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Reionization

Cosmic reionization is the epoch in the early universe during which the neutral intergalactic medium (IGM), primarily composed of hydrogen and helium, was ionized by ultraviolet (UV) and X-ray radiation from the first luminous sources, marking the last major phase transition in cosmic history.^[1] This process transformed the universe from an opaque, neutral state to a transparent, ionized one, allowing photons to propagate freely across cosmic distances.^[2] The Epoch of Reionization (EoR) spanned approximately from redshift z ≈ 15 to z ≈ 6, corresponding to 200–900 million years after the Big Bang, though recent observations suggest the onset may have begun as early as z ≈ 13, around 330 million years post-Big Bang.^[3] It followed the cosmic "Dark Ages," a period after recombination (z ≈ 1100) when the universe was neutral and devoid of stars, and preceded the formation of the familiar large-scale structure observed today.^[4] The reionization process was extended and inhomogeneous, starting in underdense regions ("outside-in" mode) where ionizing photons could travel farther before being absorbed, forming expanding H II bubbles that eventually overlapped to ionize the entire IGM by z ≈ 6.^[2] The primary drivers of reionization were UV photons (with energies >13.6 eV) escaping from star-forming galaxies, particularly low-mass systems at high redshifts, which produced the necessary ionizing flux to balance recombinations in the clumpy IGM.^[2] Contributions from active galactic nuclei (AGNs), including quasars and accreting supermassive black holes, provided harder X-ray radiation that could penetrate denser regions, though their role remains secondary to stellar sources based on current luminosity function estimates.^[4] The escape fraction of ionizing photons (f_esc) from these early galaxies is a key uncertain parameter, estimated at 5–20%, influencing the pace and topology of reionization.^[5] Observationally, the end of reionization is evidenced by the sharp increase in transmitted flux in the Lyman-α forest of quasar spectra at z < 6, indicating a highly ionized IGM.^[2] The cosmic microwave background (CMB) provides an integrated measure through the optical depth to electron scattering, τ = 0.054 ± 0.007, from Planck 2018 measurements, implying reionization began before z ≈ 8.^[6] Recent James Webb Space Telescope (JWST) detections of galaxies at z > 10, such as those showing Lyman-α emission at z ≈ 13, are revealing the first ionizing sources and constraining the neutral hydrogen fraction.^[3] Future probes, including 21 cm intensity mapping with facilities like the Square Kilometre Array (SKA), will map the spatial progression of reionization in detail.^[4]

Concept

Definition and Physical Process

Reionization refers to the phase transition in the early universe during which the neutral hydrogen in the intergalactic medium (IGM), formed after recombination, becomes predominantly ionized.^[7] This process occurred roughly between redshifts z \approx 6 and z \approx 15, transforming the IGM from a neutral state into a highly ionized warm plasma.^[8] The primary physical mechanism driving reionization is photoionization, where ultraviolet photons with energies exceeding the hydrogen ionization threshold of 13.6 eV interact with neutral hydrogen atoms, ejecting electrons and producing free protons.^[8] This process can be described by the photoionization rate per neutral atom, C_{\rm HI} = 4\pi \int_{\nu_{\rm HI}}^\infty \frac{J_\nu}{h\nu} \sigma_{\rm HI}(\nu) \, d\nu, where J_\nu is the specific intensity of the radiation field, \sigma_{\rm HI}(\nu) is the absorption cross-section, and \nu_{\rm HI} corresponds to 13.6 eV.^[8] The resulting free electrons and protons maintain a dynamic balance influenced by recombination, but the system is generally out of thermal equilibrium due to the influx of ionizing radiation. In regions approaching ionization equilibrium, the Saha equation provides a framework for estimating the ionization fraction, relating the densities of ionized and neutral states through temperature and density. For hydrogen, it takes the form

\frac{n_{\rm HII} n_e}{n_{\rm HI}} = \left( \frac{2\pi m_e k_B T}{h^2} \right)^{3/2} \exp\left( -\frac{I_{\rm H}}{k_B T} \right),

^[9] where n_{\rm HII}, n_{\rm HI}, and n_e are the number densities of protons, neutral hydrogen, and electrons, respectively; I_{\rm H} = 13.6 eV is the ionization energy. However, this equation assumes local thermodynamic equilibrium, which breaks down during reionization due to non-equilibrium conditions at propagating ionization fronts, where rapid photon absorption and dynamic IGM evolution prevent full thermal balance.^[8] Locally, photoionization creates ionized bubbles analogous to Strömgren spheres around discrete sources, where the sphere's radius balances the production and recombination of ionizations within a uniform medium.^[7] The propagation of these bubbles is limited by the high optical depth \tau to ionizing photons, which arises from the large cross-section of neutral hydrogen and results in rapid absorption over short mean free paths in the neutral IGM.^[7] While primarily driven by hydrogen photoionization, the process also sets the stage for helium reionization at lower redshifts (z ≈ 3), completing IGM ionization. Reionization concluded around z \approx 6, as evidenced by the emergence of the Gunn-Peterson trough in quasar spectra, indicating a sharp decline in neutral hydrogen density.

