我们探讨了超大质量黑洞（SMBH）对暗物质晕中心模糊暗物质（FDM）孤子核密度分布的影响。我们数值求解薛定谔-泊松方程，治疗的黑洞作为一个引力质点，并证明，这一额外的扰动项有"压缩"效应的孤子密度分布，减少核心半径，增加中心密度。在大黑洞质量的极限下，该解接近于类似于氢原子的解，其半径与黑洞质量成反比。通过将我们的分析应用到两个特定的星系（M87和银河系），并将其与已知的观测限制的中心集中的暗物质的量，我们得到了FDM粒子质量的约束，发现范围$10^{-22.12}$ eV $\lesssim m \lesssim 10^{-22.06}$ eV应被禁止（考虑到额外的因素，在附近的一个黑洞的孤子的寿命）。改进的观测质量测量的黑洞和总封闭的质量将显着扩展的下限上排除FDM质量区域，而自洽的理论模型的孤子-黑洞系统可以扩展的上限。
英文摘要：
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 applying our analysis to two specific galaxies (M87 and the Milky Way) and pairing it with known observational limits on the amount of centrally concentrated dark matter, we obtain a constraint on the FDM particle mass, finding that the range $10^{-22.12}$ eV $\lesssim m \lesssim 10^{-22.06}$ eV should be forbidden (taking into account additional factors concerning the life-time of the soliton in the vicinity of a black hole). Improved observational mass measurements of the black hole and total enclosed masses will significantly extend the lower-bound on the excluded FDM mass region, while self-consistent theoretical modeling of the soliton--black hole system can extend the upper-bound.
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 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…
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 (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…
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…
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
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 …
Stone Skipping Black Holes in Ultralight Dark Matter Solitons
Australian National University（澳大利亚国立大学）；Georg-August-Universität Göttingen（哥廷根大学）；Perimeter Institute for Theoretical Physics（理论物理珀米特研究所）；McGill University（麦吉尔大学）；University of Auckland（奥克兰大学）
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 …
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 ultra-light dark matter (ULDM) model has become a popular dark matter scenario nowadays. The mass of the ULDM particles is extremely small so that they can exhibit wave properties in the central dark matter halo region. Numerical simulations show that a soliton core with an almost constant mass density would be formed inside the ULDM halo. If our Galactic Centre has a dark matter soliton core, some of the stars orbiting about the supermassive black hole (Sgr A*) would be crossing the soliton core boundary. In this article, we report the first theoretical study on how the dark matter solito…
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 …
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…
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）
Scalar-field dark matter (SFDM) halos exhibit a core-envelope structure with soliton-like cores and CDM-like envelopes. Simulations without self-interaction (free-field case) report a core-halo mass relation $M_c\propto M_{h}^β$, with either $β=1/3$ or $β=5/9$, which can be understood if core and halo obey certain energy or velocity scalings. We extend the core-halo mass relations to include SFDM with self-interaction (SI), either repulsive or attractive, and investigate its implications for the gravitational instability and collapse of solitonic cores, leading to supermassive black hole (SMBH…
In this work, we explored the effect of the fuzzy dark matter (FDM) (or wave dark matter) halo on a supermassive black hole (SMBH). Such a dark matter introduces a soliton core density profile, and we treat it ideally as a spherical distribution that surrounds the SMBH located at its center. In this direction, we obtained a new metric due to the union of the black hole and dark matter spacetime geometries. We applied the solution to the two known SMBH - Sgr. A* and M87* and used the empirical data for the shadow diameter by EHT to constrain the soliton core radius $r_\text{c}$ given some value…
We use the Milky Way's nuclear star cluster (NSC) to test the existence of a dark matter 'soliton core', as predicted in ultra-light dark matter (ULDM) models. Since the soliton core size is proportional to mDM^{-1}, while the core density grows as mDM^{2}, the NSC (dominant stellar component within about 3 pc) is sensitive to a specific window in the dark matter particle mass, mDM. We apply a spherical isotropic Jeans model to fit the NSC line-of-sight velocity dispersion data, assuming priors on the precisely measured Milky Way's supermassive black hole (SMBH) mass and the well-measured NSC …
