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Growth of an astronomical object's mass by capture of surrounding matter. During planetary scattering, a collision can lead to accretion if material is retained by the planet; not every collision retains all material. An accretion disk is one particular geometry supplying material.

A hot, comparatively optically thin plasma region associated with an accretion flow. Thermal or nonthermal electrons can transfer energy to softer seed photons through inverse Compton scattering, producing a harder radiation component. Its geometry, heating and coupling to the cooler disc are model dependent; a hard radiation spectrum alone does not uniquely determine these properties.

An astrophysicist studying galaxy formation and cosmological gas accretion.

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.

A dense stellar-scale object such as a white dwarf, neutron star or stellar-mass black hole. accretion releases a large gravitational binding energy per unit mass because the accreting surface or inner orbit is small. A black hole has no material surface, so its radiative yield depends on the accretion flow rather than surface impact.

Integrating $L_{\mathrm{acc}}=GM\dot{M}/r_0$ at fixed radius gives this result. With negligible seed mass it supplies the radiative requirement of monatomic cloud collapse only if ${\Omega }_f=-G{M}^2/r_0$ under the adopted zero-initial-energy approximation. A different density-profile coefficient, retained accretion heat, a wind or a changing radius modifies the budget. Positive binding-energy magnitude and negative potential energy must not be interchanged silently.

A cataclysmic variable with recurrent disk outbursts associated with the hydrogen-ionization disk instability. Enhanced accretion powers the bright phase; the event does not require thermonuclear runaway on the white dwarf.

For a singular isothermal sphere with $\rho =a_s^2/(2\pi G{r}^2)$, the initial mass inside the outward front $r_{\mathrm{ew}}=a_{s}t$ is $M_{\mathrm{ew}}=2a_s^{3}t/G$. This is not all immediately accreted by the central object. The inside-out collapse of a singular isothermal sphere instead has ${\dot{M}}_{\ast }=m_0{a}_s^3/G$, with $m_0$ fixed by its dynamical similarity solution; the remainder can stay in the infalling envelope. Equating front sweeping with central accretion loses that mass budget.

At fixed stellar mass $M_{\star }$, planetary mass density ${\rho }_p$, age $t_{\star }$ and initial ratio $\kappa =a_0/a_p$, the order-unity Safronov number comparison and comet energy diffusion give boundariesTheir logarithmic slopes in planetary mass versus radius are $-3/2$ and $3/4$. Above both, strong kicks and a short estimated diffusion time favour ejection; below the escape boundary, repeated weak encounters favour collision statistically. Below the age boundary, the stated diffusion mechanism has not completed on its characteristic clock. Collision lifetimes require additional cross-section and encounter-rate information, so this map alone cannot establish retention or accretion within the age.

A transient pressure-supported stage of a collapsing cloud after rising optical depth inhibits cooling. Continued accretion and changes of the molecular equation of state can lead to further collapse. It is distinct from the later compact stellar core.

Gas can shock and radiate during a galaxy encounter, allowing it to change orbital energy in ways unavailable to an ideal collisionless stellar component. Gravitational torques can transport its angular momentum and fuel central star formation or accretion. The outcome depends on orbit, gas content and internal structure.

A cataclysmic variable whose white dwarf magnetic field does not dominate the large-scale accretion flow. It normally supports an accretion disk fed through Roche-lobe overflow. The term does not rule out a magnetized donor star or magnetic braking of a binary star.

The primary numerical study follows spherical protostellar collapse. A small central core forms before most of the envelope reaches it and subsequently grows by accretion. The abstract also describes infrared reprocessing by the dusty envelope. Spherical symmetry and the chosen radiative and thermodynamic treatment are model assumptions; rotation, magnetic fields and non-spherical accretion require additional physics.

A neutron star merger, or a neutron star tidally disrupted by a black hole outside its capture region, can leave a hot accretion disk around the remnant. Rapid accretion can power a relativistic jet and a short gamma-ray burst. Beaming means that an observer must lie sufficiently near the jet axis, and not every merger produces an observable burst. A clean binary black hole merger has no substantial baryonic fuel and is not ordinarily expected to power this mechanism. Disruption in a neutron-star–black-hole pair depends on binary mass ratio, black-hole spin and the neutron star's stellar radius.

An ultraluminous X-ray source is a compact, apparently off-nuclear source in another galaxy with an inferred isotropic X-ray luminosity typically above $10^{32}$ W, exceeding the classical Eddington luminosity of an ordinary stellar-mass accretor. Imaging X-ray surveys revealed unusually bright sources away from galactic nuclei; distance association with the host converted the observed fluxes into surprisingly high luminosities. Better angular resolution helps exclude blends and background active nuclei. The 2014 discovery of coherent pulsations established a neutron star in M82 X-2, so the class cannot be identified exclusively with black holes.^[ref]

An intermediate-mass black hole can radiate approximately isotropically below its own Eddington luminosity: this avoids extreme super-Eddington emission, but the inferred mass requires dynamical or suitable spectral/timing support and is not proved by luminosity alone. A stellar-mass accretor with a supercritical accretion disk and a wind funnel can combine genuinely super-Eddington output with geometrical beaming; this is compatible with a neutron-star accretor but requires a consistent radiation/flow/torque model. Relativistic beaming from a jet is another possibility for some objects, but orientation, spectral and variability evidence must support it. These mechanisms need not apply identically to every member of the observed class.

For spherical radiation with flux $F=L/(4\pi r^2)$, the outward acceleration is $\kappa F/c$. Equating it to $GM/r^2$ givesThe limit assumes the stated opacity, approximate spherical symmetry and coupling between the radiatively accelerated plasma and the accreting matter. It is not a universal ceiling on isotropic-equivalent luminosity for an anisotropic magnetized flow.