Importance in Cosmic History

Reionization marked a transformative phase in the universe's thermal history, as the photoionization of hydrogen in the intergalactic medium (IGM) by the first luminous sources heated the gas initially to ~20,000–30,000 K via the photoelectric effect during the passage of ionization fronts, which cools to ~10^4 K by the end of the epoch due to adiabatic expansion.^[10] The elevated temperatures increased the Jeans mass, providing thermal feedback that suppressed the collapse of gas into low-mass halos and inhibited star formation in dwarf galaxies, thereby regulating small-scale structure formation and contributing to the scarcity of observed faint satellites in the local universe.^[11] The ionization of the IGM during reionization fundamentally altered the propagation of light, transitioning the universe from an opaque, neutral state to one where ultraviolet photons could travel freely beyond the Lyman-alpha wavelength. In a neutral universe, the Gunn-Peterson effect would absorb nearly all light shortward of Lyman-alpha, rendering high-redshift sources invisible; post-reionization, the ionized IGM enables the transmission of spectral features from distant galaxies, allowing astronomers to probe the early universe directly. This shift not only unveiled the high-redshift cosmos but also facilitated observations of Lyman-alpha emitters, whose visibility serves as a tracer of ionized bubbles amid lingering neutral patches.^[3] On a broader scale, reionization bridged the cosmic dark ages—following recombination—to the era of modern structure formation, influencing the evolution of the large-scale structure through its effects on the IGM's thermal and ionization state and the observability of baryonic acoustic oscillations in post-reionization probes like the 21 cm line and Lyman-α forest.^[12] Additionally, the free electrons generated during reionization scattered cosmic microwave background (CMB) photons via Thomson scattering, contributing the bulk of the measured optical depth \tau \approx 0.054 (as of Planck 2018), which generates a large-scale polarization signal in the CMB and provides a key constraint on the timing of this epoch.^[6]

Timeline and Phases

Recombination and Dark Ages

Following the inflationary epoch and nucleosynthesis, the universe continued to expand and cool, reaching a temperature of approximately 0.3 eV at a redshift z \approx 1100, where the thermal energy became comparable to the 13.6 eV binding energy of neutral hydrogen.^[13] At this point, known as the recombination epoch, free electrons and protons began to recombine efficiently to form neutral hydrogen atoms, transitioning the universe from a fully ionized plasma to a mostly neutral state.^[13] This process was governed by the Saha equation, which balances the ionization fraction based on temperature, density, and the hydrogen binding energy, though detailed calculations account for non-equilibrium effects such as the finite speed of light and feedback from Lyman-alpha photons. Recombination occurred over a narrow redshift range, \Delta z \approx 200, lasting about 200,000 years, during which the electron fraction dropped from nearly 1 to below 10^{-4}. The recombination process is characterized by the visibility function, g(z) = -\frac{d e^{-\tau}}{dz}, where \tau(z) is the optical depth due to Thomson scattering of photons by free electrons. This function peaks sharply at z \approx 1090, marking the moment when the universe became optically thin to photons, allowing them to decouple from baryons and free-stream as the cosmic microwave background (CMB). Prior to decoupling, photons maintained tight coupling with electrons via Compton scattering, damping baryonic density perturbations on small scales, while after decoupling, the universe entered a matter-dominated era where baryons fell into dark matter potential wells, enabling further structure growth.^[2] The period immediately following recombination, spanning redshifts from z \approx 1100 to z \approx 30, is termed the cosmic dark ages, during which the universe was filled with neutral hydrogen and helium gas in a homogeneous, opaque state devoid of luminous sources.^[2] This era lasted approximately 100 million years, with the universe expanding and cooling adiabatically, reaching gas temperatures around 80 K by z \approx 30, closely coupled to the CMB temperature.^[2] Without stars or galaxies, the intergalactic medium remained dark to electromagnetic radiation beyond the CMB, though primordial density perturbations—seeded by quantum fluctuations during inflation—grew linearly under gravity in the matter-dominated regime, following the \delta \propto a scaling where a is the scale factor.^[2] During the dark ages, the first gravitationally bound structures, known as minihaloes, began to form at redshifts z \approx 20-30, with typical masses of $10^5 - 10^6 M_\odot arising from dark matter haloes that captured baryonic gas. These minihaloes cooled primarily via molecular hydrogen emission but lacked sufficient mass and temperature to ignite massive stars capable of producing significant ionizing radiation, thus preserving the neutrality of the intergalactic medium. The end of the dark ages was marked by the collapse of more massive haloes (> 10^6 M_\odot) around z \approx 20, where the first Population III stars formed, initiating the cosmic dawn and the onset of reionization.^[2]

