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courses:ast403:epoch-of-reionization [2026/03/29 07:11] – [Mapping EoR with 21-cm Hydrogen Line] shuvocourses:ast403:epoch-of-reionization [2026/03/29 09:54] (current) – shuvo
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 ===== Context: From Recombination to the Dark Ages ===== ===== 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.+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.
  
  
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 The physics of reionization is fundamentally a race between two processes: **ionization** (radiation tearing atoms apart) and **recombination** (electrons and protons finding each other to become neutral again). The physics of reionization is fundamentally a race between two processes: **ionization** (radiation tearing atoms apart) and **recombination** (electrons and protons finding each other to become neutral again).
  
-We quantify the progress of reionization using the **volume filling factor of ionized hydrogen**, denoted as $Q_{HII}$. This represents the fraction of the universe's volume that has been ionized. +We quantify the progress of reionization using the **volume filling factor of ionized hydrogen**, denoted as $Q_{HII}$. This represents the fraction of the Universe's volume that has been ionized. 
  
 The evolution of reionization is governed by a differential equation balancing the production of ionizing photons against the rate at which atoms recombine: The evolution of reionization is governed by a differential equation balancing the production of ionizing photons against the rate at which atoms recombine:
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 **The Recombination Time and Clumping:** **The Recombination Time and Clumping:**
-Recombination happens faster in dense regions. Because the universe is not perfectly smooth, we must introduce the **clumping factor** ($C$), defined as $C = \langle n_H^2 \rangle / \langle n_H \rangle^2$. The recombination time is expressed as:+Recombination happens faster in dense regions. Because the Universe is not perfectly smooth, we must introduce the **clumping factor** ($C$), defined as $C = \langle n_H^2 \rangle / \langle n_H \rangle^2$. The recombination time is expressed as:
  
 $$\bar{t}_{rec} = \frac{1}{C \alpha_B \langle n_e \rangle (1+z)^3}$$ $$\bar{t}_{rec} = \frac{1}{C \alpha_B \langle n_e \rangle (1+z)^3}$$
  
-Where $\alpha_B$ is the "Case B" recombination coefficient (which accounts for electrons cascading down energy levels) and $z$ is the redshift. If the gas is highly clumped ($C > 1$), recombination happens much faster, meaning galaxies have to work much harder to keep the universe ionized.+Where $\alpha_B$ is the "Case B" recombination coefficient (which accounts for electrons cascading down energy levels) and $z$ is the redshift. If the gas is highly clumped ($C > 1$), recombination happens much faster, meaning galaxies have to work much harder to keep the Universe ionized.
  
 **The Photon Budget:** **The Photon Budget:**
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 * $f_{esc}$ is the **escape fraction**: the critical percentage of ionizing photons that actually escape the dense gas of their host galaxy and make it into the IGM.  * $f_{esc}$ is the **escape fraction**: the critical percentage of ionizing photons that actually escape the dense gas of their host galaxy and make it into the IGM. 
  
 +
 +[{{ :courses:ast403:eor_process.webp | Fig 2: Artist impression of the evolution of the Universe.}}]
  
 ===== Observational Evidence ===== ===== Observational Evidence =====
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 The disappearance of this trough at $z \lesssim 5.8$ indicates the Universe was fully reionized by that time. The disappearance of this trough at $z \lesssim 5.8$ indicates the Universe was fully reionized by that time.
  
-2.  **CMB Polarization:** When the universe became ionized, it filled with free electrons. As the photons from the Cosmic Microwave Background (CMB) traveled toward us, some scattered off these free electrons via Thomson scattering. +2.  **CMB Polarization:** When the Universe became ionized, it filled with free electrons. As the photons from the Cosmic Microwave Background (CMB) traveled toward us, some scattered off these free electrons via Thomson scattering. 
 We measure the integrated optical depth ($\tau_e$) to the CMB: We measure the integrated optical depth ($\tau_e$) to the CMB:
  
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 The hydrogen atom consists of a single proton and a single electron. According to quantum mechanics, both of these particles have a property called "spin." When the spins of the proton and electron are **parallel** (spinning in the same direction), the atom is in a slightly higher energy state. When the electron flips so its spin is **anti-parallel** to the proton, the atom drops to a lower energy state. When this "spin-flip" occurs, the atom releases a tiny amount of energy in the form of a radio wave. The wavelength of this photon is exactly 21.1 cm, which corresponds to a rest-frame frequency of roughly 1420 MHz.  The hydrogen atom consists of a single proton and a single electron. According to quantum mechanics, both of these particles have a property called "spin." When the spins of the proton and electron are **parallel** (spinning in the same direction), the atom is in a slightly higher energy state. When the electron flips so its spin is **anti-parallel** to the proton, the atom drops to a lower energy state. When this "spin-flip" occurs, the atom releases a tiny amount of energy in the form of a radio wave. The wavelength of this photon is exactly 21.1 cm, which corresponds to a rest-frame frequency of roughly 1420 MHz. 
  
