Gunn-Peterson Trough

A black hole punched in a rainbow

Split a quasar's light into a spectrum and, in most cases, you get a bright continuum sprinkled with sharp emission and absorption lines. But point a spectrograph at one of the most distant quasars — an object whose light set out when the universe was less than a billion years old — and something startling happens. Blueward of one prominent emission line, the spectrum simply stops. Not dimmed, not reddened: black. The flux falls to zero across a wide swath of wavelength, as if someone had painted over that part of the rainbow. That dark gap is the Gunn-Peterson trough.

The cause is almost embarrassingly simple. Neutral hydrogen atoms — the most abundant baryonic matter in the universe — are voracious absorbers of one particular ultraviolet wavelength: Lyman-alpha, 1215.67 Å, the photon emitted or absorbed when hydrogen's electron jumps between its ground state and first excited state. Lay enough neutral hydrogen across a sightline and it will scatter every Lyman-alpha photon out of the beam. The trick is that, because of cosmic expansion, a quasar photon does not have to start at 1216 Å to be caught. As the photon travels toward us its wavelength stretches; somewhere along the way it inevitably passes through 1216 Å in the local rest frame of some intervening gas. If that gas is neutral, the photon is gone. The result is that the entire blue side of the spectrum is vulnerable, and the universe blacks it out.

James Gunn and Bruce Peterson worked this out in 1965, in the same year the cosmic microwave background was discovered. Their conclusion was radical for the time: the very fact that we can see continuum blueward of Lyman-alpha in nearby quasars proves the intergalactic medium is almost completely ionised. A neutral IGM would be opaque. The trough is the observational signature of the rare exception — looking far enough back to catch the gas before stars and quasars finished switching it on.

The astrophysics: an enormous cross-section

The reason a tiny neutral fraction is enough comes down to the size of the Lyman-alpha resonant scattering cross-section. At line centre it is

σ_α(ν₀) ≈ 4.5 × 10⁻¹⁸ cm²

which is gigantic by atomic standards — millions of times the Thomson cross-section of a free electron (6.65 × 10⁻²⁵ cm²). Gunn and Peterson combined this with the expansion of the universe to compute the optical depth a photon accumulates as it redshifts through the resonance. For a smoothly distributed IGM the Gunn-Peterson optical depth is

τ_GP(z) = (π e² / m_e c) f_α λ_α  · n_HI(z) / H(z)

where f_α = 0.4162 is the Lyman-alpha oscillator strength, λ_α = 1215.67 Å, n_HI(z) is the proper number density of neutral hydrogen, and H(z) is the Hubble parameter at the absorbing redshift. The H(z) in the denominator is the key cosmological ingredient: the faster space expands, the faster the photon sweeps through resonance and the less time it spends being absorbed. Plugging in standard cosmological parameters near z ≈ 6 gives the famous scaling

τ_GP ≈ 3.5 × 10⁵ · x_HI
     ≈ 4.9 × 10⁵ · x_HI · [(1+z)/7]^(3/2)

Here x_HI = n_HI / n_H is the neutral fraction. The transmitted flux is the continuum times exp(−τ_GP). Because exp(−5) ≈ 0.7%, any τ above about 5 looks black to the eye and to most instruments. From the second relation, τ = 5 corresponds to x_HI ≈ 10⁻⁵ at z ≈ 6 — so an IGM that is 99.999% ionised still produces a saturated trough. Conversely, the residual transmitted flux of the Lyman-alpha forest at lower redshift requires neutral fractions of only 10⁻⁶ to 10⁻⁵, which is exactly what is observed. The same physics, read at different neutral fractions, gives the forest and the trough.

How we observe it

The observation is conceptually a single measurement: take a high signal-to-noise spectrum of a luminous, high-redshift quasar and look at the flux just blueward of the redshifted Lyman-alpha emission peak. In practice it requires the largest telescopes — Keck, VLT, Gemini, Subaru — because z ≈ 6 quasars have apparent magnitudes around 19–20 in the z and y bands, and because the diagnostic region is at observed wavelengths of 8000–9000 Å where the night sky glows with OH airglow.

Several features of the spectrum work together:

• The proximity zone. Immediately blueward of the Lyman-alpha emission line there is usually a small region of transmitted flux — the quasar's own intense ultraviolet radiation has photoionised a bubble of gas around it, so the gas there is transparent. The size of this zone (a few proper Mpc) shrinks with redshift and is itself a probe of the surrounding neutral fraction.
• The trough. Beyond the proximity zone the flux drops to the noise floor. A "dark gap" is a contiguous stretch with no detected transmission; a complete Gunn-Peterson trough is a dark gap spanning the entire Lyman-alpha region.
• The damping wing. If the gas is substantially neutral (x_HI of order 0.1 to 1), the Lorentzian wings of the Lyman-alpha line profile become detectable, smearing absorption to the red of the line centre. Detecting a damping wing is one of the few ways to measure a high neutral fraction directly, and it has been claimed for the most distant quasars and for Lyman-alpha-emitting galaxies.
• The dark-pixel fraction. Because the trough saturates, modern analyses count the fraction of pixels consistent with zero flux in both Lyman-alpha and Lyman-beta. This "dark-pixel" statistic gives a model-independent upper limit on the neutral fraction without assuming anything about the IGM density field.