Cosmic Dawn and Epoch of Reionization

The Cosmic Dawn marks the initial phase of reionization at redshifts z \approx 20-30, when the first Population III stars formed within the smallest dark matter halos, heralding the end of the neutral Dark Ages and the onset of cosmic structure illumination. Recent James Webb Space Telescope (JWST) observations suggest the onset of reionization may have begun as early as z \approx 13.^[3] These primordial stars, along with the earliest galaxies, emitted ultraviolet photons that began ionizing pockets of the intergalactic medium (IGM), forming small H II regions or "bubbles" around their host halos.^[14] This process initiated the transition from a fully neutral universe to one increasingly permeated by ionized hydrogen, with the volume-averaged ionization fraction x_e starting from near zero and gradually rising as more sources ignited. The Epoch of Reionization (EoR) followed, spanning z \approx 6-15 over approximately 700 million years, during which the discrete nature of early sources led to patchy reionization characterized by inhomogeneous x_e evolution. Ionization bubbles expanded and overlapped, percolating through the IGM and achieving roughly 50% global ionization by z \approx 8, as the ionized volume fraction grew nonlinearly due to the clustering of sources in overdense regions. Two primary scenarios describe this progression: an inside-out mode, where denser regions ionize first around galaxies before expanding outward, versus an outside-in mode, where lower-density voids ionize earlier due to longer mean free paths for photons.^[15] Reionization culminated near z \approx 6, when the IGM became fully ionized, as indicated by the sharp decline in neutral hydrogen absorption in high-redshift quasar spectra. Helium reionization occurred later and more abruptly, with He II ionizing primarily at z \approx 3 due to harder photons from quasars, distinct from the extended hydrogen process.^[16] This phase left a legacy of patchy topology in the IGM, with x_e fluctuations persisting briefly after overlap, reflecting the finite number and distribution of discrete ionizing sources.

Ionizing Sources

Population III Stars

Population III stars represent the first generation of stars to form in the universe, emerging from pristine, metal-free gas clouds in small primordial minihalos with virial masses of $10^5 to $10^6 solar masses at redshifts z > 20.^[17] These structures collapsed under their own gravity, with cooling primarily facilitated by molecular hydrogen (H₂) rovibrational line emission, enabling the fragmentation and subsequent formation of protostellar cores.^[18] The lack of heavy elements, which in later stellar generations promote efficient radiative cooling and smaller-scale fragmentation, resulted in an initial mass function (IMF) heavily skewed toward massive stars, with characteristic masses spanning 10 to 1000 solar masses.^[19] This top-heavy IMF arises because the absence of metals limits fragmentation during collapse, favoring the accretion of larger gas reservoirs onto fewer, more massive protostars.^[20] These metal-free stars exhibited extreme physical properties, including effective temperatures exceeding $10^5 K, which produced a hard ultraviolet spectrum rich in high-energy photons capable of ionizing hydrogen and helium.^[21] For stars with initial masses above approximately 100 solar masses, this spectral hardness stemmed from their high surface temperatures and lack of line blanketing by metals, enhancing the production of photons with energies above 13.6 eV.^[22] Their lifetimes were exceptionally brief, typically lasting only a few million years—for instance, a 200 solar mass star evolves through its main sequence in about 2.4 million years—due to their high masses and rapid nuclear burning rates.^[23] At the end of their lives, many Population III stars in the mass range of 140 to 260 solar masses underwent pair-instability supernovae, explosive events triggered by electron-positron pair production in their cores, which completely disrupted the stars without leaving remnants.^[24] In the context of early cosmic reionization, Population III stars played a pivotal role during cosmic dawn by serving as the primary sources of ionizing radiation, generating small, localized H II regions or bubbles around their minihalos.^[25] The escape fraction of these ionizing photons from the dense primordial environments was relatively low, estimated at 10–20%, limited by the high gas densities and lack of pre-existing channels in the metal-free gas.^[26] Despite their efficiency in producing hard UV photons, the overall photon budget from Population III stars proves insufficient to drive the full reionization of the intergalactic medium, as their short-lived nature and limited numbers in minihalos contribute only modestly to the global ionization history.^[27] The explosions of these massive stars, however, injected the first metals into the intergalactic medium, enriching it to metallicities of order $10^{-6} to $10^{-4} solar values and transitioning subsequent star formation to metal-enriched Population II modes.^[28]

