Galaxy formation with BECDM - I. Turbulence and relaxation of idealized haloes

Self-Similar Growth of Bose Stars

We analytically solve the problem of Bose star growth in the bath of gravitationally interacting particles. We find that after nucleation of this object, the bath is described by a self-similar solution of the kinetic equation. Together with the conservation laws, this fixes mass evolution of the Bose star. Our theory explains, in particular, the slowdown of the star growth at a certain "core-halo" mass, but also predicts formation of heavier and lighter objects in magistral dark matter models. The developed "adiabatic" approach to self-similarity may be of interest for kinetic theory in general.

Deep Zoom-In Simulation of a Fuzzy Dark Matter Galactic Halo

Fuzzy dark matter (FDM) made of ultralight bosonic particles is a viable alternative to cold dark matter with clearly distinguishable small-scale features in collapsed structures. On large scales, it behaves gravitationally like cold dark matter deviating only by a cutoff 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. Investigating these highly nonlinear wave phenomena requires the spatially resolved numerical integration of the Schrödinger equation. In previous papers we introduced a hybrid zoom-in scheme that combines N-body methods to model the large-scale gravitational potential around and the mass accretion onto pre-selected halos with simulations of the Schrödinger-Poisson equation to capture wave-like effects inside these halos. In this work, we present a new, substantially improved reconstruction method for the wave function inside of previously collapsed structures. We demonstrate its capabilities with a deep zoom-in simulation of a well-studied sub-L_{*}-sized galactic halo from cosmological initial conditions. With a particle mass of m=2.5×10^{-22}  eV and halo mass M_{vir}=1.7×10^{11}  M_{⊙} in a (60  h^{-1} comoving Mpc)^{3} cosmological box, it reaches an effective resolution of 20 comoving pc. This pushes the values of m and M accessible to simulations significantly closer to those relevant for studying galaxy evolution in the allowed range of FDM masses.

Self-gravitating clusters of Bose-Einstein gas with planar, cylindrical, or spherical symmetry: Gaseous density profiles and onset of condensation

We calculate density profiles for self-gravitating clusters of an ideal Bose-Einstein gas with nonrelativistic energy-momentum relation and macroscopic mass at thermal equilibrium. Our study includes clusters with planar symmetry in dimensions D=1,2,3, clusters with cylindrical symmetry in D=2,3, and clusters with spherical symmetry in D=3. Wall confinement is imposed where needed to prevent escape. The length scale and energy scale in use for the gaseous phase render density profiles for gaseous macrostates independent of total mass. Density profiles for mixed-phase macrostates have a condensed core surrounded by a gaseous halo. The spatial extension of the core is negligibly small on the length scale tailored for the halo. The mechanical stability conditions as evident in caloric curves permit multiple macrostates to coexist. Their status regarding thermal equilibrium is examined by a comparison of free energies. The onset of condensation takes place at a nonzero temperature in all cases. The critical singularities and the nature of the phase transition vary with the symmetry of the cluster and the dimensionality of the space.

The Cusp–Core Problem in Gas-Poor Dwarf Spheroidal Galaxies

This review deals with the inconsistency of inner dark matter density profiles in dwarf galaxies, known as the cusp–core problem. In particular, we aim to focus on gas-poor dwarf galaxies. One of the most promising solutions to this cold dark matter small-scale issue is the stellar feedback, but it seems to be only designed for gas-rich dwarfs. However, in the regime of classical dwarfs, this core mechanism becomes negligible. Therefore, it is required to find solutions without invoking these baryonic processes as dark matter cores tend to persist even for these dwarfs, which are rather dark-matter-dominated. Here, we have presented two categories of solutions. One consists of creating dark matter cores from cusps within cold dark matter by altering the dark matter potential via perturbers. The second category gathers solutions that depict the natural emergence of dark matter cores in alternative theories. Given the wide variety of solutions, it becomes necessary to identify which mechanism dominates in the central region of galaxies by finding observational signatures left by them in order to highlight the true nature of dark matter.

Incoherent localized structures and hidden coherent solitons from the gravitational instability of the Schrödinger-Poisson equation

The long-term behavior of a modulationally unstable conservative nonintegrable system is known to be characterized by the soliton turbulence self-organization process. We consider this problem in the presence of a long-range interaction in the framework of the Schrödinger-Poisson (or Newton-Schrödinger) equation accounting for the gravitational interaction. By increasing the amount of nonlinearity, the system self-organizes into a large-scale incoherent localized structure that contains "hidden" coherent soliton states: The solitons can hardly be identified in the usual spatial or spectral domains, but their existence can be unveiled in the phase-space representation (spectrogram). We develop a theoretical approach that provides the coupled description of the coherent soliton component [governed by the Schrödinger-Poisson equation (SPE)] and of the incoherent structure [governed by a wave turbulence Vlasov-Poisson equation (WT-VPE)]. We demonstrate theoretically and numerically that the incoherent structure introduces an effective trapping potential that stabilizes the hidden coherent soliton and we show that the incoherent structure belongs to a family of stationary solutions of the WT-VPE. The analysis reveals that the incoherent structure evolves in the strongly nonlinear regime and that it is characterized by a compactly supported spectral shape. By relating the analytical properties of the hidden soliton to those of the stationary incoherent structure, we clarify the quantum-to-classical (i.e., SPE-to-VPE) correspondence in the limit ℏ/m→0: The hidden soliton appears as the latest residual quantum correction preceding the classical limit described by the VPE. This study is of potential interest for self-gravitating Boson models of fuzzy dark matter. Although we focus our paper on the Schrödinger-Poisson equation, we show that the regime of hidden solitons stabilized by an incoherent structure is general for long-range wave systems featured by an algebraic decay of the interacting potential. This work should stimulate nonlinear optics experiments in highly nonlocal nonlinear (thermal) media that mimic the long-range nature of gravitational interactions.