-Because the early universe is filled with unimaginably massive clouds of neutral hydrogen, these rare, individual spin-flips add up to a faint but ubiquitous background glow across the cosmos.+Because the early Universe is filled with unimaginably massive clouds of neutral hydrogen, these rare, individual spin-flips add up to a faint but ubiquitous background glow across the cosmos. 
 + 
 + 
 +[{{ :courses:ast403:hydrogen-spinflip.svg | Fig 3: Spin-flip transition.}}] 
  
 **Redshift and the Radio Window: **Redshift and the Radio Window:
 ** **
-Just like the Lyman break, the 21-cm signal is redshifted as the universe expands. To figure out where we should tune our radio dials to hear the EoR (which occurred between redshifts $z = 6$ and $z = 10$), we use the frequency redshift equation:+Just like the Lyman break, the 21-cm signal is redshifted as the Universe expands. To figure out where we should tune our radio dials to hear the EoR (which occurred between redshifts $z = 6$ and $z = 10$), we use the frequency redshift equation:
  
 $$\nu_{\text{obs}} = \frac{1420 \text{ MHz}}{1+z}$$ $$\nu_{\text{obs}} = \frac{1420 \text{ MHz}}{1+z}$$
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 If we want to map neutral hydrogen at $z = 8$ (deep in the EoR), the frequency we observe on Earth is shifted down to roughly 157 MHz.  If we want to map neutral hydrogen at $z = 8$ (deep in the EoR), the frequency we observe on Earth is shifted down to roughly 157 MHz. 
  
-This presents an interesting quirk for observational astronomy: this frequency falls squarely within the VHF band used for FM radio and television broadcasts on Earth. To map the early universe, astronomers must build telescopes far away from human interference, in places like the remote deserts of Australia or the Karoo in South Africa.+This presents an interesting quirk for observational astronomy: this frequency falls squarely within the VHF band used for FM radio and television broadcasts on Earth. To map the early Universe, astronomers must build telescopes far away from human interference, in places like the remote deserts of Australia or the Karoo in South Africa.
  
 **The Mathematics of the Signal: Brightness Temperature **The Mathematics of the Signal: Brightness Temperature
-**+**\\ 
 Radio astronomers do not just measure the raw brightness of the 21-cm line; they measure its contrast against the omnipresent backlight of the Cosmic Microwave Background (CMB). This contrast is expressed as the **differential brightness temperature** ($\delta T_b$).  Radio astronomers do not just measure the raw brightness of the 21-cm line; they measure its contrast against the omnipresent backlight of the Cosmic Microwave Background (CMB). This contrast is expressed as the **differential brightness temperature** ($\delta T_b$). 
  
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 * $T_S$ vs $T_{\gamma}$: $T_S$ is the "spin temperature" of the gas, and $T_{\gamma}$ is the temperature of the CMB. The signal is only visible if the gas temperature decouples from the CMB ($T_S \neq T_{\gamma}$).\\ * $T_S$ vs $T_{\gamma}$: $T_S$ is the "spin temperature" of the gas, and $T_{\gamma}$ is the temperature of the CMB. The signal is only visible if the gas temperature decouples from the CMB ($T_S \neq T_{\gamma}$).\\
  
-**The Tomographic Map:** Because $\delta T_b$ drops to zero wherever $x_{HI}$ drops to zero, ionized bubbles surrounding early galaxies appear as **"dark holes"** in the 21-cm signal. By tuning their receivers to different frequencies (which correspond to different redshifts, and therefore different "slices" of time), astronomers can build a 3D tomographic map of these dark, growing bubbles eating away at the glowing neutral universe.+**The Tomographic Map:** Because $\delta T_b$ drops to zero wherever $x_{HI}$ drops to zero, ionized bubbles surrounding early galaxies appear as **"dark holes"** in the 21-cm signal. By tuning their receivers to different frequencies (which correspond to different redshifts, and therefore different "slices" of time), astronomers can build a 3D tomographic map of these dark, growing bubbles eating away at the glowing neutral Universe.
  
  
 +[{{ :courses:ast403:global21cm.png | Fig 4: The global 21cm neutral hydrogen signal over redshift (and frequency) where the top image is the spatially fluctuating 21cm neutral hydrogen and the bottom is the globally averaged 21cm signal. The 21cm signal is strongly coupled to the CMB, which means it is undetectable until the temperature of the neutral hydrogen deviates from the CMB. Borrowed from http://pritchardjr.github.io/research.html.}}]
  
 **The Telescope Arrays: HERA and the SKA:** **The Telescope Arrays: HERA and the SKA:**
courses/ast403/epoch-of-reionization.1774789887.txt.gz · Last modified: by shuvo
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