Reionization

From dark ages to cosmic dawn

For the first 380,000 years after the Big Bang the universe was an opaque plasma of free electrons, protons and helium nuclei, kept ionized by the heat of the radiation it had emerged from. As the universe expanded and cooled below about 3000 K those electrons and nuclei combined into neutral atoms, and the cosmic microwave background — which had been bouncing off electrons like fog scattering a flashlight — was released to free-stream forever. From that moment forward the cosmos was transparent to most photons but full of neutral hydrogen, opaque to ultraviolet light because any UV photon would be absorbed by an n=1 hydrogen atom long before it could travel cosmologically.

The next 100 million years are the cosmic Dark Ages. There were no stars yet — the first overdensities were still collapsing under gravity, slowly pulling baryons into the dark-matter mini-haloes that would eventually host the first stellar systems. The universe was uniformly dim, full of neutral atoms, growing colder.

Cosmic dawn breaks at z ≈ 20–25, when the first generation of stars (Population III) ignites in dark-matter haloes of about 10⁶ M☉. These stars were made entirely of the hydrogen and helium left over from BBN; they had no metals and therefore could not cool below 200 K via molecular emission, which forced them to grow to huge masses (50–500 M☉) before fragmenting. Massive, hot, short-lived, they emit copious ultraviolet photons. The first ionized regions begin to grow around them as small bubbles in an otherwise neutral cosmos.

From cosmic dawn to the end of reionization is the epoch of reionization (EoR). It is not a single moment but a gradual phase transition: ionized bubbles around the first sources expand, overlap with one another, and eventually merge into a connected ionized network until almost no neutral hydrogen remains in the diffuse IGM.

The bubble-overlap picture

Reionization is a percolation problem. Each ionizing source carves out an HII region whose radius depends on the source's photon output and the local gas density. The Strömgren sphere — the equilibrium radius at which photoionizations balance recombinations — sets the boundary of an isolated source. Once a sufficient number of sources have switched on, their HII spheres start to touch. Where they touch, the ionized regions merge and grow much faster than recombinations can refill them. By the end of reionization, a single connected ionized cosmic-scale region fills almost the whole universe, with vanishing islands of neutral hydrogen still embedded in the densest, most self-shielded regions (Lyman-limit systems and damped Lyman-α absorbers).

This bubble-overlap structure makes reionization spatially patchy. Two adjacent sightlines can encounter different ionization fractions at the same redshift, so the transition is sharper along some lines than others. The 21-cm signal — the spin-flip emission of neutral hydrogen at rest-frame 1420 MHz, redshifted to 100–200 MHz today — encodes this morphology, and is the ultimate observational target for radio cosmology arrays like HERA, LOFAR, MWA, and the future SKA.

Who provided the photons?

Counting the photons required to reionize the universe is straightforward arithmetic. The mean baryon density today is n_b,0 ≈ 2.5×10⁻⁷ cm⁻³, of which 92% (by number) is hydrogen. To ionize each hydrogen atom requires at least one Lyman-continuum (LyC) photon (energy > 13.6 eV), but recombinations during the epoch consume more. The dimensionless number that closes the budget is

N_ion / N_H = (1 + n_rec) / f_esc
       where n_rec ≈ 2–5 (recombinations per H over EoR)
       and f_esc is the fraction of LyC photons escaping galaxies

Plugging in n_rec = 3 and f_esc = 0.1, every hydrogen atom must be hit by about 40 ionizing photons produced inside galaxies. Galactic ionizing-photon production rates (ξ_ion) and dust extinctions are known well enough from H-α and UV continuum surveys to translate that into a required UV luminosity density. Star-forming galaxies — both massive and dwarf — meet this budget at z = 6–10, with dwarf galaxies (M_UV > −18) probably providing the bulk of the photons because they are far more numerous than the bright sources. Quasars contribute at the few-percent level for hydrogen and dominate later for helium.

