisson (GPP) equations. In the free-field (fuzzy) limit of SFDM (FDM), structure is inhibited below the de Broglie wavelength $λ_{\text{deB}}$, but resembles CDM on larger scales. Virialized haloes have solitonic cores of radius $\sim λ_{\text{deB}}$ that follow …
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…
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…
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 …
Fuzzy dark matter dynamical friction: stalling of globular clusters induced by dynamical heatings
Observatoire de Paris, Université PSL, Sorbonne Université, Université Paris Cité, CY Cergy Paris Université, CNRS（巴黎天文台，巴黎文理研究大学，索邦大学，巴黎西岱大学，塞吉-蓬图瓦兹大学，法国国家科学研究中心）；David A. Dunlap Department of Astronomy and Astrophysics, University of Toronto（多伦多大学戴维·A·邓普尔天文学与天体物理学系）
Fuzzy dark matter (FDM) made of ultra-light bosonic particles is a viable alternative to cold dark matter (CDM) with clearly distinguishable small-scale features in collapsed structures. On large scales, it behaves gravitationally like CDM deviating only by a cut-off in the initial power spectrum and can be studied using N-body methods. In contrast, wave interference effects near the de Broglie scale result in new phenomena unique to FDM. Interfering modes in filaments and halos yield a stochastically oscillating granular structure which condenses into solitonic cores during halo formation. In…
Self-gravitating quantum matter may exist in a wide range of cosmological and astrophysical settings from the very early universe through to present-day boson stars. Such quantum matter arises in a number of different theories, including the Peccei-Quinn axion and UltraLight (ULDM) or Fuzzy (FDM) dark matter scenarios. We consider the dynamical evolution of perturbations to the spherically symmetric soliton, the ground state solution to the Schrödinger-Poisson system common to all these scenarios. We construct the eigenstates of the Schrödinger equation, holding the gravitational potential fix…
An ultra-light axion field with mass $\sim 10^{-22}\ {\rm eV}$, also known as wave or fuzzy dark matter, has been proposed as a component of the dark matter in the Universe. We study the evolution of the axion dark matter distribution in the central region of a halo, assuming the mass is dominated by this axion field, and that gravity is the only important interaction. We calculate the excited axion states in the spherical gravitational potential generated by the self-gravitating ground-state, also known as soliton. These excited states are similar to the states of the hydrogen atom with quant…
Although still under debate, observations generally suggest that dwarf spheroidal (dSph) galaxies exhibit large constant-density cores in the centers, which can hardly be explained by dissipationless cold dark matter simulations without baryonic feedback. Wave dark matter (${ψ{\rm DM}}$), characterized by a single parameter, the dark matter particle mass $m_ψ$, predicts a central soliton core in every galaxy arising from quantum pressure against gravity. Here we apply Jeans analysis assuming a soliton core profile to the kinematic data of eight classical dSphs so as to constrain $m_ψ$, and obt…
We simulate the gravitational dynamics of a massive object interacting with Ultralight / Fuzzy Dark Matter (ULDM/FDM), non-relativistic quantum matter described by the Schrodinger-Poisson equation. We first consider a point mass moving in a uniform background, and then a supermassive black hole (SMBH) moving within a ULDM soliton. After replicating simple dynamical friction scenarios to verify our numerical strategies, we demonstrate that the wake induced by a moving mass in a uniform medium may undergo gravitational collapse that dramatically increases the drag force, albeit in a scenario unl…
