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--- courses:ast403:gunn-peterson-test [2026/03/23 00:06] – shuvo
+++ courses:ast403:gunn-peterson-test [2026/03/28 01:37] (current) – [Implications and Sensitivity] shuvo
@@ Line 1: / Line 1: @@
-====== Gunn-Peterson Test ======
+====== Gunn-Peterson Effect ======
-The Gunn-Peterson test is a key observational method used in astrophysics to probe the state of the intergalactic medium (IGM)—the vast space between galaxies—in the very early universe. Specifically, it tests for the presence of neutral hydrogen.
+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.
-Here’s how it works and what it tells us about the history of the universe.
+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.
-**The Science Behind the Test: Lyman-Alpha Absorption
-:**\\
-The core principle relies on how neutral hydrogen atoms interact with light. Specifically, neutral hydrogen has a very high probability of absorbing photons that have an energy corresponding exactly to its **Lyman-alpha transition**. This transition happens when the hydrogen electron jumps from its lowest energy level (ground state) to the first excited state, absorbing a photon with a specific wavelength of **1216 Angstroms** ($\text{\AA}$) in the ultraviolet.
+[{{ :courses:ast403:gp_trough_series.jpg?600 | 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.}}]
+===== Physical Concept =====
+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.
-**Applying the Test to Quasars:**\\
-To perform the test, astronomers use the light from extremely distant **quasars**—the incredibly bright, active cores of distant galaxies.
-When a high-redshift (very distant) quasar is observed, its light must travel through billions of light-years of intergalactic space to reach Earth. If the early universe contained a uniform, significant amount of neutral hydrogen (even a very small fraction of all hydrogen), this gas would create distinctive features in the quasar's spectrum.
-.  **Quasar’s Point of View:** The quasar emits a bright continuum of light across all wavelengths. This light includes a strong, broad emission peak right at $1216 \text{ \AA}$ in its own rest frame.
+[{{ :courses:ast403:gpt.jpg?600 | Fig 2: Spectrum of a quasar showing the Gunn-Peterson effect.}}]
-.  **The Intervening Medium (Redshifted Absorption):** As the quasar's light travels toward us, it is constantly redshifted due to the expansion of the universe. Simultaneously, it passes through the IGM, which is also at a lower redshift than the quasar.
+===== Mathematical Formulation =====
-.  **The Resonance Condition:** For any patch of light, at some specific point in its journey, its redshifted wavelength will match the local Lyman-alpha transition ($1216 \text{ \AA}$) of the neutral hydrogen gas it is passing through. At that precise location, the light will be strongly absorbed.
+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.
-If the early IGM was mostly neutral (as it was before the Epoch of Reionization), this absorption would be continuous. Since there is always some hydrogen at *every* redshift along the line of sight, the entire spectrum on the short-wavelength (bluer) side of the quasar’s *own* (redshifted) Lyman-alpha emission line should be completely "eaten away," forming a deep, continuous absorption trough.
+===== Relation to Cosmological Parameters =====
+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:
-This expected feature is called the **Gunn-Peterson trough**.
+$$\tau_{GP}(z) \approx 4.9 \times 10^5 \left( \frac{\Omega_m h^2}{0.13} \right)^{-1/2} \left( \frac{\Omega_b h^2}{0.02} \right) \left( \frac{1+z}{10} \right)^{3/2} \left( \frac{n_{HI}}{n_H} \right)$$
-### The Key Result: The Epoch of Reionization
+Where:
+$\Omega_m$ and $\Omega_b$: Density parameters for matter and baryons.\\
+$n_{HI} / n_H$: The neutral fraction of hydrogen.
-The presence or absence of the Gunn-Peterson trough is the ultimate test.
-* **Weak/Narrow Absorption (The Lyman-Alpha Forest):** When we observe quasars at moderate distances (moderate redshift, e.g., $z < 6$), we *do not* see a continuous trough. Instead, we see hundreds of distinct, narrow absorption lines called the "Lyman-Alpha Forest." This indicates that the IGM at these times was almost entirely **ionized** (electrons stripped from protons). The few remaining neutral clouds are tiny and create individual, separate lines rather than a complete block.
+===== Implications and Sensitivity =====
+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.
-* **The Complete Trough:** The true Gunn-Peterson trough was only detected relatively recently, when astronomers began observing quasars at very high redshifts ($z > 6$). In these ancient spectra, the flux on the blue side of the Lyman-alpha peak drops to effectively zero over a significant wavelength range.
+[{{ :courses:ast403:iniozation_model.jpeg?600 | Fig 3: Cosmic ionnizaton history.}}]
+===== Comparison: LLS vs. Gunn-Peterson =====
+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 $1216 \text{ Å}$).
-This breakthrough observation provided the first direct proof that the early IGM was indeed largely neutral. It successfully pinpointed the **Epoch of Reionization**, confirming that the universe transitioned from neutral to ionized by about redshift 6, when the first stars and galaxies finally reionized the vast cosmic ocean.
+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.