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courses:ast403:photometry-and-spectroscopy [2026/02/12 00:39] – shuvocourses:ast403:photometry-and-spectroscopy [2026/02/12 08:50] (current) – shuvo
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 **Surface Brightness and Isophotes:** The fundamental measurement in galaxy photometry is surface brightness ($I(\mathbf{x})$), defined as the amount of light per square arcsecond at a specific point in a galaxy's image. Mathematically, it is expressed as: **Surface Brightness and Isophotes:** The fundamental measurement in galaxy photometry is surface brightness ($I(\mathbf{x})$), defined as the amount of light per square arcsecond at a specific point in a galaxy's image. Mathematically, it is expressed as:
 $$I(\mathbf{x}) = \frac{L}{4\pi D^2}$$ $$I(\mathbf{x}) = \frac{L}{4\pi D^2}$$
-where $L$ is luminosity and $D$ is the physical diameter of a patch of the galaxy. Surface brightness is typically measured in mag arcsec$^{-2}$ or $L_\odot \text{ pc}^{-2}$. A crucial property of surface brightness is that it is independent of the observer's distance, except at very large cosmological distances where the expansion of the Universe causes it to dim. Contours of constant surface brightness are called isophotes.+where $L$ is luminosity and $D$ is the physical diameter of a patch of the galaxy. Surface brightness is typically measured in $\rm mag \ arcsec^{-2}$ or $L_\odot \text{ pc}^{-2}$. A crucial property of surface brightness is that it is independent of the observer's distance, except at very large cosmological distances where the expansion of the Universe causes it to dim. Contours of constant surface brightness are called isophotes.
  
 **Structural Profiles**: Astronomers use mathematical models to describe how a galaxy's light is distributed: **Structural Profiles**: Astronomers use mathematical models to describe how a galaxy's light is distributed:
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 Galactic Disks: The surface brightness of spiral and S0 disks generally follows an exponential profile: $I(R) = I(0) \exp(-R/h_R)$, where $h_R$ is the radial scale length (typically 1–10 kpc). Galactic Disks: The surface brightness of spiral and S0 disks generally follows an exponential profile: $I(R) = I(0) \exp(-R/h_R)$, where $h_R$ is the radial scale length (typically 1–10 kpc).
  
-Bulges and Ellipticals: These systems are often modeled using the Sérsic formula: $I(R) = I(0) \exp[-(R/R_0)^{1/n}]$. A specific version of this where $n=4$ is known as the **de Vaucouleurs $R^{1/4}$ law**, which provides a good description for luminous elliptical galaxies.+Bulges and Ellipticals: These systems are often modeled using the Sérsic formula: $I(R) = I(0) \exp[-(R/R_0)^{1/n}]$. A specific version of this where $n=4$ is known as the de Vaucouleurs $R^{1/4}$ law, which provides a good description for luminous elliptical galaxies.
  
 Effective Radius ($R_e$): A standard measure of size, $R_e$ is the radius of a circle on the sky that encloses half of a galaxy's total light. Effective Radius ($R_e$): A standard measure of size, $R_e$ is the radius of a circle on the sky that encloses half of a galaxy's total light.
  
-[{{ :courses:ast403:gal_radial.jpg?400 | Fig 1: Surface brightness profile for NGC 7331 in the I band, near 8000 Â+[{{ :courses:ast403:gal_radial.jpg?600  | Fig 1: Surface brightness profile for NGC 7331 in the I band, near 8000 Â
 The dashed line is an exponential with $h_R = 55′′$; the dotted line represents additional The dashed line is an exponential with $h_R = 55′′$; the dotted line represents additional
 light – R. Peletier. }}] light – R. Peletier. }}]
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 **Emission Lines:** Ionized gas in **H II regions** produces distinct emission lines like **$H\alpha$ ($\lambda 6563$)**, which serves as a primary tracer for recent star formation. **Forbidden lines**, designated with square brackets such as **[O III] $\lambda 5007$** and **[O II] $\lambda 3727$**, provide information on the density and temperature of the interstellar gas. **Emission Lines:** Ionized gas in **H II regions** produces distinct emission lines like **$H\alpha$ ($\lambda 6563$)**, which serves as a primary tracer for recent star formation. **Forbidden lines**, designated with square brackets such as **[O III] $\lambda 5007$** and **[O II] $\lambda 3727$**, provide information on the density and temperature of the interstellar gas.
  
-**Post-Starburst (E + A) Spectra:** Some galaxies exhibit deep **Balmer absorption lines** characteristic of A stars, but lack the emission lines of ionized gas; this indicates a "post-starburst" phase where star formation ceased abruptly roughly 1 Gyr ago.+**Post-Starburst Spectra:** Some galaxies exhibit deep **Balmer absorption lines** characteristic of A stars, but lack the emission lines of ionized gas; this indicates a "post-starburst" phase where star formation ceased abruptly roughly 1 Gyr ago.
  
 **Active Galactic Nuclei (AGN)**: Spectra from galaxies with active nuclei (like quasars or Seyfert galaxies) are distinguished by radiation that does not originate from stars. A few spectral features are: **Active Galactic Nuclei (AGN)**: Spectra from galaxies with active nuclei (like quasars or Seyfert galaxies) are distinguished by radiation that does not originate from stars. A few spectral features are:
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 **Broad-Line Region:** These systems show **broad emission lines** with Doppler-shifted widths corresponding to velocities exceeding 5000 km s$^{-1}$.  **Broad-Line Region:** These systems show **broad emission lines** with Doppler-shifted widths corresponding to velocities exceeding 5000 km s$^{-1}$. 
 **High Ionization:** AGN spectra contain lines from atoms that are much more **highly ionized** than those found in star-forming regions, such as **C IV**, **N V**, and **O VI**. **High Ionization:** AGN spectra contain lines from atoms that are much more **highly ionized** than those found in star-forming regions, such as **C IV**, **N V**, and **O VI**.
 +
 **Narrow-Line Region:** Narrower forbidden lines (widths $< 1000$ km s$^{-1}$) originate in lower-density gas further from the central black hole. **Narrow-Line Region:** Narrower forbidden lines (widths $< 1000$ km s$^{-1}$) originate in lower-density gas further from the central black hole.
  
 **Chemical Enrichment**: Spectroscopy allows astronomers to measure a galaxy's **metallicity ($Z$)**. Luminous elliptical galaxies tend to be more metal-rich and redder, while smaller galaxies are often metal-poor and bluer. In many systems, the central regions are more metal-rich than the periphery, a trend detectable through the varying strength of absorption features like the **Mgb** and **Na D** lines. **Chemical Enrichment**: Spectroscopy allows astronomers to measure a galaxy's **metallicity ($Z$)**. Luminous elliptical galaxies tend to be more metal-rich and redder, while smaller galaxies are often metal-poor and bluer. In many systems, the central regions are more metal-rich than the periphery, a trend detectable through the varying strength of absorption features like the **Mgb** and **Na D** lines.
 +
 +[{{ :courses:ast403:spectra_spiral.jpg?600 | Fig 2: Spectra of galaxies from ultraviolet to near-infrared wavelengths; incompletely
 +removed emission lines from the night sky are marked. From below: a red S0 spectrum; a
 +bluer Sb galaxy; an Sc spectrum showing blue and near-ultraviolet light from hot young
 +stars, and gas emission lines; and a blue starburst galaxy, that has made many of its stars
 +in the past 100 Myr – A. Kinney.}}]
 +
courses/ast403/photometry-and-spectroscopy.1770881941.txt.gz · Last modified: by shuvo
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