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Ultralight scalars as cosmological dark matter

Lam Hui, Jeremiah P. Ostriker, Scott Tremaine, Edward Witten

TL;DR

Fuzzy dark matter proposes ultralight scalar particles (m ~ 10^{-22} eV) whose large de Broglie wavelengths modify structure on galactic scales while preserving CDM-like behavior on large scales. The framework treats FDM as a Schrödinger–Poisson system, yielding soliton cores embedded in NFW-like envelopes and a superfluid-like MADelung description with quantum pressure. Key predictions include a minimum halo mass, soliton cores that alleviate cusps, and suppressed subhalo populations that address the missing satellite and too-big-to-fail problems, along with potential dynamical-friction suppression in dwarfs and possible thickened inner disks. However, Lyman-α forest constraints and reionization history tension the simplest realizations, favoring m in the 10–20×10^{-22} eV range and motivating further simulations tailored to FDM observables.

Abstract

An intriguing alternative to cold dark matter (CDM) is that the dark matter is a light ( $m \sim 10^{-22}$ eV) boson having a de Broglie wavelength $λ\sim 1$ kpc, often called fuzzy dark matter (FDM). We describe the arguments from particle physics that motivate FDM, review previous work on its astrophysical signatures, and analyze several unexplored aspects of its behavior. In particular, (i) FDM halos smaller than about $10^7 (m/10^{-22} {\rm eV})^{-3/2} M_\odot$ do not form. (ii) FDM halos are comprised of a core that is a stationary, minimum-energy configuration called a "soliton", surrounded by an envelope that resembles a CDM halo. (iii) The transition between soliton and envelope is determined by a relaxation process analogous to two-body relaxation in gravitating systems, which proceeds as if the halo were composed of particles with mass $\sim ρλ^3$ where $ρ$ is the halo density. (iv) Relaxation may have substantial effects on the stellar disk and bulge in the inner parts of disk galaxies. (v) Relaxation can produce FDM disks but an FDM disk in the solar neighborhood must have a half-thickness of at least $300 (m/10^{-22} {\rm eV})^{-2/3}$ pc. (vi) Solitonic FDM sub-halos evaporate by tunneling through the tidal radius and this limits the minimum sub-halo mass inside 30 kpc of the Milky Way to roughly $10^8 (m/10^{-22} {\rm eV})^{-3/2} M_\odot$. (vii) If the dark matter in the Fornax dwarf galaxy is composed of CDM, most of the globular clusters observed in that galaxy should have long ago spiraled to its center, and this problem is resolved if the dark matter is FDM.

Ultralight scalars as cosmological dark matter

TL;DR

Fuzzy dark matter proposes ultralight scalar particles (m ~ 10^{-22} eV) whose large de Broglie wavelengths modify structure on galactic scales while preserving CDM-like behavior on large scales. The framework treats FDM as a Schrödinger–Poisson system, yielding soliton cores embedded in NFW-like envelopes and a superfluid-like MADelung description with quantum pressure. Key predictions include a minimum halo mass, soliton cores that alleviate cusps, and suppressed subhalo populations that address the missing satellite and too-big-to-fail problems, along with potential dynamical-friction suppression in dwarfs and possible thickened inner disks. However, Lyman-α forest constraints and reionization history tension the simplest realizations, favoring m in the 10–20×10^{-22} eV range and motivating further simulations tailored to FDM observables.

Abstract

An intriguing alternative to cold dark matter (CDM) is that the dark matter is a light ( eV) boson having a de Broglie wavelength kpc, often called fuzzy dark matter (FDM). We describe the arguments from particle physics that motivate FDM, review previous work on its astrophysical signatures, and analyze several unexplored aspects of its behavior. In particular, (i) FDM halos smaller than about do not form. (ii) FDM halos are comprised of a core that is a stationary, minimum-energy configuration called a "soliton", surrounded by an envelope that resembles a CDM halo. (iii) The transition between soliton and envelope is determined by a relaxation process analogous to two-body relaxation in gravitating systems, which proceeds as if the halo were composed of particles with mass where is the halo density. (iv) Relaxation may have substantial effects on the stellar disk and bulge in the inner parts of disk galaxies. (v) Relaxation can produce FDM disks but an FDM disk in the solar neighborhood must have a half-thickness of at least pc. (vi) Solitonic FDM sub-halos evaporate by tunneling through the tidal radius and this limits the minimum sub-halo mass inside 30 kpc of the Milky Way to roughly . (vii) If the dark matter in the Fornax dwarf galaxy is composed of CDM, most of the globular clusters observed in that galaxy should have long ago spiraled to its center, and this problem is resolved if the dark matter is FDM.

Paper Structure

This paper contains 29 sections, 106 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. The physics of FDM
  3. Light fields of spin zero
  4. FDM as a superfluid
  5. Astrophysics of FDM in the Milky Way and nearby galaxies
  6. Introductory remarks
  7. Minimum size and maximum density
  8. Relaxation in systems composed of FDM
  9. Disruption of star clusters:
  10. Disruption of wide binary stars:
  11. Thickening of the Galactic disk:
  12. Galactic bulges:
  13. Orbital decay of supermassive black holes:
  14. The cusp-core problem
  15. Lower bound on FDM halo masses
  16. ...and 14 more sections

Figures (3)

  • Figure 1: The lifetime of a stellar system in the ground state of the Schrödinger--Poisson equation when a spherically symmetric tidal field is present. The vertical axis gives the dimensionless lifetime $\tau$ in units of the orbital period (eq. \ref{['eq:taudef']}) and the horizontal axis gives the ratio of the central density to the mean density of the host averaged over the orbital radius.
  • Figure 2: The dynamical friction force on a test object of mass $m_{\rm cl}$ traveling at speed $v$ through FDM with density $\rho$ is given by Eq. (\ref{['eq:cdef']}), with the dimensionless function $C$ plotted in this figure. The horizontal axis is $kr$ where $k=mv/\hbar$ is the wavenumber of the FDM particles in the rest frame of the test object, and $r$ is an upper cutoff to the distance from the test object that approximately represents the smaller of the radius of the orbit and the size of the host system. Each curve is for a fixed value of $\Lambda=v^2r/Gm_{\rm cl}$, which by the virial theorem is approximately the ratio of the mass of the host to the mass of the test object; from bottom to top $\Lambda=3,10,30,100,300$. The dashed red line shows the asymptotic behavior in the limit $\Lambda\to\infty$ (Eq. \ref{['eq:casymp']}).
  • Figure 3: Density evolution in a self-similar FDM solution, according to Eq. (\ref{['psistep']}). The dimensionless time $\tilde{t}$ and distance $\tilde{x}$ are defined in Eq. (\ref{['txrescaled']}), where $x_0$ is an arbitrary length scale. The overall normalization of the density $\rho$ is also arbitrary. With the choice ${\cal A} = {\cal B}$ made here, the ratio of the asymptotic density at $x \rightarrow \pm \infty$ is $({\cal A} + {\cal B})^2/{\cal B}^2 = 4$.