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An accelerating universe has $\ddot{a}>0$, equivalently $q<0$ while expansion continues.

Here $a$ is the scale factor and $q=-a\ddot{a}/{\dot{a}}^2$ the deceleration parameter. Accelerating expansion means $\dot{a}>0$ and $\ddot{a}>0$; the Hubble parameter $H=\dot{a}/a$ can still decrease. The observational challenge is to reconstruct that history from a past light cone, rather than watch a distant galaxy speed up over the observing campaign.

If a hole gains mass $\Delta M_{\mathrm{BH}}$ at constant radiative efficiency $\eta =L/({\dot{M}}_{\mathrm{in}}{c}^2)$, the radiated energy is $\eta \Delta M_{\mathrm{BH}}{c}^2/(1-\eta )$. For negligible seed mass, final hole mass $\alpha M$, and total three-dimensional galaxy dispersion $\sigma$, its ratio to $|W|\simeq M{\sigma }^2$ is $\eta \alpha (c/\sigma {)}^2/(1-\eta )$. The net virial unbinding energy is half $|W|$ when surface terms are negligible.

An active galactic nucleus is the compact luminous centre of a galaxy powered mainly by black-hole accretion onto a supermassive black hole. Its radiation can dominate the host at some wavelengths even though the emitting region is small compared with the galaxy. Observers identify activity using combinations of emission lines, a compact radio wave source, energetic X-rays and brightness changes. Different components respond on different timescales: reverberation mapping measures the delay between changes in the central radiation and the response of surrounding line-emitting gas, giving a light-travel estimate of its distance. Combining that distance with the Doppler broadening of the emission lines constrains the central mass if the emitting gas is gravitationally bound. Activity can be episodic; the existence of a central black hole alone does not imply a luminous nucleus.^[ref]

Alar Toomre connected the stability of a stellar galactic disk to the competition between self-gravity, rotation and random stellar motion. His 1964 analysis gave a local axisymmetric stability criterion, commonly expressed through the Toomre parameter. A dynamically cold disk can be more vulnerable to gravitational structure formation than one with larger velocity dispersion.^[ref]

With Juri Toomre, he also modeled the tidal bridges and tails of interacting galaxies. Their test-particle encounters showed how gravity alone can draw long structures out of rotating galactic disks.^[ref]

An astronomer investigates stars, planets, galaxies and other astronomical systems through observation and mathematical models. Telescopes collect signals, spectroscopy separates their wavelength components, and repeated measurements reveal changes over time.

The distinctive difficulty is that the object under study is usually inaccessible to a controlled laboratory intervention. An astronomer instead compares independent observables: stellar parallax constrains Euclidean distance, a radiation spectrum constrains physical conditions, and orbital motion constrains mass. Agreement among these measurements can test a model more strongly than fitting a single observable.

Astronomy studies celestial objects and phenomena, including stars, planets and galaxies. Astrometry measures their positions and motion; astrophysics uses physics to explain their properties and behaviour.

Much of astronomy begins with incoming light. An image tells us which direction the light arrived from, rather than directly providing the source's three-dimensional position. Two stars close together on the sky may be very far apart in space. The celestial sphere organizes these viewing directions; locating an object on it is a different task from measuring how far away that object is. Repeated observations turn this limitation into an opportunity: the changing direction of light contains evidence about both Euclidean distance and motion.

The particularly satisfying combination is stellar parallax with proper motion. The first supplies a geometric Euclidean distance, while the second measures how rapidly the viewing direction changes after accounting for the observer's annual motion. Together they give a transverse speed, connecting tiny angles on an image to kilometres travelled each second. This bridge from a flat sky map to moving stars is one reason astrometry matters to the study of the Milky Way.

Astrophysics uses physics to explain stars, planets, galaxies, and their electromagnetic radiation; cosmology extends the questions to the universe as a whole. Much of its evidence arrives as light. The challenge is to infer the source's physical properties from what reaches an observer: a bright star might be nearby, unusually luminous, or both. Stellar parallax and observed radiative flux make this distinction quantitative.

This is an inverse problem. A forward problem predicts observations from a source model and the intervening radiative transfer; the inverse problem works backwards from observations to possible models. A spectral line can constrain chemical elements, temperature, and motion through the Doppler effect, but its strength also depends on the stellar atmosphere. Combining different measurements is therefore more informative than interpreting brightness alone. The attraction is that a tiny change in the direction of light can supply a distance, turning received radiative flux into intrinsic luminosity. ^[ref].

Primordial atomic line cooling becomes effective near the temperature where electronic excitations are accessible, of order ten thousand kelvin. Molecular hydrogen has lower-energy transitions and can cool colder gas if it forms and survives. The corresponding virial temperature thresholds translate into epoch-dependent halo mass thresholds. Radiation, molecular chemistry, metal-line cooling and gas density qualify a single universal minimum galaxy mass.

