Wave dark matter

Wave dark matter is dark matter made of particles so light that, at the densities found in galaxies, enormous numbers of them share each quantum state, so that a halo behaves as a classical wave field rather than as a gas of particles. The waves of such a field scatter off one another and pile into the lowest-energy states, building a dense coherent core called a Bose star; if the particles also attract one another, the core has a maximum mass and collapses when it exceeds it. This section is established literature. The Broken-Born program uses it on the wave island, the light-mass branch of its test of momentum clumping.

Literature only: all five pages are established physics, so the section ranks no claims of the program’s own; those are tracked in the registers of claims that stand, the graveyard, open problems and the queue, conjectures and superseded statements. Where a page says how the program uses a result, it gives the program’s tags. The literature here reaches the program through the Debt-3 notes and the checkpoint’s references [13]†–[15]†, all cited from model memory and awaiting the † literature battery; no verify/ script covers any number in this section.

Map#

All five pages are established physics, in the order the wave-island calculation uses them: when dark matter is a wave, how a wave halo relaxes, where an attractive condensate ends, how such a field is made, and how light it may be.

Occupation number: particles or waves comes first. The occupation number N_occ = ρ/(m⁴σ³), the number of particles in a cube one de Broglie wavelength on a side, decides whether dark matter behaves as particles or as a classical wave, and sets the Bose enhancement of a wave halo’s relaxation. The program’s classicality theorem turns on it: collective velocity-space behavior needs masses at which N_occ ~ 10²⁰ (on the regime in which Debt 3a evaluates that number, see flag 19 in review/wiki-build-flags.md). The page records the two normalizations of Debt 3b and the three statements of the wave island’s upper edge.

Wave kinetics and Bose-star formation describes how a wave halo relaxes: two-wave scattering conserves both the number of quanta and their energy, which drives quanta into the lowest modes and builds a Bose-star core. It gives the Levkov–Panin–Tkachev gravitational rate Γ_gr ≈ 8πG²ρ²Λ/(m³σ⁶) and the t^{1/2} slowdown of core growth, the anchor of the program’s gated condensation rate, whose coefficients remain uncalibrated against that anchor.

Attractive condensates: critical mass and the bosenova explains why a condensate whose particles attract one another has a maximum mass, M_crit ≈ 3.6 M_P/(m√g), and the collapse-and-regrowth cycle above it. Under Scenario A, now dead, the cycle would have drained the ultra-faint dwarf galaxies; the page shows where Scenario A’s scaling M_crit ∝ m^{−7/4} comes from and the two branches it divides the wave island into.

The misalignment mechanism explains how such a light field is produced coherently in the early universe, frozen by the expansion and then oscillating as cold matter, without thermal contact with ordinary matter. The wave island borrows it for its relic abundance; the 5.4 : 1 ratio of dark to ordinary matter stays open for both dark-sector candidates.

Bounds on fuzzy dark matter closes the section with the observations that limit how light wave dark matter can be: stellar heating in ultra-faint dwarfs (Dalal–Kravtsov, a bound the notes give as ≈ 3×10⁻¹⁹ eV and flag for verification) and the Lyman-α forest, for which the record gives no number or reference. These bounds set the wave island’s lower edge and close Scenario A’s light-mass escape. The page also records the unresolved conflict with Scenario B’s fuzzy-core option at m ~ 10⁻²² eV.

Boundaries#

The program’s gated version of this physics — the condensation rate, Scenarios A and B, and the falsification — is in The wave island, part of Momentum clumping. The knee-shape test that tells particle χ from wave χ is row 3, the island discriminant. Halo observations in general — cores, ultra-faint dwarfs, streams — are in Halo astrophysics. The X-condensate candidate is a coherent oscillation of the massive momentum graviton, a different object from the condensates of the conjugate field χ described here; no source relates the two.