Early Galaxies

Early galaxies, which began forming at redshifts [z](/page/Z) \gtrsim 10, are compact systems with low metallicities typically below [Z](/page/Z) \approx 0.1 Z_\odot, fostering environments conducive to intense, bursty star formation driven by rapid gas accretion onto dark matter halos of masses $10^8 - 10^{10} M_\odot. These galaxies exhibit irregular star formation histories characterized by short bursts interspersed with quiescence, influenced by the hierarchical merging of progenitors and limited metal enrichment from prior generations. The ultraviolet (UV) continuum emission from these galaxies traces their star formation and is described by the Schechter luminosity function, with faint-end slope \alpha \approx -2.0, characteristic magnitude M^* \approx -20.5 at [z](/page/Z) \sim 7, and normalization \phi^* \approx 10^{-3} Mpc^{-3} mag^{-1}, indicating a steep increase in the abundance of low-mass systems toward higher redshifts. This distribution highlights their role as numerous, small contributors to the cosmic UV background during reionization. The ionizing photon output from early galaxies primarily arises from Population II stars, which dominate the stellar mass in these metal-enriched systems and produce spectra softer than those of metal-free Population III stars, with production efficiencies \xi_{\rm ion} \approx 10^{25.5} Hz erg^{-1}.^[29] Low dust content in these young galaxies, due to inefficient enrichment and limited grain formation, enables high Lyman continuum escape fractions f_{\rm esc} > 20\%, allowing a substantial portion of ionizing photons to permeate the interstellar medium. Models integrating the UV luminosity function suggest that these galaxies supplied approximately 70-80% of the ionizing photons required for reionization, outpacing contributions from quasars and underscoring their dominance in sustaining the expanding ionized volume. Radiative feedback from young stars ionizes surrounding gas, creating H II regions that expand and regulate further accretion, while supernova explosions from massive stars inject momentum and energy, dispersing gas clouds and suppressing star formation in low-mass halos through outflows reaching velocities of hundreds of km/s.^[30] These processes facilitate the overlap of ionized bubbles around neighboring galaxies, accelerating the transition to a fully ionized intergalactic medium by enhancing photon propagation and reducing neutral hydrogen absorption.^[2] Recent James Webb Space Telescope (JWST) observations from 2024-2025 have identified thousands of such galaxies at z > 10, including catalogs exceeding 1,000 candidates up to z \sim 18, confirming their prevalence and bolstering models of galaxy-driven reionization.

Quasars and Active Galactic Nuclei

Quasars and active galactic nuclei (AGNs) are powered by accretion onto supermassive black holes (SMBHs), which form seeds at redshifts z > 10 through mechanisms such as the direct collapse of pristine, atomically cooled gas clouds or remnants of Population III stars, subsequently growing rapidly via gas accretion and mergers to reach masses of 10^8–10^9 solar masses by the end of reionization.^[31] These SMBHs achieve bolometric luminosities up to 10^47 erg/s, enabling them to emit intense radiation capable of influencing the intergalactic medium (IGM) during the late stages of cosmic reionization.^[32] The spectral energy distribution of quasars features a hard continuum extending from ultraviolet (UV) to X-ray wavelengths, producing photons with energies exceeding 1 keV that can penetrate dense, neutral gas more effectively than softer stellar radiation.^[33] This hard spectrum allows quasars to contribute approximately 10% to the total ionizing photon budget for hydrogen reionization at z ≈ 6, with their role increasing to dominate helium (HeII) reionization due to the higher energy threshold (54.4 eV) required to ionize singly ionized helium.^[34] Overall, quasars provide less than 7–20% of the photons needed to sustain ionization in the IGM, underscoring their secondary but non-negligible influence compared to stellar sources.^[35] At redshifts z < 7, quasars play a key role in carving out large-scale ionized bubbles in the IGM, with their high luminosity ionizing volumes up to several megaparsecs across and facilitating the overlap of HII regions toward the end of reionization.^[36] Additionally, quasar-driven outflows and winds, reaching velocities of thousands of km/s, exert negative feedback by expelling gas from host galaxies, thereby suppressing subsequent star formation and regulating galaxy growth during this epoch.^[37] Quasars are rare at high redshifts due to the limited time available for SMBH growth, with over 300 confirmed examples known at z > 6 as of 2025, primarily selected from optical and near-infrared surveys.^[38] Recent James Webb Space Telescope (JWST) observations have identified candidate quasars or AGN at z ≈ 10, including obscured systems in luminous galaxies, providing new insights into the earliest SMBH activity and their potential contributions to pre-reionization ionization.^[32]

