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Galaxy photometry is the quantitative measurement of light emitted by galaxies across different regions and wavelengths. Unlike stars, which appear as points, galaxies are extended objects whose images are blurred by atmospheric turbulence, a phenomenon known as seeing. Because of this, ground-based optical telescopes generally cannot distinguish details smaller than about $1/3''$.

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: $$I(\mathbf{x}) = \frac{L}{4\pi D^2}$$ 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:

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.

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.

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 light – R. Peletier.

Observational Challenges

Sky Brightness: The night sky itself emits light (from airglow and moonlight), which is often brighter than the faint outer parts of galaxies. Accurate photometry requires precise sky subtraction to isolate the galaxy’s light.

Detectors: Modern photometry primarily uses Charge-Coupled Devices (CCDs) and/or Complementary Metal-Oxide Semiconductor (CMOS), which have quantum efficiencies above 90% in the visible spectrum. CCD/CMOS images must be corrected using flat fields to account for pixel-to-pixel sensitivity variations and calibrated using stars of known brightness.

Dust Extinction: Interstellar dust in both the target galaxy and our own Milky Way absorbs and scatters light, necessitating corrections for reddening and dimming.

Cosmological Effects: For distant galaxies at high redshift ($z$), several factors complicate photometry:

Surface Brightness Dimming: The bolometric surface brightness decreases rapidly as $(1+z)^{-4}$, making high-redshift systems extremely difficult to observe.

K-Correction: Because the expansion of space shifts a galaxy’s spectrum to longer wavelengths, a fixed observational filter samples different parts of the galaxy’s rest-frame light depending on its redshift.

Photometric Redshifts: By comparing a galaxy’s apparent brightness across multiple filter bands (e.g., U, B, V, R, I), astronomers can estimate its redshift without taking a full spectrum.

The spectroscopic properties of galaxies are fundamentally composite, representing the integrated light from a diverse mixture of stellar populations with varying temperatures, ages, and chemical compositions.

Stellar Contributions and Morphological Trends: The spectral appearance of a galaxy shifts systematically along the Hubble sequence:

Early-type Galaxies (Ellipticals and S0s): These spectra are dominated by older, cooler K stars, which produce most of the red light. They exhibit deep absorption lines of heavy elements such as calcium (H and K lines), magnesium (Mgb at 5175 Å), and the G band of CH at 4300 Å. These systems typically show a prominent 4000 Å break, where metal line absorption significantly reduces the flux at shorter wavelengths.

Late-type Galaxies (Sc and Irregulars): These are characterized by hot, young stars that emit most of their light at blue and near-ultraviolet wavelengths. Their spectra frequently show strong emission lines from gas that has been ionized by the ultraviolet radiation of massive stars.

Key Spectral Features

Absorption Line Broadening: Because galaxies are composed of millions of stars in motion, their observed absorption lines are wider and shallower than those of individual stars. This broadening is used to calculate the velocity dispersion ($\sigma$), which measures the spread of random stellar velocities.

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 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:

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.

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.

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.