Recombination & Surface of Last Scattering
For the first 380,000 years, the universe was an opaque ionized fog because free electrons constantly scattered photons via Thomson scattering. When cosmic expansion cooled the plasma to ~2,970 K (redshift z ≈ 1,090), protons captured electrons to form neutral hydrogen ('recombination'), increasing the photon mean free path beyond the Hubble horizon and creating the spherical Surface of Last Scattering we observe as the CMB.
Physical Mechanism & Dynamics
Although hydrogen's ground-state ionization energy is 13.6 eV (corresponding to k_B T ≈ 158,000 K), recombination did not occur until T dropped to ~3,000 K (k_B T ≈ 0.26 eV). Because photons outnumbered baryons by 1.6 billion to one, the high-energy exponential Wien tail of the Planck distribution kept hydrogen ionized until the temperature dropped by a factor of ~50 below the binding energy, as described by the cosmological Saha equation.
Furthermore, direct recombination to the n = 1 ground state immediately emits a 13.6 eV Lyman- continuum photon that ionizes a neighboring atom, resulting in zero net progress. Neutral hydrogen formed primarily through the 'Peebles two-photon' 2s → 1s decay and cosmological redshifting of Lyman-alpha photons out of resonance.
Quantitatively, this mechanism is governed by Saha Ionization Equilibrium and Thomson Optical Depth ([x_e² / (1 − x_e)] = (1 / n_H) (m_e k_B T / 2πℏ²)^(3/2) e^(−E_I / k_B T) ; dτ = n_e σ_T c dt). Last scattering occurs at optical depth τ(z_*) = 1, where the free electron fraction x_e drops below ~0.1 at z_* = 1089.80 ± 0.21.
Saha Ionization Equilibrium and Thomson Optical Depth
[x_e² / (1 − x_e)] = (1 / n_H) (m_e k_B T / 2πℏ²)^(3/2) e^(−E_I / k_B T) ; dτ = n_e σ_T c dtLast scattering occurs at optical depth τ(z_*) = 1, where the free electron fraction x_e drops below ~0.1 at z_* = 1089.80 ± 0.21.
Quantitative Benchmarks & Parameters
| Parameter / Observable | Measured Value / Scale | Method & Context |
|---|---|---|
| Last-scattering redshift z_* | 1089.80 ± 0.21 | Planck 2018 recombination visibility peak |
| Cosmic age at decoupling t_* | 379,000 ± 2,000 years | Integrated ΛCDM expansion history |
| Plasma temperature T_* | 2,970 K (k_B T ≈ 0.256 eV) | T₀ (1 + z_*) = 2.7255 K × 1090.8 |
| Thickness of surface Δz_* | Δz ≈ 80 (Δt ≈ 40,000 yr) | FWHM of visibility function g(z) = (dτ/dz)e^(−τ) |
Observational Evidence & How Scientists Know
The finite thickness of the last-scattering surface (Δz ≈ 80) causes photon diffusion ('Silk damping') that exponentially suppresses CMB temperature anisotropies at small angular scales (ℓ > 1,000), matching Planck and ACT measurements with sub-percent precision.
Across reference datasets (Planck 2018 Cosmological Parameters (PR3)), quantitative benchmarks for recombination & surface of last scattering are anchored by: Last-scattering redshift z_* (1089.80 ± 0.21, via Planck 2018 recombination visibility peak); Cosmic age at decoupling t_* (379,000 ± 2,000 years, via Integrated ΛCDM expansion history); Plasma temperature T_* (2,970 K (k_B T ≈ 0.256 eV), via T₀ (1 + z_*) = 2.7255 K × 1090.8); Thickness of surface Δz_* (Δz ≈ 80 (Δt ≈ 40,000 yr), via FWHM of visibility function g(z) = (dτ/dz)e^(−τ)).
Uncertainties, Systematics & Open Questions
Future centimeter-to-terahertz space spectrometers aim to detect the faint primordial hydrogen and helium recombination spectral lines superimposed on the CMB blackbody spectrum.
Real Astronomical Benchmarks & Cross-Domain Links
Planck Space Observatory
Measured z_* = 1089.80 ± 0.21 and the Silk damping tail
Cosmic Microwave Background
Observed radiation emitted from the surface of last scattering
What Was the Universe Like Before Stars?
Explainer covering recombination and the subsequent Dark Ages
Guided Learning Path
Related Concepts, Methods & Explorers
Scientific Sources & Provenance
- Planck 2018 Cosmological Parameters (PR3) (PR3 (2020 A&A 641, A6)) — Planck Collaboration, Aghanim, N., et al. 2020, A&A, 641, A6. Archive / Reference ↗
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