Coherent Soliton States Hidden in Phase Space and Stabilized by Gravitational Incoherent Structures

We consider the problem of the formation of soliton states from a modulationally unstable initial condition in the framework of the Schrödinger-Poisson (or Newton-Schrödinger) equation accounting for gravitational interactions. We unveil a previously unrecognized regime: By increasing the nonlinearity, the system self-organizes into an incoherent localized structure that contains "hidden" coherent soliton states. The solitons are hidden in the sense that they are fully immersed in random wave fluctuations: The radius of the soliton is much larger than the correlation radius of the incoherent fluctuations, while its peak amplitude is of the same order of such fluctuations. Accordingly, the solitons can hardly be identified in the usual spatial or spectral domains, while their existence is clearly unveiled in the phase-space representation. Our multiscale theory based on coupled coherent-incoherent wave turbulence formalisms reveals that the hidden solitons are stabilized and trapped by the incoherent localized structure. Furthermore, hidden binary soliton systems are identified numerically and described theoretically. The regime of hidden solitons is of potential interest for self-gravitating Boson models of "fuzzy" dark matter. It also sheds new light on the quantum-to-classical correspondence with gravitational interactions. The hidden solitons can be observed in nonlocal nonlinear optics experiments through the measurement of the spatial spectrogram.

Jeans Instability of Dissipative Self-Gravitating Bose–Einstein Condensates with Repulsive or Attractive Self-Interaction: Application to Dark Matter

We study the Jeans instability of an infinite homogeneous dissipative self-gravitating Bose–Einstein condensate described by generalized Gross–Pitaevskii–Poisson equations [Chavanis, P.H. Eur. Phys. J. Plus2017, 132, 248]. This problem has applications in relation to the formation of dark matter halos in cosmology. We consider the case of a static and an expanding universe. We take into account an arbitrary form of repulsive or attractive self-interaction between the bosons (an attractive self-interaction being particularly relevant for the axion). We consider both gravitational and hydrodynamical (tachyonic) instabilities and determine the maximum growth rate of the instability and the corresponding wave number. We study how they depend on the scattering length of the bosons (or more generally on the squared speed of sound) and on the friction coefficient. Previously obtained results (notably in the dissipationless case) are recovered in particular limits of our study.

Dark Matters on the Scale of Galaxies

The cold dark-matter model successfully explains both the emergence and evolution of cosmic structures on large scales and, when we include a cosmological constant, the properties of the homogeneous and isotropic Universe. However, the cold dark-matter model faces persistent challenges on the scales of galaxies. Indeed, N-body simulations predict some galaxy properties that are at odds with the observations. These discrepancies are primarily related to the dark-matter distribution in the innermost regions of the halos of galaxies and to the dynamical properties of dwarf galaxies. They may have three different origins: (1) the baryonic physics affecting galaxy formation is still poorly understood and it is thus not properly included in the model; (2) the actual properties of dark matter differs from those of the conventional cold dark matter; (3) the theory of gravity departs from General Relativity. Solving these discrepancies is a rapidly evolving research field. We illustrate some of the solutions proposed within the cold dark-matter model, and solutions when including warm dark matter, self-interacting dark matter, axion-like particles, or fuzzy dark matter. We also illustrate some modifications of the theory of gravity: Modified Newtonian Dynamics (MOND), MOdified Gravity (MOG), and f(R) gravity.

Lighting the Dark: Evolution of the Postinflationary Universe

In simple inflationary cosmological scenarios, the near-exponential growth can be followed by a long period in which the Universe is dominated by the oscillating inflaton condensate. The condensate is initially almost homogeneous, but perturbations grow gravitationally, eventually fragmenting the condensate if it is not disrupted more quickly by resonance or prompt reheating. We show that the gravitational fragmentation of the condensate is well-described by the Schrödinger-Poisson equations and use numerical solutions to show that large overdensities form quickly after the onset of nonlinearity. This is the first exploration of this phase of nonlinear dynamics in the very early Universe, which can affect the detailed form of the inflationary power spectrum and the dark matter fraction when the dark sector is directly coupled to the inflaton.