Observational Probes

Quasar Spectra and Gunn-Peterson Trough

High-redshift quasars serve as backlights for probing the intergalactic medium (IGM) through absorption in their spectra, particularly by neutral hydrogen (H I) via the Lyman-alpha (Lyα) resonance line at 1216 Å. As quasar light travels through the IGM, neutral hydrogen atoms absorb photons at the redshifted Lyα wavelength, creating a series of absorption lines known as the Lyα forest at lower redshifts. At z > 6, when the ionized fraction x_e falls below unity during the final stages of reionization, this absorption becomes nearly complete, manifesting as the Gunn-Peterson trough—a broad, deep absorption feature in the quasar continuum spectrum blueward of the Lyα emission line. This trough arises from the damping wing of the Lyα line profile, where resonant scattering by neutral hydrogen suppresses transmission over a wide wavelength range, providing direct evidence of residual neutral gas.^[39] The depth of the Gunn-Peterson trough enables quantitative measurement of the neutral hydrogen fraction in the IGM. The effective optical depth τ_eff is derived from the observed transmission T_obs, where T_obs ≈ e^{-τ_eff} in regions of complete absorption, though actual spectra show sporadic transmission spikes due to ionized bubbles. For a uniform IGM, the Gunn-Peterson optical depth is approximated as

\tau_{\rm GP} = \frac{n_{\rm HI} \sigma_\alpha (1+z)^2}{H(z)},

where n_HI is the proper number density of neutral hydrogen, σ_α ≈ 4.5 × 10^{-18} cm² is the Lyα absorption cross-section at line center, and H(z) is the Hubble parameter at redshift z. In practice, during patchy reionization, τ_eff is related to the volume-averaged neutral fraction ⟨x_HI⟩ via models incorporating IGM inhomogeneities, with τ_eff ≈ 2.5–6 corresponding to ⟨x_HI⟩ ≈ 0.01–0.1 at z ≈ 6. Spectra from surveys like the Sloan Digital Sky Survey (SDSS) are analyzed by fitting the trough profile, accounting for the quasar's intrinsic spectrum and foreground absorption, to infer the evolution of x_HI.^[40]^[41] Key observations from SDSS quasars at z ≈ 5.7–6.4 reveal a sharp decline in Lyα transmission at z ≈ 6.2, marking the end of reionization, with the mean transmitted flux dropping from T ≈ 0.05 at z < 6 to T < 10^{-3} in complete troughs at z > 6.2, implying a volume-averaged neutral fraction ⟨x_HI⟩ ≈ 0.01–0.04 just after reionization completion. At higher redshifts (z > 6.5), the troughs exhibit patchy absorption with occasional transmission spikes (T ≈ 10^{-5}–10^{-4}), consistent with an incomplete, inhomogeneous reionization process where ionized regions coexist with neutral pockets. Recent James Webb Space Telescope (JWST) spectra of z > 6 quasars confirm these findings, detecting Gunn-Peterson troughs with similarly low transmission levels (T ≈ 10^{-5}) and providing higher-resolution views of the damping wings, reinforcing that reionization concluded around z ≈ 6 while highlighting small-scale IGM variations.^[40]^[42]

Cosmic Microwave Background Signals

The cosmic microwave background (CMB) provides key constraints on cosmic reionization through the effects of Thomson scattering between CMB photons and free electrons produced during this epoch. This scattering process damps small-scale temperature anisotropies in the CMB by diffusing photon directions, while simultaneously generating large-scale E-mode polarization from the quadrupole moment of the radiation field.^[43] The resulting polarization signal is particularly prominent at low multipoles (low-ℓ), where a characteristic "bump" in the E-mode power spectrum arises from scattering at redshifts corresponding to reionization.^[43] The primary observable from these interactions is the Thomson optical depth τ_e, which quantifies the integrated probability of photon scattering along the line of sight from the last scattering surface to the observer. This parameter is defined as

\tau_e = \int n_e(z) \sigma_T \frac{dr}{dz} dz,

where n_e(z) is the free electron density at redshift z, σ_T is the Thomson cross-section, and dr/dz is the radial comoving distance element. Measurements from the Planck satellite yield τ_e ≈ 0.054, reflecting the cumulative ionization fraction over reionization history.^[44] Updated analyses in 2024, incorporating refined foreground subtraction and polarization data, maintain this value within uncertainties of about 0.007. These CMB signals constrain the timing and duration of reionization, indicating a relatively late midpoint at z_reion ≈ 7–8 to match the position and amplitude of the low-ℓ polarization bump.^[43] However, this inference creates tensions with observations of high-redshift galaxies from the James Webb Space Telescope (JWST), which suggest more abundant ionizing sources at z > 10, implying an earlier or more extended reionization phase that would produce a higher τ_e.^[45] Recent 2025 analyses of CMB data, combined with quasar absorption spectra, support an extended tail in helium reionization extending to z < 6, allowing partial reconciliation by distributing the optical depth over a broader redshift range.

