Abekta

The Encyclopédie of CASSA

User Tools

Site Tools

You are here: root » Courses » AST 403: Galaxies and Intergalactic Medium » Sunyaev-Zeldovich (SZ) Effect
courses:ast403:sunyaev-zeldovich-sz-effect

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revisionPrevious revision
Next revision		Previous revision
courses:ast403:sunyaev-zeldovich-sz-effect [2026/03/10 05:32] – shuvocourses:ast403:sunyaev-zeldovich-sz-effect [2026/03/10 07:38] (current) – [Mathematical Formulation] shuvo
Line 14: Line 14:
 **Significance:** Because this effect depends on the density and temperature of the cluster—not its distance—the SZ effect is "redshift independent," making it a perfect tool for finding the most distant clusters in the universe. **Significance:** Because this effect depends on the density and temperature of the cluster—not its distance—the SZ effect is "redshift independent," making it a perfect tool for finding the most distant clusters in the universe.
  
 +[{{ :courses:ast403:sze_notmal.jpg?600 | Fig 1: The influence of the Sunyaev–Zeldovich effect on the cosmic background radiation. The dashed curve represents the Planck distribution of the unperturbed CMB spectrum, the solid curve shows the spectrum after the radiation has passed through a cloud of hot electrons.}}]
 ===== Mathematical Formulation ===== ===== Mathematical Formulation =====
  
Line 25: Line 25:
  
 // The Dimensionless Frequency ($x$):// \\ // 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: The function $f(x)$ determines the shape of the spectral distortion:
  
  
-$$x = \frac{h\nu}{k_B T_{cmb}} \approx \frac{\nu}{56.8 \text{ GHz}}$$ 
  
 $$f(x) = \left( x \frac{e^x + 1}{e^x - 1} - 4 \right)$$ $$f(x) = \left( x \frac{e^x + 1}{e^x - 1} - 4 \right)$$
Line 58: Line 60:
  
  
-[{{ :courses:ast403:sze.png?600 | Fig 1: Plots of thermal (left) and kinematic (right) SZ effect.}}]+ 
 +[{{ :courses:ast403:sze_total.png?600 | Fig 2: Plots showing individual and total SZ effects.}}] 
 ===== Observational Characteristics ===== ===== Observational Characteristics =====
  
Line 75: Line 79:
 2. Map Large Scale Structure: Detecting clusters that are too faint to see in visible light.\\ 2. Map Large Scale Structure: Detecting clusters that are too faint to see in visible light.\\
 3. Study Dark Energy: Tracking how the number of clusters has grown over cosmic time. 3. Study Dark Energy: Tracking how the number of clusters has grown over cosmic time.
 +
 +
 +
 +===== Composite Observational Analysis of Galaxy Cluster "COMA-B1" =====
 +
 +[{{ :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.}}]
 +
 +
 +**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.\\
 +**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.
  
  
Line 103: Line 119:
  
  
-**Deriving the Distance ($D_A$) +**Deriving the Distance ($D_A$):**\\
-**+
 If we assume the cluster is roughly spherical with a physical thickness $L$, the line-of-sight integrals can be simplified to $L \approx \theta D_A$, where $\theta$ is the angular size measured on the sky. If we assume the cluster is roughly spherical with a physical thickness $L$, the line-of-sight integrals can be simplified to $L \approx \theta D_A$, where $\theta$ is the angular size measured on the sky.
  
Line 134: Line 149:
  
 **Why This is a "Standard Candle"? **Why This is a "Standard Candle"?
-** +**\\ 
-This measurement is powerful because it is **independent of the cosmic distance ladder** (it doesn't rely on Cepheid variables or Supernovae).+This measurement is powerful because it is independent of the cosmic distance ladder (it doesn't rely on Cepheid variables or Supernovae).
  
 | **Measurement** | **Tool** | **Dependency** | | **Measurement** | **Tool** | **Dependency** |
Line 153: Line 168:
 While elegant in theory, this "SZ + X-ray" distance measurement has two main hurdles: While elegant in theory, this "SZ + X-ray" distance measurement has two main hurdles:
  
-1. **Cluster Geometry:** Clusters aren't perfect spheres. If a cluster is elongated along our line of sight ("prolate"), we will overestimate its distance. +1. Cluster Geometry: Clusters aren't perfect spheres. If a cluster is elongated along our line of sight ("prolate"), we will overestimate its distance.\\ 
-2. **Gas Temperature:** You need an accurate measurement of the electron temperature ($T_e$) from X-ray spectroscopy to calibrate the $y$-parameter and the cooling function.+2. Gas Temperature: You need an accurate measurement of the electron temperature ($T_e$) from X-ray spectroscopy to calibrate the $y$-parameter and the cooling function.
  
-**Would you like to explore how this method was used by the Planck satellite to constrain the Hubble Constant compared to the "Standard Candle" method?** 
  
  
courses/ast403/sunyaev-zeldovich-sz-effect.1773142365.txt.gz · Last modified: by shuvo
Donate Powered by PHP Valid HTML5 Valid CSS Driven by DokuWiki