The Epoch of Reionization (EoR) marks a fundamental transition in the history of the Universe during which the neutral intergalactic medium (IGM) was transformed into an ionized state by the radiation from the first generations of stars and active galactic nuclei (AGNs).

### Context: From Recombination to the Dark Ages After the Big Bang, the Universe was a hot plasma of free electrons and nuclei. Approximately 380,000 years after the Big Bang ($z \sim 1100$), the temperature dropped to roughly 3000 K, allowing electrons to combine with protons to form neutral hydrogen atoms. This event, known as recombination, made the Universe transparent to photons, which we observe today as the cosmic microwave background (CMB). Following recombination, the Universe entered the “Dark Ages,” a period where no luminous sources yet existed and the IGM was almost entirely neutral.

### The Onset of Reionization Reionization began as the first structures collapsed under gravity to form the earliest stars (Population III) and AGNs. * The First Stars (Population III): These stars formed in low-mass dark matter halos ($M \sim 10^4 M_{\odot}$). Because the gas was metal-free, cooling—a prerequisite for star formation—could only occur via molecular hydrogen ($H_2$). * Mathematical Condition (Jeans Mass): For gas to fall into dark halos and collapse, the mass must exceed the Jeans mass ($M_J$). For $z \lesssim 140$, this is given by:

  $$M_J = 5.7 \times 10^3 \left( \frac{\Omega_m h^2}{0.15} \right)^{-1/2} \left( \frac{\Omega_b h^2}{0.022} \right)^{-3/5} \left( \frac{1+z}{10} \right)^{3/2} M_{\odot}$$.

* Molecular Dissociation: The first Population III stars produced photons that dissociated $H_2$ at energies between 11.26 eV and 13.6 eV. This “self-regulation” temporarily suppressed further star formation until more massive halos ($T_{vir} > 10^4$ K) formed, allowing for cooling via atomic hydrogen.

### The Reionization Process As more stars and quasars formed, they created expanding bubbles of ionized hydrogen (H II regions) around them. * Equilibrium of Ionization: The density of neutral hydrogen ($n_{HI}$) in the IGM is determined by the balance between the photoionization rate ($\Gamma_{HI}$) and the recombination rate ($\alpha$):

  $$n_{HI} = \frac{\alpha}{\Gamma_{HI}} n_p^2$$.

* Recombination Rate: The number of recombinations per unit volume per second is given by:

  $$-\frac{dn_e}{dt} = n_e^2 \alpha(T_e)$$.

* Completion: The epoch ended when these H II regions overlapped, rendering the entire IGM effectively ionized.

### Observational Evidence 1. The Gunn-Peterson Test: Spectra of high-redshift quasars ($z \gtrsim 6$) show a “Gunn-Peterson trough,” where all radiation blueward of the $Ly\alpha$ emission line is absorbed by diffuse neutral hydrogen. The optical depth ($\tau$) for this absorption is expressed as:

  $$\tau \approx 4.14 \times 10^{10} h^{-1} \frac{n_{HI}(z)}{\text{cm}^{-3}} (1+z)^{-1} (1+\Omega_m z)^{-1/2}$$.
  The disappearance of this trough at $z \lesssim 5.8$ indicates the Universe was fully reionized by that time.

2. CMB Polarization: Results from the WMAP satellite detected unexpectedly high polarization in the CMB on large angular scales. This polarization results from the Thomson scattering of CMB photons by free electrons in the reionized IGM. These measurements suggest that reionization occurred much earlier than previously thought, at a redshift of $z \sim 15$.

3. Metal Enrichment: Even the most distant quasars ($z \sim 6$) show metallicities near 1/10th of the solar value, proving that significant star formation and supernova explosions had already enriched the IGM during the reionization process.