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An interacting pair of spiral galaxies undergoing a galaxy merger. Their long tidal tails contain stars displaced by the encounter. They are also a nearby example of a starburst galaxy, with vigorous star formation accompanying the interaction.^[ref]

The Hubble Space Telescope image below combines observations from its Wide Field Camera 3 and Advanced Camera for Surveys. Bright young stars, emitting regions of the interstellar medium and obscuring interstellar dust reveal different aspects of the encounter. The close view emphasizes the interacting central regions; wider views show the long outer tidal tails.^[ref]

Emission or absorption from the Milky Way contributes a foreground when observing sources beyond it. For cosmic microwave background measurements, important components include thermal interstellar dust, synchrotron radiation and free-free emission. Their spectral and spatial behavior helps distinguish them from a near-isotropic blackbody background.

Galactic multiwavelength astronomy compares observations of the Milky Way in different parts of the electromagnetic spectrum to distinguish its overlapping physical components. The neutral-hydrogen 21-centimeter line traces neutral atomic gas, carbon monoxide spectral lines trace molecular clouds, and infrared emission reveals warm interstellar dust and stars hidden at visible wavelengths. Radio waves from synchrotron radiation trace energetic electrons in magnetic fields, while X-rays reveal hot plasma and compact sources. Maps of the same sky region can therefore test whether a feature is a stellar concentration, an obscuring cloud or shocked gas. Comparing them also requires attention to differing angular resolution and foreground absorption.^[ref]

The plane of a disk-shaped galaxy contains most of its stellar disk. In ordinary sky-coordinate usage the galactic plane refers to the Milky Way's disk plane. A concentration of interstellar dust near that plane produces a prominent component of galactic foreground emission.

A galaxy is a gravitationally bound system of stars, stellar remnants and usually gas, interstellar dust and a substantial dark matter component. Its appearance reflects both its contents and their motion: a spiral galaxy has a rotating galactic disk, whereas an elliptical galaxy is largely supported by disordered stellar motion. Star formation makes luminous young populations from gas, while stellar feedback returns material and energy to the interstellar medium. A photograph therefore samples only part of the system: galaxy dynamics uses motions to constrain the underlying mass, including matter that emits little light. Spiral arms also redistribute angular momentum and changes the galactic disk over time.^[ref]

The interstellar medium is the gas, interstellar dust, magnetic field and cosmic rays between stars in a galaxy. It is a changing reservoir: molecular clouds supply star formation, while stellar winds and supernova remnants return material and stir or heat it. Different regions occupy different temperature and ionization states, so no single observation measures the whole medium. For example, the neutral-hydrogen 21-centimeter line probes neutral atomic hydrogen, whereas X-rays reveal much hotter plasma. Even neutral atomic gas can occupy cold and warm phases: the heating and cooling balance in the interstellar medium permits both over a restricted range of pressure.^[ref]

Messier 82, also called M82, is a nearby starburst galaxy used to study how intense star formation drives a large galactic outflow. Its bright stellar disk, obscuring interstellar dust and extended gas emission trace different components; a bright feature in one wavelength band need not represent most of the outflow's mass or energy.

A concrete measurement is to compare diffuse X-ray emission above the disk with compact sources inside it. ROSAT imaging and spectroscopy detected the wind's X-rays to roughly six kiloparsecs from the plane. The observations separated point sources from diffuse emission and found that the latter was not well described as a freely expanding wind: shocked material interacting with the flow could instead account for the emission.^[ref]

This makes M82 an illuminating stellar feedback laboratory. The inference runs from spatially resolved spectra to gas conditions and then to a physical outflow model; a photograph of gas extending away from the disk does not by itself determine its temperature, energy source or escape rate.