Avishai Dekel studies the physical assembly of galaxies, including how they acquire the gas needed for star formation. With collaborators he used cosmological numerical simulations and clustering theory to investigate rapidly star-forming galaxies in the young Universe.

Their model showed narrow cold streams penetrating the hot gas of massive dark-matter haloes. Such inflows can supply an extended rotating galactic disk without requiring every episode of rapid star formation to be triggered by a destructive major merger. The paper distinguished smoother stream-fed growth from the rarer, more extreme merger-driven starbursts.^[ref]

An empirical scaling between a disk galaxy's total baryonic mass and its characteristic flat rotation speed. The ideal isolated deep-MOND limit predicts $v_f^4=G{M}_b{a}_0$. Observational tests must specify the speed estimator, distances, gas masses and stellar mass-to-light ratios; the empirical relation alone does not determine a unique theory of gravity.

A merging galaxy cluster exhibiting the bullet Cluster dark-matter separation: peaks of weak gravitational lensing mass lie nearer the galaxies than the displaced X-ray gas. Combining the components supports a dominant less-collisional gravitating component under the usual gravitational model.^[ref]

The circumgalactic medium is gas surrounding a galaxy's main stellar body and interstellar gas, typically associated with its halo. accretion, outflow and recycling exchange matter through it. Its observational boundary and inferred mass depend on the adopted halo convention and the gas phases sampled by absorption or emission.

If every counted halo hosts one counted galaxy and the baryon fraction and conversion efficiency are mass-independent without scatter, galactic stellar mass is a constant multiple of halo mass. The galaxy mass function is obtained by changing variable with $dM/d{M}_{\ast }=1/{ϵ}_{\ast }$. Satellites, efficiency variation and scatter prevent this mapping from being generally exact.

Gas in a collapsing halo is heated toward a virial temperature. If its cooling time is short compared with the dynamical time, thermal support is removed and rapid condensation can form a galaxy. If cooling is slower, a hot atmosphere can persist or condense only gradually. This criterion links baryonic galaxy formation to the dark-matter assembly hierarchy without making every halo into one luminous object.

Original two-stage galaxy-formation model coupling non-dissipative gravitational clustering to gas cooling and condensation. Full title includes the subtitle A two-stage theory for galaxy formation and clustering. DOI: doi.org/10.1093/mnras/183.3.341 . Primary abstract: ui.adsabs.harvard.edu/abs/1978MNRAS.183..341W/abstract .

The cosmological two-point correlation function measures excess pairing or correlated density fluctuations at a separation. For a statistically homogeneous and isotropic mean-zero density contrast, $\xi (r)=⟨\delta (\mathbf{x})\delta (\mathbf{x}+\mathbf{r})⟩$. For distinct points in a discrete galaxy population it instead specifies the factorial pair density, ${\bar{n}}^2[1+\xi (r)]$. The latter excludes self-pairs; an unsmoothed discrete-density covariance also contains a Dirac delta at zero separation. These definitions connect large-scale galaxy clustering with the matter power spectrum while keeping galaxy power spectrum shot noise separate.

Cosmic shear is the statistically correlated lensing shear of distant galaxies produced by the intervening large-scale matter distribution. Correlations across angle and source redshift constrain clustering, the growth of structure and distance geometry, thereby testing dark matter and dark energy. Intrinsic galaxy alignments and measurement errors must be separated from the lensing signal.

A cosmic void is a large region with lower matter or galaxy density than its surroundings in the large-scale structure of the universe. It is not an exactly empty volume; voids can contain galaxies, gas and dark matter.

Voids emerge as initially underdense regions evolve relative to denser filaments and walls. An observational void depends on the tracer population, survey selection and identification algorithm, so a galaxy-defined void need not coincide exactly with a matter-defined underdensity. Their shapes, abundance and dynamics can test cosmological structure-growth models.

The cosmological principle assumes that the universe is statistically homogeneous and isotropic on sufficiently large spatial scales. It applies to a coarse-grained description, not to each galaxy or local void. Combined with the Copernican principle, cosmological isotropy around us supports a homogeneous description rather than a specially centred model. It motivates an FRW metric, whose expansion is governed by a few time-dependent quantities. Observations sample only a finite past light cone, so they support this hypothesis without proving global spatial homogeneity beyond the observed region.

A damped Lyman-alpha system has a sufficiently high neutral-hydrogen column density that the Lorentzian wings of its Voigt profile are conspicuous. These wings come from the finite lifetime of the excited atomic state, not from unusually high gas temperature. Damped systems usually trace substantial neutral reservoirs associated with galaxies.