Lyman-Alpha Emission and Forest

The Lyman-alpha forest consists of a dense series of absorption lines in the spectra of distant quasars and galaxies, primarily arising from neutral hydrogen (HI) in the intergalactic medium (IGM), which traces the density fluctuations of the IGM along the line of sight.^[46] These absorption features appear blueward of the Lyman-alpha emission line at 1216 Å, with the forest's opacity increasing at higher redshifts due to the rising neutral hydrogen fraction during the epoch of reionization (EoR). Transmission spikes within the forest—regions of higher flux transmission—correspond to underdense, ionized voids in the IGM, where the neutral fraction is low, allowing Lyman-alpha photons to propagate more freely and providing a direct probe of the topology of reionized bubbles.^[46] In the extreme case of complete absorption, the forest transitions to the Gunn-Peterson trough, marking regions of high neutrality.^[46] Lyman-alpha emitters (LAEs) are galaxies detected through their prominent Lyman-alpha emission line, which is resonant scattering of ultraviolet photons by neutral hydrogen in the galaxy's interstellar medium and surrounding IGM, making them key tracers of ionized regions during reionization. Narrow-band imaging surveys, such as those from the Subaru Intense Lyman-alpha Survey (SILVERRUSH) and its extensions, have identified thousands of LAEs at redshifts z ≈ 5–9 by isolating the redshifted Lyman-alpha line in narrow filters, revealing luminosity functions that decline toward higher redshifts as neutral gas increasingly attenuates the emission.^[47] The damping wing—a broad, redshifted absorption feature in LAE spectra—arises from resonant scattering by residual neutral hydrogen in the surrounding IGM, with its shape and extent probing the column density of neutral gas and the size of local ionized bubbles, typically on scales of 0.1–1 proper Mpc.^[48] For instance, models of damping wings in high-z spectra indicate that visible LAEs must reside within ionized bubbles to escape the damping absorption, constraining the neutral hydrogen fraction to below ~20% in their vicinity.^[49] Key metrics from LAE observations include the ionized coverage fraction f_{\rm cov}, which quantifies the volume fraction of the IGM that is ionized and allows LAE visibility, and the characteristic bubble size inferred from clustering and transmission statistics, often estimated at ~1–10 Mpc^3 comoving volume for z ≈ 6–8 sources.^[50] Recent James Webb Space Telescope (JWST) observations in the Cosmic Evolution Early Release Science (CEERS) survey reveal a sharp drop in the LAE fraction at z > 7, with only ~10% of UV-selected galaxies showing strong Lyman-alpha emission (equivalent widths > 50 Å) compared to ~40% at z ≈ 6, attributed to increasing IGM neutrality and smaller ionized bubbles around fainter galaxies. A 2025 study using JWST/NIRSpec spectroscopy of a galaxy at z ≈ 13 demonstrates the onset of reionization through Lyman-α emission, revealing a local ionized bubble of ~0.2 proper Mpc amid a mostly neutral IGM, with an inferred LyC escape fraction near unity.^[3] These findings highlight LAEs as sensitive indicators of bubble growth, with visibility requiring both high intrinsic production rates and local ionization to overcome damping.^[51]