The Milky Way is the barred spiral galaxy containing the Solar system. Its galactic disk, central stellar bar and surrounding stellar halo are viewed from inside the disk, so distance and obscuration complicate attempts to reconstruct the whole system. Radio astronomy supplies a geometric route through the obscuring interstellar dust: masers near young massive stars act as compact markers whose parallaxes and proper motions can be measured by very-long-baseline interferometry. A 2019 analysis of about 200 such markers mapped spiral structure and constrained the rotation curve using their three-dimensional motions. These measurements connect the familiar bright band along the galactic plane with a spatial and dynamical model.^[ref]

A molecular cloud is a cold region of the interstellar medium in which hydrogen is predominantly molecular hydrogen. Shielding against dissociating ultraviolet radiation helps molecules survive, and radiative cooling allows dense regions to develop. Gravitational collapse within these clouds produces stars, although turbulence, magnetic fields and stellar feedback affect which regions collapse. Cold molecular hydrogen is difficult to detect directly, so observers often map carbon monoxide spectral lines or interstellar dust emission as indirect tracers. Converting either signal into cloud mass requires assumptions about abundance, excitation or dust properties; a bright tracer is not itself a direct weighing of the cloud.^[ref]

A planetary nebula combines a hot post-asymptotic-giant-branch stellar core, its ionized expelled envelope, neutral/molecular material and interstellar dust. Its ultraviolet-to-infrared spectral energy distribution is therefore not a single-temperature blackbody. The principal components are:

The observed mixture also contains attenuation by internal and foreground interstellar extinction. A spectrum containing all these components need not spatially coincide: stellar light, ionized gas, dusty clumps and the molecular envelope sample different regions.

gas heats when compression, shocks or absorbed radiation increase its internal energy. Important sources include accretion shocks, stellar winds, supernovae, photoionization, photoelectric emission from interstellar dust, cosmic rays and energy deposited by active galactic nuclei. photoionization heating uses the photoelectron energy above the ionization threshold; compression contributes mechanical work rather than photon absorption.

For specific internal energy $u$, an idealized thermal balance isHere $\mathcal{H},\mathcal{C}$ are powers per volume and $Z$ describes abundances. The electron-hydrogen normalization of the cooling function must be specified: some conventions instead factor out $n_H^2$. For a monatomic gas with total particle density $n$,when heating is negligible. Compare this with the dynamical time: rapid cooling permits loss of pressure support, whereas long cooling times allow a hot atmosphere to persist.

collisional excitation followed by spontaneous emission cools partially ionized gas; radiative recombination also produces continuum cooling. metal lines enhance cooling over substantial intermediate-temperature ranges, while thermal bremsstrahlung gives a roughly $\Lambda \propto T^{1/2}$ high-temperature tail. Atomic hydrogen cooling becomes inefficient below roughly $10^4\mathrm{K}$, where molecular line cooling and interstellar dust can be important. inverse Compton scattering cools hot electrons against a colder radiation field. A tabulated cooling curve assumes a composition and ionization model; photoionization or nonequilibrium ionization can change it.^[ref]

X-ray line ratios and continuum shape constrain temperature and ionization, while the emission measure constrains $\int n_e{n}_{H}dV$. Turning that into a density and radiative gas cooling time also requires a geometry; unresolved clumping, foreground absorption and multiphase gas are important controls.

Write $v={\sigma }_{\mathrm{int}}^2$, $r_s={\sigma }_{O,s}^2$ and $o_s={\hat{O}}_s$. A flat density in $\log \tau$ means $p(\tau )\propto 1/\tau$ with respect to $d\tau$; likewise $p(v)\propto 1/v$. The Jacobian determinant must therefore appear when using the original scale variables. The joint hierarchical Bayesian model kernel, with respect to $d{\mu }_{C}dvd\tau {\prod }_{s}d{o}_{s}d{C}_{s}d{E}_s$, isThis is a kernel, not a normalized joint probability distribution, because the stated priors are improper. Conditioning on $o$ would still require posterior propriety. In fact that check fails here, as shown in part (iii)(c); proper formal full conditionals alone do not repair it. The Gaussian–exponential hierarchical colour model distinguishes the intrinsic normal colour, positive interstellar dust reddening, and measurement noise.

