Gunn-Peterson Effect

The Gunn-Peterson effect is a feature in the spectra of distant quasars caused by the presence of neutral hydrogen in the Intergalactic Medium (IGM). It serves as a powerful diagnostic tool for determining the ionization state of the Universe and marks the transition from the “Cosmic Dark Ages” to the era of Reionization.

According to Gunn-Peterson effect beyond a certain redshift the Universe has not re-ionized yet and thus the hydrogen is neutral throughout and can absorb the $\text{Ly}\alpha$ line at any redshift and not just at redshifts corresponding to the localized clouds of neutral hydrogen.

Fig 1: Spectra for high redshift SDSS quasars. The Gunn-Peterson trough bluewards of the Lyman alpha emission that is clearly apparent in the highest redshift ones indicates that the Universe is somewhat more neutral at these redshifts.

As light from a distant quasar travels toward Earth, it is continuously redshifted. If it encounters any neutral hydrogen ($HI$) along the way, photons that have been redshifted into the Lyman-alpha ($\text{Ly}\alpha$) resonance frequency ($121.6 \text{ nm}$) will be scattered.

If the IGM is significantly neutral (as it was before the first stars and galaxies fully reionized the universe), this scattering happens at every point along the line of sight. This creates a continuous “trough” of absorption, completely suppressing the flux of the quasar at wavelengths shorter than the $\text{Ly}\alpha$ emission line.

Fig 2: Spectrum of a quasar showing the Gunn-Peterson effect.

The strength of the effect is measured by the Gunn-Peterson optical depth, denoted as $\tau_{GP}$. The optical depth for $\text{Ly}\alpha$ scattering at a redshift $z_{abs}$ is given by:

$$\tau_{GP}(z_{abs}) = \frac{\pi e^2}{m_e c} f_{\alpha} \lambda_{\alpha} H^{-1}(z_{abs}) n_{HI}(z_{abs})$$

Where: $e$ and $m_e$: Electron charge and mass.
$f_{\alpha}$: The oscillator strength of the $\text{Ly}\alpha$ transition ($\approx 0.416$).
$\lambda_{\alpha}$: The rest-frame wavelength ($121.6 \text{ nm}$).
$H(z)$: The Hubble parameter at redshift $z$.
$n_{HI}(z)$: The number density of neutral hydrogen.

In a standard $\Lambda$CDM cosmology, for high redshifts where the Universe is approximately Einstein-de Sitter ($H(z) \approx H_0 \Omega_m^{1/2} (1+z)^{3/2}$), the formula simplifies to:

$$\tau_{GP}(z) \approx 4.9 \times 10^5 \left( \frac{\Omega_m h^2}{0.13} \right)^{-1/2} \left( \frac{\Omega_b h^2}{0.02} \right) \left( \frac{1+z}{10} \right)^{3/2} \left( \frac{n_{HI}}{n_H} \right)$$

Where: $\Omega_m$ and $\Omega_b$: Density parameters for matter and baryons.
$n_{HI} / n_H$: The neutral fraction of hydrogen.

The most striking aspect of the formula is the coefficient ($~10^5$). This indicates that even a tiny amount of neutral hydrogen causes massive absorption:
High Sensitivity: A neutral fraction of only $10^{-4}$ (0.01% neutral gas) is enough to create an optical depth $\tau_{GP} > 1$, which makes the IGM appear opaque.
The Reionization “Wall”: For many years, astronomers observed the “Lyman-alpha Forest” (thin lines of absorption), indicating a highly ionized IGM. However, when quasars at $z > 6$ were discovered (most notably by the Sloan Digital Sky Survey), the flux suddenly dropped to zero, signaling that we had reached the era when the Universe was still substantially neutral.

Fig 3: Cosmic ionnizaton history.

While the Lyman-limit systems (LLSs) mentioned previously represent discrete, dense clouds (optically thick at $912 \text{ Å}$), the Gunn-Peterson effect represents the global, diffuse state of the IGM (optically thick at $1216 \text{ Å}$).

If the Gunn-Peterson trough is present, it suggests the observer is looking back into the Epoch of Reionization, providing a “curtain” beyond which it is difficult to see the Universe in UV light.