Multiple sightlines are essential, because reionization is patchy: one quasar may show a long trough while another at the same redshift shows transmission, reflecting whether the line of sight happens to thread ionised bubbles or neutral islands.

The trough across cosmic time

The strength of the absorption climbs steeply with redshift as the neutral fraction rises and the gas gets denser. The following figures track a single Lyman-alpha sightline from the local, fully ionised universe back to the epoch of reionization.

Redshift z	Cosmic age	Neutral fraction x_HI	Effective τ_α	Mean transmission	Spectral appearance
2.0	3.3 Gyr	~3 × 10⁻⁶	~0.15	~85%	Thin Lyman-α forest
3.0	2.1 Gyr	~7 × 10⁻⁶	~0.4	~67%	Moderate forest
4.0	1.5 Gyr	~1.5 × 10⁻⁵	~1.0	~37%	Thick forest
5.0	1.2 Gyr	~3 × 10⁻⁵	~2.2	~11%	Dense forest, dark gaps
5.7	1.0 Gyr	~6 × 10⁻⁵	~4–5	~1–4%	Onset of complete troughs
6.0	0.94 Gyr	≳ 10⁻⁴	≳ 6	< 0.5%	Complete Gunn-Peterson trough
7.0	0.75 Gyr	~0.1–1 (patchy)	≫ 10	~0%	Trough + damping wing

The redshift-evolution of the effective optical depth is steep and non-linear: between z = 5 and z = 6 the mean transmission collapses from roughly 11% to below half a percent, and its scatter from sightline to sightline grows dramatically. That sudden increase in variance — some sightlines black, others still transmitting at the same redshift — is itself a signature of the patchy, bubble-by-bubble nature of the final phase of reionization.

Lyman-alpha forest versus Gunn-Peterson trough

The single most common point of confusion is the relationship between the Lyman-alpha forest and the Gunn-Peterson trough. They are not different phenomena — they are the same resonant scattering seen at different neutral fractions and densities.

Property	Lyman-α forest	Gunn-Peterson trough
Typical redshift	z ≈ 2–5	z ≳ 6
Absorber	Discrete dense filaments (overdensities)	Smoothly distributed IGM
Spectral look	Many narrow lines with transparent gaps	Continuous black absorption
Optical depth	Patchy, often τ < 1 between lines	τ ≳ 5 everywhere (saturated)
Neutral fraction probed	10⁻⁶ – 10⁻⁵	≳ 10⁻⁴ (only a lower limit)
Information content	Density field, temperature, UV background	Presence of neutral gas; onset of reionization
Limiting weakness	Needs an ionising background model	Saturates — loses sensitivity above ~10⁻³

As you push a sightline to higher redshift, the forest "lines" crowd together because the mean density of the universe rises as (1+z)³ and the neutral fraction creeps up. Eventually the transparent gaps between absorption lines vanish entirely, and the forest becomes a trough. The transition is not a single redshift but a gradual thickening that becomes complete near z ≈ 6 — and varies from one direction on the sky to another.

Worked example: how neutral must the gas be?

Suppose a spectrograph can detect transmitted flux down to 1% of the quasar continuum. What is the largest neutral fraction the intergalactic medium can have at z = 6 and still show a measurable transmission spike — i.e. not a complete trough?

Set the transmission threshold exp(−τ) = 0.01, so τ = ln(100) ≈ 4.6. Using the scaling relation at z = 6 (so (1+z)/7 = 1):

τ_GP ≈ 4.9 × 10⁵ · x_HI
4.6  ≈ 4.9 × 10⁵ · x_HI
x_HI ≈ 9.4 × 10⁻⁶

So the moment the neutral fraction climbs above roughly 10⁻⁵ — one neutral atom per hundred thousand — the transmission drops below the 1% floor and the trough goes black. The corresponding neutral hydrogen number density is

n_H(z=6) ≈ n_H,0 (1+z)³ ≈ 1.9 × 10⁻⁷ × 343 ≈ 6.5 × 10⁻⁵ cm⁻³
n_HI     ≈ x_HI · n_H ≈ 9.4 × 10⁻⁶ × 6.5 × 10⁻⁵ ≈ 6 × 10⁻¹⁰ cm⁻³

That is about one neutral hydrogen atom in every 1,700 cubic metres of space — and it is enough to extinguish the light of a quasar a hundred times more luminous than the entire Milky Way. The lesson Gunn and Peterson drew is the one that still holds: the trough is a fabulously sensitive detector of neutral gas, but precisely because it is so sensitive it saturates almost immediately, and a black trough cannot distinguish a 0.001%-neutral universe from a 100%-neutral one.

