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--- courses:ast403:gunn-peterson-test [2026/03/23 11:16] – shuvo
+++ courses:ast403:gunn-peterson-test [2026/03/28 01:37] (current) – [Implications and Sensitivity] shuvo
@@ Line 1: / Line 1: @@
 ====== 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.
+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.
+[{{ :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.
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+[{{ :courses:ast403:gpt.jpg?600 | Fig 2: Spectrum of a quasar showing the Gunn-Peterson effect.}}]
 ===== Mathematical Formulation =====
 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:
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 Where:
-* $e$ and $m_e$: Electron charge and mass.
+$e$ and $m_e$: Electron charge and mass.\\
-* $f_{\alpha}$: The oscillator strength of the $\text{Ly}\alpha$ transition ($\approx 0.416$).
+$f_{\alpha}$: The oscillator strength of the $\text{Ly}\alpha$ transition ($\approx 0.416$).\\
-* $\lambda_{\alpha}$: The rest-frame wavelength ($121.6 \text{ nm}$).
+$\lambda_{\alpha}$: The rest-frame wavelength ($121.6 \text{ nm}$).\\
-* $H(z)$: The Hubble parameter at redshift $z$.
+$H(z)$: The Hubble parameter at redshift $z$.\\
-* $n_{HI}(z)$: The number density of neutral hydrogen.
+$n_{HI}(z)$: The number density of neutral hydrogen.
 ===== 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:
+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.
+$\Omega_m$ and $\Omega_b$: Density parameters for matter and baryons.\\
-* $n_{HI} / n_H$: The **neutral fraction** of hydrogen.
+$n_{HI} / n_H$: The neutral fraction of hydrogen.
----
 ===== 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:
+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.
+**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 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.
-### 4. Comparison: LLS vs. Gunn-Peterson
+[{{ :courses:ast403:iniozation_model.jpeg?600 | 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 $1216 \text{ Å}$).
+===== 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 $1216 \text{ Å}$).
-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.
+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.