We investigate Scalar Field Wave Dark Matter in the context of galactic Dark Matter halos. In particular, we offer an analysis of the Baryonic Tully-Fisher Relation (BTFR). We detail a particular family of excited state solutions to the Einstein-Klein-Gordon equations, and use it to provide a novel theoretical model for producing the BTFR. We then solve this model computationally to simulate the BTFR. Interpreting the Dark Matter scalar field as an ultralight boson, this returns a conservative mass constraint of $m\geq 10^{-23}eV$. Assuming slightly stronger conditions suggests $m\geq 10^{-22}eV$ to be more compatible with the BTFR. We provide a discussion of Scalar Field Dark Matter rotation curves and the structure of Scalar Field Dark Matter halos. Compatibility with the BTFR requires the excited state solutions to obey particular boundary conditions; this may have implications for the behavior of Dark Matter halos and the formation of galaxies.
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.
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, and solve it to find the evolution of the v…
Red and blue galaxies are traditionally classified using some specific cuts in colour or other galaxy properties, which are supported by empirical arguments. The vagueness associated with such cuts are likely to introduce a significant contamination in these samples. Fuzzy sets are vague boundary sets which can efficiently capture the classification uncertainty in the absence of any precise boundary. We propose a method for classification of galaxies according to their colours using fuzzy set theory. We use data from the SDSS to construct a fuzzy set for red galaxies with its members having di…
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…
Given the absence of directly detected dark matter (DM) as weakly interacting massive particles, there is strong interest in the possibility that DM is an ultra-light scalar field, here denoted as fuzzy DM. Ultra-diffuse galaxies, with the sizes of giant galaxies and the luminosities of dwarf galaxies, have a wide range of DM halo masses, thus providing new opportunities for exploring the connections between galaxies and their DM halos. Following up on new integral field unit spectroscopic observations and dynamics modeling of the DM-dominated ultra-diffuse galaxy Dragonfly 44 in the outskirts…
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) consisting of ultra-light axions has been invoked to alleviate galactic-scale problems in the cold dark matter scenario. FDM fluctuations, created via the superposition of waves, can impact the motion of a central supermassive black hole (SMBH) immersed in an FDM halo. The SMBH will undergo a random walk, induced by FDM fluctuations, that can result in its ejection from the central region. This effect is strongest in dwarf galaxies, accounting for wandering SMBHs and the low detection rate of AGN in dwarf spheroidal galaxies. In addition, a lower bound on the allowed ax…
Fuzzy Dark Matter and the Impact of Core--Halo Diversity on Its Particle Mass Constraints
Astronomical Institute, Tohoku University（东北大学天体物理研究所）；National Institute of Technology, Sendai College（国立仙台工业高等专门学校）；ICRR, The University of Tokyo（东京大学宇宙线研究所）；Kavli IPMU (WPI), UTIAS, The University of Tokyo（东京大学 Kavli 宇宙物质起源与演化国际卓越中心（WPI），UTIAS）
Although highly successful on cosmological scales, Cold Dark Matter (CDM) models predict unobserved over-dense `cusps' in dwarf galaxies and overestimate their formation rate. We consider an ultra-light axion-like scalar boson which promises to reduce these observational discrepancies at galactic scales. The model, known as Fuzzy Dark Matter (FDM), avoids cusps, suppresses small-scale power, and delays galaxy formation via macroscopic quantum pressure. We compare the substructure and density fluctuations of galactic dark matter haloes comprised of ultra-light axions to conventional CDM results…
Dark matter may be composed of light bosons, ${m_b \sim 10^{-22}\, \mathrm{eV}}$, with a de Broglie wavelength $λ\sim 1 \,\mathrm{kpc}$ in typical galactic potentials. Such `fuzzy' dark matter (FDM) behaves like cold dark matter (CDM) on much larger scales than the de Broglie wavelength, but may resolve some of the challenges faced by CDM in explaining the properties of galaxies on small scales ($\lesssim 10\,\mathrm{kpc}$). Because of its wave nature, FDM exhibits stochastic density fluctuations on the scale of the de Broglie wavelength that never damp. The gravitational field from these fluc…
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 …
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 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.
Extremely light bosonic wave dark matter ($ψ$DM) is an emerging dark matter candidate contesting the conventional cold dark matter paradigm and a model subject to intense scrutiny of late. This work for the first time reports testable salient features pertinent to gravitational lenses of $ψ$DM halos. $ψ$DM halos are distinctly filled with large-amplitude, small-scale density fluctuations with $δρ/ρ_{\rm halo}\sim 1$ in form of density granules. This halo yields ubiquitous flux ratio anomalies of a few tens of percent, as is typically found for lensed quasars, and may also produce rare hexad an…
We present a non-parametric reconstruction of the rotation curves (RC) for 88 spiral galaxies under the LOESS+SIMEX technique. In order to compare methods we also perform the parametric approach assuming core and cuspy dark matter (DM) profiles: PISO, NFW, Burkert, Spano, the soliton and two fuzzy soliton$+$NFW. As result of this two approaches, a comparison of the RC obtained is carried out by computing the distance between central curves and the distance between 1$σ$ error bands. Furthermore, we perform a model selection according to two statistical criteria, the BIC and the value of $χ^2_{r…
Fuzzy Dark Matter (FDM), consisting of ultralight bosons ($m_{\rm b} \sim 10^{-22}\ \rm eV$), is an intriguing alternative to Cold Dark Matter. Numerical simulations that solve the Schrödinger-Poisson (SP) equation show that FDM halos consist of a central solitonic core, which is the ground state of the SP equation, surrounded by an envelope of interfering excited states. These excited states also interfere with the soliton, causing it to oscillate and execute a confined random walk with respect to the halo center of mass. Using high-resolution numerical simulations of a $6.6 \times 10^9 M_{\o…
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…
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 …
The evolution of a dark matter halo in a dark matter only simulation is governed purely byNewtonian gravity, making a clean testbed to determine what halo properties drive its fate.Using machine learning, we predict the survival, mass loss, final position, and merging time of subhalos within a cosmological N-body simulation, focusing on what instantaneous initial features of the halo, interaction, and environment matter most. Survival is well predicted, with our model achieving 96.5% accuracy using only 3 model inputs from the initial interaction.However, the mass loss, final location, and mer…
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）
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…
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…
The Impact of Fuzzy Dark Matter Dynamics on the Accumulation and Fragmentation of Primordial Gas
Fakultät für Physik, Universität Bielefeld（比勒费尔德大学物理学院）；Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik（海德堡大学天文学中心理论天体物理研究所）；Universität Heidelberg, Interdisziplinäres Zentrum für Wissenschaftliches Rechnen（海德堡大学科学计算跨学科中心）
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 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…
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…
Modeling Solitonic Cores, Stabilization of Bar, and Suppression of Bar Dissolution in DDO 168 via GPP Formalism: A Detailed Analysis of Bose--Einstein Condensate/Fuzzy Dark Matter Halo Structure and Bar Dynamics in the Dwarf Galaxy DDO 168
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…
