The Crossing–Spin-Temperature Coupling: Amplitude, Sign and Shape of the ISO Dark-Ages Feature

Abstract

The dark-ages programme companion paper derived the coordinate of ISO's 21cm feature with no free parameter (z = 19.5, 69.4 MHz) and left amplitude, sign and width open. This paper computes all three from one mechanism: the resonance crossing transiently opens a thermal channel between baryons and ISO's dark sector (ordinary matter at electromagnetically inaccessible θ). The sign is derived — the θ-displaced sector is colder, so the channel cools the gas and deepens absorption. The width is selected by dynamical self-consistency: ΔL_θ = ¼ (the joint zero-point of the factorised invariant); the sub-MHz sharp candidate is eliminated. The amplitude follows from the mirror reading of the dark sector (equal comoving number density → m_χ = 5.4 m_p ≈ 5.0 GeV, equal heat capacities): equilibration halves the gas temperature, giving T_K = 3.5 K and a trough depth of −475 mK at z = 17.2 — twice the standard ceiling of −219 mK, inside the EDGES 99% interval and within 5% of its central −500 mK. Unlike particle dark-matter coolants, the channel is transient: today's detuning suppresses residual interaction by e^(−167), so no laboratory, stellar or fifth-force bound applies. Explicit assumptions, kill criteria, and scripted verification throughout.