Interstellar dust both hides and reveals galaxies. Absorption and scattering remove short-wavelength photons from a line of sight, causing interstellar extinction, reddening, anisotropic scattering, and polarization. These effects obscure embedded star formation, bias luminosities, colours, stellar masses, and star-formation rates, and can make an edge-on or dusty galaxy appear older and fainter. Dust also converts absorbed ultraviolet and optical power into far-infrared and submillimetre thermal radiation. That reradiation exposes otherwise hidden star formation, constrains dust temperature and mass, and helps map cold molecular material; polarization traces magnetic-field orientation. Grain surfaces also catalyse molecular-hydrogen formation, while photoelectric emission from grains heats interstellar gas.

One spherical grain has emitting area $4\pi a^2$. Since isotropic blackbody intensity $B_{\nu }$ gives surface flux $\pi B_{\nu }$, its spectral luminosity isFor $N=M_d/m_d$ optically thin grains at distance $D$, the inverse-square law givesDefining the grain mass absorption coefficientthe optically thin dust-mass estimator is

For a constant source function and no incident background, the radiative transfer equation integrates toIf the cloud subtends solid angle $\Omega$, uniform intensity givesThe physical projected area is $A=\Omega D^2$. Its grain column density is $N/A=M_d/(m_d\Omega D^2)$, so the dust optical depth isEliminating ${\tau }_{\nu }$ gives the finite-optical-depth resultIt requires $F_{\nu }<\Omega B_{\nu }$, as demanded by the blackbody brightness limit. When ${\tau }_{\nu }\ll 1$, $1-e^{-{\tau }_{\nu }}={\tau }_{\nu }+O({\tau }_{\nu }^2)$, so $F_{\nu }\simeq \Omega B_{\nu }{\tau }_{\nu }={\kappa }_{\nu }{M}_d{B}_{\nu }/D^2$ and the result reduces to the optically thin estimator.

Interstellar dust absorbs ultraviolet and optical starlight and thermally reradiates it. Far-infrared emission comes mainly from large cool grains near thermal equilibrium and probes dust column density times a temperature-dependent emissivity. Mid-infrared emission emphasizes warmer grains, stochastically heated small grains, and aromatic features near star-forming regions. These bands therefore trace both dust mass and the intensity of the radiation field that heats it.

Optical continuum light maps photospheric emission from stars and therefore depends on stellar density, luminosity, temperature, age, and composition. Recombination and forbidden lines additionally trace warm ionized gas. Strong wavelength-dependent absorption and scattering by interstellar dust obscure the inner disk, so an optical map is also a map of the foreground extinction.

Near-infrared light is dominated over much of the Milky Way by old, cool, low-mass stars, with extra emission from young stars and hot dust in active regions. Because interstellar dust attenuates it much less strongly than optical light, near-infrared surface brightness and star counts are useful tracers of stellar mass and the obscured Galactic bulge and bar.

Thermal interstellar dust produces a bright galactic foreground concentrated toward the Milky Way plane, with additional cloud structure. Its emission spectrum differs from the approximately $2.73\mathrm{K}$ blackbody spectrum of the cosmic microwave background, so comparisons across frequencies help separate it. In the sketch below this is the bright equatorial band.

Timothy M. Heckman investigates how activity in galaxies drives large outflows of gas. His team used sodium absorption spectral lines in infrared-bright starburst galaxies to detect material moving toward the observer relative to each galaxy's overall velocity.

Absorption samples gas in front of the emitting background. A systematic blueshift can therefore reveal an outflow on the near side. The study found strongly shifted lines in twelve systems and argued, using their viewing geometry, that ambient gas was being accelerated along the minor axis by a hot starburst-driven galactic wind. Associated reddening also linked the outflow to interstellar dust transport.^[ref]