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--- courses:ast403:sunyaev-zeldovich-sz-effect [2026/03/10 07:33] – shuvo
+++ courses:ast403:sunyaev-zeldovich-sz-effect [2026/03/10 07:38] (current) – [Mathematical Formulation] shuvo
@@ Line 25: / Line 25: @@
 // The Dimensionless Frequency ($x$):// \\
+$$x = \frac{h\nu}{k_B T_{cmb}} \approx \frac{\nu}{56.8 \text{ GHz}}$$
 The function $f(x)$ determines the shape of the spectral distortion:
-$$x = \frac{h\nu}{k_B T_{cmb}} \approx \frac{\nu}{56.8 \text{ GHz}}$$
 $$f(x) = \left( x \frac{e^x + 1}{e^x - 1} - 4 \right)$$
@@ Line 82: / Line 84: @@
 ===== Composite Observational Analysis of Galaxy Cluster "COMA-B1" =====
-[{{ :courses:ast403:sze_cluster.png?600 | Fig 3: A simulated galaxy cluster.}}]
+[{{ :courses:ast403:sze_cluster.png?600 | Fig 3: This infographic illustrates the multi-messenger approach used to study the Intra-Cluster Medium (ICM) and calculate cosmological distances.}}]
-This infographic illustrates the multi-messenger approach used to study the Intra-Cluster Medium (ICM) and calculate cosmological distances.
 **Primary Map (Center):** A simulated 30-arcminute field of view showing the tSZ Decrement (dark blue) at $z=0.45$. The background "noise" represents the primary fluctuations of the CMB, while the central void is the "shadow" cast by the cluster. Overlaid white contours show the X-ray Surface Brightness, highlighting the higher-density core where $n_e^2$ emission dominates.\\
-**Cluster Profiles (Top-Left):** A comparison of the radial distribution of the three primary signals. The Thermal SZ profile shows a broad pressure distribution, while the **X-ray** profile is more peaked toward the center. The Kinematic SZ profile remains nearly flat, reflecting the uniform bulk velocity of the cluster's gas.\\
+**Cluster Profiles (Top-Left):** A comparison of the radial distribution of the three primary signals. The Thermal SZ profile shows a broad pressure distribution, while the X-ray profile is more peaked toward the center. The Kinematic SZ profile remains nearly flat, reflecting the uniform bulk velocity of the cluster's gas.\\
-**SZ Spectrum (Bottom-Left):** The characteristic spectral "S-curve" of the Sunyaev-Zeldovich effect. It identifies the **Null Point (~217 GHz)**, which serves as the transition between the low-frequency intensity decrement and the high-frequency intensity increment.
+**SZ Spectrum (Bottom-Left):** The characteristic spectral "S-curve" of the Sunyaev-Zeldovich effect. It identifies the Null Point (~217 GHz), which serves as the transition between the low-frequency intensity decrement and the high-frequency intensity increment.\\
-**Scale and Mass (Right):** The color bar indicates a peak temperature deviation of **$-750 \mu\text{K}$**, typical for a massive system of $10^{15} M_{\odot}$. This data, when combined with X-ray luminosity, allows for an absolute distance measurement independent of the cosmic distance ladder.
+**Scale and Mass (Right):** The color bar indicates a peak temperature deviation of $-750 \mu\text{K}$, typical for a massive system of $10^{15} M_{\odot}$. This data, when combined with X-ray luminosity, allows for an absolute distance measurement independent of the cosmic distance ladder.