21-cm Hydrogen Line

The 21-cm hydrogen line arises from the hyperfine spin-flip transition between the parallel and antiparallel spin states of the electron and proton in neutral hydrogen atoms, with a rest-frame frequency of 1420.4057 MHz corresponding to a wavelength of 21 cm. This transition probes the neutral intergalactic medium (IGM) during the cosmic dark ages and the epoch of reionization, as the signal is emitted or absorbed by neutral hydrogen (HI) before it is ionized by ultraviolet photons from the first stars and galaxies.^[52] Due to cosmological redshift, observations at redshifts z ≈ 6–20 shift the frequency to the low-radio band of 70–200 MHz, enabling ground-based detection despite foreground contamination from galactic and extragalactic synchrotron emission.^[52] The primary observable is the differential brightness temperature δT_b, which quantifies the contrast between the 21-cm signal and the cosmic microwave background (CMB) in the Rayleigh-Jeans tail of the spectrum. In the limit of low optical depth, the brightness temperature is approximated as \delta T_b \approx 27 \, \mathrm{mK} \left(1 - \frac{T_{\mathrm{CMB}}}{T_s}\right) x_{\mathrm{HI}} (1 + \delta_b), where T_{\mathrm{CMB}} \approx 2.725 (1+z) K is the CMB temperature, T_s is the spin temperature of the hydrogen atoms (which determines the excitation of the hyperfine levels), x_{\mathrm{HI}} is the neutral hydrogen fraction, and \delta_b is the baryonic overdensity. The optical depth \tau of the transition is small (\tau \ll 1), typically \tau \approx 0.01 x_{\mathrm{HI}} (1 + \delta_b) (1+z)^{3/2} / T_s at z ≈ 10, but it contributes a correction term -\tau in more precise expressions for δT_b when foregrounds or high densities are considered. The spin temperature T_s is set by couplings to the CMB, the kinetic temperature of the gas T_k (via collisions), and the color temperature of the Ly-α background (via Wouthuysen-Field effect), allowing δT_b to trace thermal evolution in the IGM.^[52] The 21-cm signal manifests in two regimes relative to the CMB: absorption when T_s < T_{\mathrm{CMB}} (yielding negative δT_b) and emission when T_s > T_{\mathrm{CMB}} (positive δT_b). During the cosmic dark ages (z ≳ 30), collisional decoupling keeps T_s \approx T_{\mathrm{CMB}}, producing negligible signal. At cosmic dawn (z ≈ 15–30), the first UV photons from Population III stars couple T_s to the cooling gas kinetic temperature (T_k < T_{\mathrm{CMB}} due to adiabatic expansion), resulting in global absorption signals with δT_b ≈ -100 to -500 mK.^[52] Subsequent X-ray heating from early sources raises T_k > T_{\mathrm{CMB}}, shifting to emission with δT_b > 0 mK. During reionization (z ≈ 6–15), the declining x_{\mathrm{HI}} suppresses the signal amplitude, but spatial fluctuations in density, ionization, and temperature enable 21-cm tomography—three-dimensional mapping of neutral hydrogen distribution to reveal ionized bubbles carved by UV sources.^[52] These fluctuations, quantified via the power spectrum P(k), show scale-dependent features: large-scale modes (k ≈ 0.1 h Mpc⁻¹) trace bubble morphology, while small scales probe minihalos and density peaks.^[52] Key experiments target both the global (sky-averaged) signal and statistical fluctuations. The Experiment to Detect the Global Epoch of Reionization Signature (EDGES) reported in 2018 the first putative detection of an absorption trough centered at 78 MHz (z ≈ 17), with amplitude ≈ -500 mK and duration ≈ 80 MHz in frequency (Δz ≈ 4), far deeper than standard predictions of -200 mK and suggesting enhanced cooling or radio backgrounds.^[53] This result remains debated due to potential foreground systematics and foreground removal challenges, with subsequent analyses questioning its astrophysical origin.^[54] For power spectrum measurements, the Hydrogen Epoch of Reionization Array (HERA) uses a 350-antenna interferometer in South Africa to target z = 7–12, achieving upper limits such as Δ²_{21} ≤ 457 mK² (95% confidence level) at k ≈ 0.34 h Mpc^{-1} and z ≈ 7.9 using 94 nights of Phase I data (as of 2023), with analyses of subsequent seasons, including Year 6 in 2025, providing deeper constraints and progressing toward detection of reionization-era fluctuations.^[55] The upcoming Square Kilometre Array (SKA) Low will extend sensitivity to z = 6–15, enabling high-fidelity imaging of ionized bubbles. Forecasts indicate that 21-cm tomography with SKA-Low can detect signatures of reionization bubbles—regions of suppressed signal corresponding to ionized volumes of 10–100 Mpc diameter—at z = 6–12, distinguishing between inside-out (galaxy-driven) and outside-in (quasar-dominated) reionization scenarios with signal-to-noise ratios exceeding 10 after 1000 hours of observation.