Famous examples and milestones

• The 1965 prediction. James E. Gunn and Bruce A. Peterson published "On the Density of Neutral Hydrogen in Intergalactic Space" in The Astrophysical Journal. With only the quasar 3C 9 (z = 2.01) to look at, they found no trough — the continuum was visible blueward of Lyman-alpha — and concluded that the IGM must be highly ionised, with x_HI below about 10⁻⁶.
• SDSS J1030+0524 (2001). Robert Becker and collaborators, using a Sloan Digital Sky Survey quasar at z = 6.28, reported the first detection of a complete Gunn-Peterson trough — an extended region of zero flux — providing direct evidence that the neutral fraction rises sharply by z ≈ 6 and that reionization was ending around that epoch.
• ULAS J1120+0641 (2011). At z = 7.085, the most distant quasar known for years, its spectrum showed a strong Lyman-alpha damping wing, interpreted as a neutral fraction of order 0.1 in the surrounding IGM — pushing the trough diagnostic into the heart of the reionization era.
• J0313–1806 (2021). At z = 7.64, this remains among the most distant quasars known, with a damping-wing analysis suggesting a substantially neutral IGM and a black hole already 1.6 × 10⁹ solar masses — a puzzle for early black-hole growth in its own right.
• The patchy late-reionization picture. Surveys of dozens of z ≈ 5.5–6.5 quasars (e.g. with Keck and VLT) reveal enormous sightline-to-sightline scatter in dark-gap lengths, including extremely long (> 100 comoving Mpc) troughs at z ≈ 5.5 that argue reionization may not have completed until z ≈ 5.3 — later than once thought.

Beating saturation: complementary probes

Because the Lyman-alpha trough saturates near x_HI ≈ 10⁻⁴, the central decades of reionization (neutral fractions from 10⁻³ up to 1) are invisible to it. Astronomers stitch the picture together with methods that remain sensitive in that regime:

Probe	Sensitive to x_HI	What it measures	Example mission/instrument
Lyman-α Gunn-Peterson trough	10⁻⁵ – 10⁻³	Onset/end of reionization	Keck/HIRES, VLT/X-shooter
Lyman-β & higher series troughs	up to ~10⁻²	Extends sensitive range (σ smaller)	Same spectrographs
Lyman-α damping wing	0.05 – 1	Bulk neutral fraction near quasar	z > 7 quasar spectra
Lyman-α emitter visibility	0.1 – 1	IGM opacity to galaxy Lyman-α	JWST, Subaru/HSC narrowband
CMB Thomson optical depth τ_e	integrated	Total free electrons → midpoint z_re	Planck (τ_e ≈ 0.054)
21 cm hyperfine signal	10⁻² – 1	Maps neutral gas tomographically	SKA, HERA, LOFAR

The combined picture from Planck's electron-scattering optical depth (τ_e ≈ 0.054, implying a reionization midpoint near z ≈ 7.7) and the quasar troughs (end near z ≈ 5.3–6) is that reionization was a relatively rapid, patchy process spanning roughly z ≈ 9 to z ≈ 5.5. The 21 cm experiments aim to fill the gap the trough cannot — directly imaging the neutral islands while they still exist.

Common misconceptions and edge cases

• "The trough is at the Lyman-alpha line." No — it lies blueward of the quasar's redshifted Lyman-alpha emission. The emission line sits at the quasar's own redshift; absorption happens at all the lower redshifts the photon passes through on its way to us, which corresponds to shorter rest-frame wavelengths that have been stretched into that blue region of the observed spectrum.
• "A black trough means the universe was fully neutral." It does not. Saturation means a 99.999%-ionised universe and a fully neutral one produce identical black troughs. The trough sets a lower limit on neutrality, not a measurement — this is its defining limitation.
• "It is the same as the Lyman-alpha forest." Same physics, different regime. The forest is patchy partial absorption from dense filaments in an ionised IGM; the trough is continuous saturated absorption from a more neutral, smoother IGM.
• "Reionization ended cleanly at z = 6." The long dark gaps seen toward some z ≈ 5.5 quasars suggest neutral islands survived later than the classic z ≈ 6 endpoint — reionization likely finished around z ≈ 5.3, and it was spatially patchy rather than uniform.
• "Only hydrogen matters." Helium has its own Gunn-Peterson effect at the He II Lyman-alpha line (304 Å rest), which reionizes later (around z ≈ 3) because it requires harder photons from quasars. He II troughs observed in the far-UV (with HST/COS) trace the separate, later reionization of helium.
• "The proximity zone is part of the trough." The transmitted region right next to the emission line is the quasar's own ionised bubble, not IGM transmission. Mistaking the proximity zone for residual IGM flux biases neutral-fraction estimates, so it is masked out in careful analyses.