The phase transition in numbers

Redshift z	Cosmic age	Neutral fraction x_HI	Stage	Probe
1100	380 kyr	≈ 0	Recombination — first ionization ends	CMB last scattering
50–25	50–130 Myr	≈ 1	Dark Ages, fully neutral, cold	21-cm absorption against CMB (predicted)
20–15	180–280 Myr	≈ 1	Cosmic Dawn — first stars switch on	EDGES global 21-cm signal candidate
10	480 Myr	~ 0.7	Mid-EoR, bubbles forming and merging	JWST high-z galaxy LF, Ly-α equivalent widths
7.7	700 Myr	~ 0.5	Reionization midpoint (CMB τ_e)	Planck E-mode reionization bump
6	970 Myr	≲ 0.01	Late EoR, isolated neutral patches	Gunn-Peterson trough in z > 6 quasars
5.3	1.1 Gyr	~ 10⁻⁴	End of reionization	Lyman-α forest opacity becomes uniform
3	2.2 Gyr	~ 10⁻⁵	Post-EoR, post-helium reionization	He II Lyman-α forest in UV-bright quasars

The neutral fraction x_HI does not fall to exactly zero — the densest regions of the IGM remain neutral or partially neutral as Lyman-limit systems even today, but the diffuse component is fully ionized for z < 5.

Worked example: ionizing photon budget

How many ionizing photons per hydrogen atom does galactic star formation need to produce to keep the universe ionized at z = 6? Start with the present-day mean hydrogen number density:

n_H,0 = (1 − Y_p) × Ω_b ρ_crit / m_p
      = 0.755 × 0.0224 × 9.47×10⁻³⁰ g/cm³ / (1.67×10⁻²⁴ g)
      ≈ 1.91 × 10⁻⁷ cm⁻³

At z = 6 the hydrogen density is higher by (1+z)³ = 343:

n_H(z=6) ≈ 6.55 × 10⁻⁵ cm⁻³

The recombination time at z = 6 with a clumping factor C ≈ 3 and IGM temperature T = 10⁴ K is

t_rec = 1 / (α_B × n_H × C) ≈ 1 / (2.6×10⁻¹³ × 6.55×10⁻⁵ × 3) cm³/s · cm⁻³
      ≈ 1.96 × 10¹⁶ s ≈ 0.62 Gyr

The age of the universe at z = 6 is t(z=6) ≈ 0.97 Gyr. So during reionization each hydrogen atom recombines about t / t_rec ≈ 1.6 times. Including the ionizing event itself, the total photon budget per hydrogen atom is

N_γ / N_H = (1 + n_rec) / f_esc
          = (1 + 3) / 0.1
          ≈ 40

where we have used a slightly higher n_rec to allow for clumping uncertainty and an escape fraction f_esc = 0.1, the canonical value for high-redshift galaxies inferred from low-redshift LyC leakers. Galaxies must therefore produce 40 × n_H ≈ 2.6 × 10⁻³ ionizing photons per cm³ of comoving volume, or about 10⁷⁰ ionizing photons inside the observable universe by z = 6. Recent JWST observations of z = 6–10 galaxy luminosity functions, multiplied by typical ionizing-photon production efficiencies of 25.5 ≲ log₁₀(ξ_ion / Hz erg⁻¹) ≲ 25.8, comfortably reach this budget — but only if escape fractions are 5–20% and the faint-end slope of the luminosity function is steep.

Variants and extensions

• Helium reionization. The second ionization potential of helium (54.4 eV) requires harder photons than stars typically produce. Helium II reionization happens later, around z = 3, driven by the much harder ultraviolet output of quasars. The He II Lyman-α forest in UV-bright quasars (HE 2347-4342, HS 1700+6416) shows the rapid drop in He II opacity that marks the completion of this second phase transition.
• Patchy reionization and CMB B-mode contamination. Bubble-by-bubble Thomson scattering off the patchy ionized network induces a small kinetic Sunyaev-Zel'dovich signal and, at the second order, contaminates CMB B-mode polarization on small scales. Future CMB-S4 experiments will need to model this carefully when searching for primordial gravitational-wave B-modes.
• Inhomogeneous recombinations. Reionization is not a uniform race between sources and sinks. Dense filaments and Lyman-limit systems can absorb ionizing photons faster than they ionize, slowing the global progress and producing tail-end opacity fluctuations seen in the post-reionization Lyman-α forest at z = 5–6.
• Extended reionization. If reionization began as early as z = 15 with low-luminosity sources contributing most of the photons, the redshift distribution of x_HI is wider than a sharp transition. Planck rules out the most extended models; JWST is now constraining the early end.
• 21-cm cosmology. The neutral hydrogen 21-cm spin-flip line, observed in absorption against the CMB or in emission, traces neutral hydrogen directly. HERA's first-season upper limits already constrain the temperature of the IGM at z = 8, ruling out very cold-IGM models. SKA-Low will deliver tomographic maps in the 2030s.