Theoretical Models and Recent Insights

Semi-Analytic and Radiative Transfer Models

Semi-analytic models provide an efficient framework for simulating the large-scale evolution of reionization by combining halo mass functions from extended Press-Schechter theory with prescriptions for ionizing photon production and escape. These models track the volume-averaged ionized fraction x_e over time, incorporating parameters such as the escape fraction f_\mathrm{esc} of ionizing photons from early galaxies and Population III stars, which determine the overall photon budget. The extended Press-Schechter formalism is used to derive the distribution of ionized bubble sizes, treating reionization as a stochastic process where halos above a minimum mass threshold host sources that expand H II regions until overlap occurs. A key application of these models is in semi-numeric simulations like 21cmFAST, which approximate the ionization field by assigning photons to grid cells based on excursion set theory and propagate them with a one-step filtering approach, enabling rapid exploration of parameter space. These methods evolve x_e by balancing photon production rates against recombinations, often assuming a uniform intergalactic medium density, and predict the transition from neutral to ionized phases around redshift z \sim 6-10. By linking halo collapse fractions to source properties, such models highlight how variations in f_\mathrm{esc} influence the timing and patchiness of reionization. Radiative transfer (RT) simulations offer more detailed treatments by solving the equations of photon propagation, absorption, and scattering in three dimensions, typically post-processing N-body hydrodynamic simulations of structure formation. Codes such as Enzo, extended with ray-tracing modules like Moray, perform adaptive mesh refinement to resolve small-scale gas dynamics while capturing large ionized bubbles, coupling RT to hydrodynamics for self-consistent evolution of ionization fronts. Similarly, RAMSES-RT integrates multi-frequency RT into the adaptive mesh refinement framework of RAMSES, handling photon transport via a moment-based method that accounts for Doppler shifts and radiative feedback on galaxy formation. These RT approaches simulate the inhomogeneous propagation of ionizing radiation from discrete sources, revealing effects like shadowing and bubble merging that semi-analytic models approximate.^[56]^[57] Both semi-analytic and RT models generate predictions for key observables, including the topology of ionized regions, the 21-cm power spectrum from neutral hydrogen fluctuations, and the Thomson optical depth \tau_e to the cosmic microwave background. Reionization is parameterized by the ionization efficiency \zeta, which quantifies the number of ionizing photons per collapsed atom in halos, and the mean free path R_\mathrm{mfp} of photons through the intergalactic medium, which sets the scale for recombination-limited bubble growth. For instance, typical values of \zeta \approx 10-100 and R_\mathrm{mfp} \approx 10-50 Mpc yield \tau_e \sim 0.05-0.09, consistent with Planck measurements, while the 21-cm power spectrum exhibits a characteristic "bump" from large-scale ionization modes during the mid-to-late stages. These models collectively predict a patchy reionization process, where ionized bubbles grow around overdensities and reach characteristic sizes of approximately 10–100 comoving Mpc by the end of the epoch, reflecting the hierarchical buildup of structure and photon escape efficiencies.

JWST Observations and Model Tensions

Recent observations from the James Webb Space Telescope (JWST), particularly through the UNCOVER and CEERS surveys, have revealed an unexpectedly high abundance of faint, low-mass galaxies at redshifts z > 10, suggesting these systems played a pivotal role in driving cosmic reionization.^[58]^[59] The UNCOVER survey, targeting the Abell 2744 cluster, has identified dozens of such galaxies with vigorous star formation, exhibiting UV luminosity densities up to four times higher than pre-JWST predictions from semi-analytic models.^[60] Similarly, CEERS data confirm a surplus of UV-bright galaxies at z ≈ 9–11, with spectroscopic follow-up indicating these faint sources dominate the early ionizing photon budget.^[61]^[62] These findings create significant tensions with established reionization models, particularly regarding the timing and sources of ionization. The abundance of early galaxies implies a reionization redshift z_reion > 10, conflicting with cosmic microwave background (CMB) measurements of the electron scattering optical depth τ_e ≈ 0.058 ± 0.006 from Planck PR4 (2025), which favor a later reionization ending around z ≈ 6–8.^[63]^[64] This discrepancy, dubbed the "JWST reionization crisis," suggests overproduction of ionizing photons in standard ΛCDM simulations unless adjusted for higher Lyman-continuum escape fractions (f_esc > 0.2–0.5) in these compact systems.^[65] Debates persist on f_esc evolution, with JWST spectra showing blue UV continua consistent with near-unity escape in some z > 10 galaxies, challenging assumptions of low escape in dense early environments.^[3] As of 2025, Planck PR4 data refine τ_e constraints, while JWST surveys like UNCOVER and CEERS continue to reveal high galaxy abundances at z > 10, pushing simulations to incorporate bursty star formation and higher efficiencies to address ongoing tensions.^[66]^[67] The implications extend to revising source efficiencies and simulation frameworks. Small, faint galaxies appear to contribute over 50% of the ionizing photons required for reionization, as inferred from their collective UV output and high f_esc, thereby diminishing the expected dominance of quasars and active galactic nuclei.^[68]^[4] This necessitates updated radiative transfer models incorporating bursty star formation histories (SFH) to account for episodic high-efficiency ionization from these dwarfs, rather than steady-state assumptions.^[69] Ongoing studies as of November 2025 emphasize the need for deeper JWST surveys to resolve these tensions and refine the photon budget.^[4]

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