A Quantum Model for the Dynamics of Cold Dark Matter

A model for cold dark matter is given by the solution of a coupled Schrödinger–Poisson equation system. We present a numerical scheme for integrating these equations, discussing the problems arising from their nonlinear and nonlocal character. After introducing and testing our numerical approach, we illustrate key features of the system by numerical examples in 1 + 1 dimensions. In particular, we study the properties of asymptotic states to which the numerical solutions converge for artificial initial conditions.

First Star-Forming Structures in Fuzzy Cosmic Filaments

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 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 ∼10^{-22}  eV boson and the primordial stars are expected to form along dense dark matter filaments. Using a first-of-its-kind cosmological hydrodynamical simulation, we explore the interplay between baryonic physics and unique wavelike features inherent to FDM. In our simulation, the dark matter filaments show coherent interference patterns on the boson de Broglie scale and develop cylindrical solitonlike cores, which are unstable under gravity and collapse into kiloparsec-scale spherical solitons. Features of the dark matter distribution are largely unaffected by the baryonic feedback. On the contrary, the distributions of gas and stars, which do form along the entire filament, exhibit central cores imprinted by dark matter-a smoking gun signature of FDM.

Dark Matter Haloes and Subhaloes

The development of methods and algorithms to solve the N-body problem for classical, collisionless, non-relativistic particles has made it possible to follow the growth and evolution of cosmic dark matter structures over most of the universe’s history. In the best-studied case—the cold dark matter or CDM model—the dark matter is assumed to consist of elementary particles that had negligible thermal velocities at early times. Progress over the past three decades has led to a nearly complete description of the assembly, structure, and spatial distribution of dark matter haloes, and their substructure in this model, over almost the entire mass range of astronomical objects. On scales of galaxies and above, predictions from this standard CDM model have been shown to provide a remarkably good match to a wide variety of astronomical data over a large range of epochs, from the temperature structure of the cosmic background radiation to the large-scale distribution of galaxies. The frontier in this field has shifted to the relatively unexplored subgalactic scales, the domain of the central regions of massive haloes, and that of low-mass haloes and subhaloes, where potentially fundamental questions remain. Answering them may require: (i) the effect of known but uncertain baryonic processes (involving gas and stars), and/or (ii) alternative models with new dark matter physics. Here we present a review of the field, focusing on our current understanding of dark matter structure from N-body simulations and on the challenges ahead.

Missing Satellites Problem: Completeness Corrections to the Number of Satellite Galaxies in the Milky Way are Consistent with Cold Dark Matter Predictions

A critical challenge to the cold dark matter (CDM) paradigm is that there are fewer satellites observed around the Milky Way than found in simulations of dark matter substructure. We show that there is a match between the observed satellite counts corrected by the detection efficiency of the Sloan Digital Sky Survey (for luminosities L≳340  L_{⊙}) and the number of luminous satellites predicted by CDM, assuming an empirical relation between stellar mass and halo mass. The "missing satellites problem," cast in terms of number counts, is thus solved. We also show that warm dark matter models with a thermal relic mass smaller than 4 keV are in tension with satellite counts, putting pressure on the sterile neutrino interpretation of recent x-ray observations. Importantly, the total number of Milky Way satellites depends sensitively on the spatial distribution of satellites, possibly leading to a "too many satellites" problem. Measurements of completely dark halos below 10^{8}  M_{⊙}, achievable with substructure lensing and stellar stream perturbations, are the next frontier for tests of CDM.

SIDM on FIRE: hydrodynamical self-interacting dark matter simulations of low-mass dwarf galaxies

We compare a suite of four simulated dwarf galaxies formed in 10¹⁰ M_☉ haloes of collisionless cold dark matter (CDM) with galaxies simulated in the same haloes with an identical galaxy formation model but a non-zero cross-section for DM self-interactions. These cosmological zoom-in simulations are part of the Feedback In Realistic Environments (fire) project and utilize the fire-2 model for hydrodynamics and galaxy formation physics. We find the stellar masses of the galaxies formed in self-interacting dark matter (SIDM) with σ/m = 1 cm² g^-1 are very similar to those in CDM (spanning M _★ ≈ 10^5.7-7.0 M_☉) and all runs lie on a similar stellar mass-size relation. The logarithmic DM density slope (α = d log ρ/d log r) in the central 250-500 pc remains steeper than α = -0.8 for the CDM-Hydro simulations with stellar mass M _★ ~ 10^6.6 M_☉ and core-like in the most massive galaxy. In contrast, every SIDM hydrodynamic simulation yields a flatter profile, with α > -0.4. Moreover, the central density profiles predicted in SIDM runs without baryons are similar to the SIDM runs that include fire-2 baryonic physics. Thus, SIDM appears to be much more robust to the inclusion of (potentially uncertain) baryonic physics than CDM on this mass scale, suggesting that SIDM will be easier to falsify than CDM using low-mass galaxies. Our fire simulations predict that galaxies less massive than M _★ ≲ 3 × 10⁶ M_☉ provide potentially ideal targets for discriminating models, with SIDM producing substantial cores in such tiny galaxies and CDM producing cusps.