Where reionization shows up

• Quasar absorption spectra (SDSS, DESI, Subaru). The flux blueward of Lyman-α in quasars at z = 5.7, 6.3 and 7.5 falls from a transmissive forest to an opaque Gunn-Peterson trough as redshift increases. ULAS J1342+0928 (z = 7.54) shows damping wings consistent with x_HI > 0.3 along its sightline.
• Planck CMB polarization. The "reionization bump" at large angular scales (ℓ < 10) in the E-mode polarization spectrum constrains τ_e = 0.054 ± 0.007. Planck 2018 ruled out high-τ models that earlier WMAP9 had suggested.
• JWST high-redshift galaxy surveys. NIRCam imaging plus NIRSpec spectroscopy of CEERS, JADES and PRIMER fields finds galaxies at z = 8–14 with star formation rates of 0.5–10 M☉/yr, ionizing-photon production efficiencies that match what the LyC budget requires, and Lyman-α equivalent widths suppressed by the surrounding neutral IGM.
• Lyman-α emitters at z = 6–7. The fraction of Lyman-break galaxies showing strong Lyman-α emission drops sharply between z = 6 and z = 7 as the IGM transmission decreases — a direct probe of the late-stage neutral fraction.
• 21-cm experiments (HERA, LOFAR, MWA, SKA-Low). Currently producing upper limits on the 21-cm power spectrum at z = 7–10. Detection of the spectrum would map the bubble morphology of reionization. The disputed EDGES global 21-cm absorption signal at z ≈ 17, if confirmed, dates cosmic dawn to t ≈ 200 Myr.

When did reionization end? Recent shift to z ≈ 5.3

The traditional picture placed the end of reionization at z ≈ 6 based on the appearance of complete Gunn-Peterson saturation in z > 6 quasars. More recent work — high-resolution Lyman-α forest measurements out to z ≈ 5.5, statistically large samples of quasar sightlines, and dark-pixel statistics — finds that the post-reionization IGM remains spatially highly inhomogeneous in opacity until z ≈ 5.3. Some sightlines have transmission consistent with a fully ionized IGM at z = 5.5; others show extended opaque troughs of length ~50 cMpc consistent with x_HI ≈ 0.1 along part of the sightline. This "late reionization" picture pushes the completion of the cosmic phase transition about 100 million years later than was thought a decade ago, with significant implications for the photon budget and the duration of the EoR.

Common pitfalls

• Confusing recombination with reionization. Recombination at z ≈ 1100 is the first phase transition, when free electrons captured onto nuclei. Reionization at z ≈ 6–10 is a much later, completely different process driven by stellar UV. They are easy to mix up because both involve the ionization state of hydrogen.
• Treating τ_e as the redshift of reionization. τ_e ≈ 0.054 is an integrated optical depth. To convert it to a midpoint redshift requires assuming a parametric reionization history. A sharp transition gives z_re ≈ 7.7; an extended history with a long high-z tail gives a different z_re for the same τ_e.
• Ignoring escape fraction. Galaxies produce far more ionizing photons than escape into the IGM. Most LyC photons are absorbed by neutral hydrogen and dust inside the galaxy itself. Plausible reionization budgets require escape fractions of 5–20%; assuming f_esc = 1 makes reionization "trivial" in a way that is observationally inconsistent.
• Calling EDGES a confirmed cosmic-dawn detection. The 2018 EDGES report of a 78 MHz absorption feature has not been confirmed by other experiments (notably SARAS-3 has reported a non-detection). The signal might be reionization-era 21-cm absorption or might be terrestrial / instrumental. Treat it as a candidate, not a measurement.
• Underestimating helium reionization. Hydrogen and helium-I reionize together, but helium-II requires much harder photons and reionizes later, around z = 3. Conflating "reionization" with hydrogen-only reionization misses a quarter of the energy injected into the IGM.