Halo astrophysics

A dark-matter halo is the extended cloud of dark matter in which a galaxy or a galaxy cluster sits; it outweighs the visible stars and gas and sets their orbits. How dense a halo is at its center, how fast its matter moves (its velocity dispersion), and how lumpy it is on small scales all depend in part on whether dark matter scatters off itself, and the observations of dwarf galaxies, galaxy clusters and stellar streams constrain each of these. This section is established literature: the observations and models against which the Broken-Born program’s dark-matter claims are tested.

Literature only: all six 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those are tracked in the registers of claims that stand, the graveyard, open problems and the queue, conjectures and superseded statements.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; no verify/ script covers any number in this section, and the program’s observational inputs (the dwarf-core value σ₀/m ≈ 30 cm²/g, the Segue 1 data) are uncited in every source. One superseded input is folded into a page here: Debt 3b’s ultra-faint-dwarf row, replaced by Segue 1’s values.

Map#

The six pages come first in Dark matter because the program’s claims are stated against them. They run from the spread of velocities against which the program’s gate is measured, through the physics the gate modifies and the cross-section in which it is measured, through the galaxies that fixed and then tested its numbers and the cluster collision that limits it, to the probes of the program’s withdrawn predictions.

The velocity dispersion σ comes first: the spread of the velocities of a system’s stars or particles about their mean, the standard deviation along one direction. The page gives the Maxwellian distribution, the virial and Jeans relations that tie σ to a system’s mass and size, how σ is measured from stars’ line-of-sight speeds in a dwarf galaxy, and the spread of pair speeds that a two-body process sees. The values the program’s notes use run from 3 km/s, for an ultra-faint dwarf, to 1000 km/s, for a cluster, and none of them is cited. σ is the scale against which the program’s velocity gate is measured: below the gate velocity v*, as in dwarfs, most pairs of particles interact, and above it only particles moving together do. Through that comparison it enters the stream criterion of the particle island, the occupation number and condensation rate of the wave island, and the power law (v*/σ)⁴ of row 3.

Self-interacting dark matter follows. It explains how self-scattering turns a halo’s central cusp into a core, why the observable is the momentum-transfer cross-section per unit mass σ_T/m, and how its speed dependence follows from the mediator: constant and isotropic for a contact force, a v⁻⁴ fall with a Coulomb logarithm and forward peaking for a light Yukawa mediator. Those are the standard expectations of row 1 and row 2. It covers the Born regime and gravothermal evolution, whose elastic relaxation keeps a halo’s mass, and summarizes the Bullet Cluster. It then shows where the program departs: its amplitude keeps the Yukawa propagator in the momentum transfer and adds a velocity gate in the incoming relative momentum, which gives a knee in σ_T(v) and isotropy below it.

The transfer cross-section σ_T gives the quantity itself. σ_T = ∫(1 − cos θ) dσ counts each collision by the forward momentum it removes, so a grazing collision counts for almost nothing; that is why σ_T, and not the plain count of collisions, measures how fast scattering moves momentum and heat through a halo. Observations, which see the mass density of dark matter but not the mass of its particles, constrain it per unit mass, in cm²/g. The page sets out its speed dependence for contact and long-range forces and what one number leaves out of an angular distribution, then the program’s uses: the gated law σ_T(v), the first three rows of the predictions table, the scattering benchmark, the wave island where σ_T is not the observable, and the withdrawn soliton candidate’s σ_T/M.

Dwarf galaxies: cores and ultra-faint dwarfs follows with the observations the program used. It sets out the cusp–core problem and its two families of explanation, dark-matter physics and baryonic feedback, and shows where each of the program’s dark-matter options, alive or dead, gets its cores. The classical dwarfs fix the program’s scattering benchmark at σ₀/m ≈ 30 cm²/g. The ultra-faint dwarfs, with Segue 1 as the test case, falsified Scenario A of the wave island; their inputs are uncited and are to be source-checked before external use.

The Bullet Cluster is the test at cluster speeds: two galaxy clusters seen after a collision, in which the mass mapped by gravitational lensing moved on with the galaxies while the X-ray-emitting gas was slowed. It is read as evidence for a separate, nearly collisionless dark matter, and it limits self-scattering at the speed of the collision. The program calls its conjugate matter “Bullet-Cluster-safe”: it lenses as ordinary matter does, by the equivalence principle, and its gate is closed at cluster speeds, so row 1 requires “zero cluster signal (particle χ)”. No program document quotes a value of the limit or compares the gate’s remaining tail with it.

Halo-substructure probes: streams and dynamical friction closes the section with cold stellar streams such as GD-1 and Palomar 5, which record the passage of dark subhalos, and with dynamical friction on the globular clusters of the Fornax dwarf. These were the probes of the lab notebook’s rows 3 and 4, the velocity granularity and suppressed friction of the founding image. The page records how Debt 3 withdrew both rows; the obituaries are old row 3 and old row 4.

Boundaries#

Wave dark matter’s own physics and its mass bounds are in Wave dark matter. The program’s gated scattering is in Conjugate matter and the velocity gate, and the obituaries of the claims these probes were meant to test are in Momentum clumping. The tests themselves are rows of the predictions table.