Self-similar solutions for Fuzzy Dark Matter

Abstract

Fuzzy Dark Matter (FDM) models admit self-similar solutions which are very different from their Cold Dark Matter (CDM) counterparts and do not converge to the latter in the semiclassical limit. In contrast with the familiar CDM hierarchical collapse, they correspond to an inverse-hierarchy blow-up. Constant-mass shells start in the nonlinear regime, at early times, with small radii and high densities, and expand to reach at late times the Hubble flow, up to small linear perturbations. Thus, larger masses become linear first. This blow-up approximately follows the Hubble expansion, so that the central density contrast remains constant with time, although the width of the self-similar profile shrinks in comoving coordinates. As in a gravitational cooling process, matter is ejected from the central peaks through successive clumps. As in wave systems, the velocities of the geometrical structures and of the matter do not coincide, and matter slowly moves from one clump to the next, with intermittent velocity bursts at the transitions. These features are best observed using the density-velocity representation of the nonrelativistic scalar field, or the mass-shell trajectories, than with the Husimi phase-space distribution, where an analogue of the Heisenberg uncertainty principle blurs the resolution in the position or velocity direction. These behaviours are due to the quantum pressure and the wavelike properties of the Schrödinger equation. Although the latter has been used as an alternative to N-body simulations for CDM, these self-similar solutions show that the semiclassical limit needs to be handled with care.

arXiv comment21 pages,10 figures

References in corpus (23)

• Cold and Fuzzy Dark Matter
• Ultralight scalars as cosmological dark matter
• The Structure of Dark Matter Haloes in Dwarf Galaxies
• Cosmic Structure as the Quantum Interference of a Coherent Dark Wave
• The Core-Cusp Problem
• Mass-radius relation of Newtonian self-gravitating Bose-Einstein condensates with short-range interactions: I. Analytical results
• Direct Detection of WIMP Dark Matter: Concepts and Status
• Repulsive Dark Matter
• Formation of Solitonic Stars Through Gravitational Cooling
• Galaxy Formation with BECDM: I. Turbulence and relaxation of idealised haloes
• Simulations of solitonic core mergers in ultra-light axion dark matter cosmologies
• Mass-radius relation of Newtonian self-gravitating Bose-Einstein condensates with short-range interactions: II. Numerical results
• Galactic Searches for Dark Matter
• Formation and structure of ultralight bosonic dark matter halos
• Gravitational cooling of self-gravitating Bose-Condensates
• On the Schrodinger-Poisson--Vlasov-Poisson correspondence
• Newtonian Collapse of Scalar Field Dark Matter
• Schrödinger method as N-body double and UV completion of dust
• Non-linear hydrodynamics of axion dark matter: relative velocity effects and "quantum forces"
• Multiple Ultralight Axionic Wave Dark Matter and Astronomical Structures
• Self Similar Spherical Collapse Revisited: a Comparison between Gas and Dark Matter Dynamics
• Impact of kinetic and potential self-interactions on scalar dark matter
• The Schrödinger-Poisson method for Large-Scale Structure

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