Write the available accretion power as $L=\eta \dot{M}{c}^2$. ThenAccretion as the energy source alone does not fix $\eta$. For radiatively efficient Newtonian accretion onto a slowly rotating stellar surface, $\eta \simeq GM/(R{c}^2)$ and the corresponding surface accretion Eddington rate isThis is the appropriate convention for the numerical neutron-star estimates below, rather than imposing a separate reference efficiency of $0.1$.

Using $M=1.4M_{\odot }$, $R=10^4$ m and the stated opacity givesIf the observed X-rays represent isotropic, radiatively efficient surface accretion power, thenA bolometric correction, beaming, radiation advected into the flow or energy carried by a wind would change the mapping from the measured band luminosity to the supplied mass rate. This estimate keeps the assumptions needed for comparison with the torque calculation.

In magnetically channelled accretion, an outer accretion disk supplies nearly Keplerian material. Near the magnetospheric truncation radius, magnetic stresses disrupt the disk and guide matter along field lines onto polar accretion columns. Shocks and settling near the surface release gravitational binding energy, and an oblique magnetic geometry makes the rotating emission pattern pulsate.

The corotation radius satisfies ${\Omega }_K(r_{\mathrm{co}})={\Omega }_{\ast }=2\pi /P$, henceThe accretion Alfvén radius estimates where magnetic stress becomes comparable with the inflow's dynamical stress; it is the magnetic truncation scale in this application, not the Alfvén critical point of an outward stellar wind. The supplied seventh-root scaling follows from a dipole's rapidly decreasing magnetic pressure and an accretion-pressure estimate. Its coefficient depends on disk geometry. Ordinary inward surface accretion requires the magnetosphere to remain outside the star and usually inside or near corotation, $R\lesssim r_{\mathrm{Alf}}\lesssim r_{\mathrm{co}}$. Beyond corotation, a rapidly moving magnetosphere can transfer angular momentum outward and inhibit inflow through the propeller effect.

A protoplanetary disk is a flattened, rotating reservoir of gas and solids around a young star. Its radial gravity is usually dominated by the host, making its rotation close to Keplerian rotation, ${\Omega }_K=(G{M}_{\star }/r^3{)}^{1/2}$. Gas pressure provides vertical support and a small radial correction to the orbital speed; it does not make the disk a nonrotating spherical atmosphere.

At height $|z|\ll r$, vertical hydrostatic equilibrium in the stellar gravitational field givesFor a locally vertically isothermal ideal gas, $P_g={\rho }_g{c}_s^2$ with $c_s^2=k_{B}T/(\mu m_H)$, where $\mu$ is mean molecular weight. Integration givesHere ${\Sigma }_g$ is the vertically integrated gas surface density of a disk, and $H$ is the isothermal disk scale height. The disk aspect ratio $H/r=c_s/v_K$ is small in a geometrically thin disk. For $T\propto r^{-q}$ it scales as $r^{(1-q)/2}$, so $q<1$ produces disk flaring. This illustrative local vertical model does not determine a unique radial surface-density law or temperature normalization from the information given.

The gas is predominantly molecular hydrogen and helium. A much smaller component consists of heavier elements, partitioned between vapor, solid refractory grains and condensed volatile ices. A gas-to-solid mass ratio of order $100$ is a common initial fiducial model, not a universal measurement applying at every disk radius or evolutionary stage. Solids can grow and settle while gas accretes or disperses, changing the local ratio substantially.^[ref]

Thermal structure organizes composition. In the hottest inner region, grains can sublimate and much of their material remains in the gas. Refractory silicate minerals and metallic grains survive at lower temperatures; farther out, water and then other sufficiently volatile species can condense when their local condensation conditions are met. The water snow line can raise the solid inventory available to planet formation. Its location depends on stellar irradiation, accretion heating, opacity and gas pressure, and evolves with time; it is not fixed merely by naming a star or adopting a solar-system distance.

Stellar radiation heats the exposed surface of a passive disk. Beneath it, shielding can leave a cooler, molecule-rich interior with a higher mass density. In the inner actively accreting disk, dissipation can instead make the optically thick midplane the hottest region. These are distinct heating regimes; a vertically isothermal profile is an analytic approximation rather than a claim that every real layer has the same temperature. Dust opacity controls how radiation is absorbed and re-emitted. Infrared and millimetre emission probe solid material, while spectral lines probe gas; neither observable alone supplies a model-free inventory of the whole disk.

Dust settling in an astrophysical disk makes larger, less tightly coupled particles more concentrated toward the midplane, while turbulence and mixing oppose that settling. For an aerodynamic stopping time $t_s$ short compared with ${\Omega }_K^{-1}$, terminal vertical balance gives $v_z\simeq -{\Omega }_K^2{t}_{s}z$. Small grains remain better coupled to the gas. Radial drift also changes the distribution of solids and their access to snow lines and embryos.

The disk evolves through accretion and angular momentum transport, potentially involving turbulent stresses, magnetorotational instability or magnetically driven winds where conditions permit. Protoplanetary disk dispersal eventually removes gas through accretion and mass loss, including photoevaporation. In standard evolutionary pictures this occurs on a scale of a few million years, with substantial system-to-system variation. That finite reservoir lifetime is central to whether an embryo acquires a massive gaseous envelope.^[ref]

The essential structure is a nearly Keplerian gas disk with vertical pressure support, radial and vertical thermal gradients, and an evolving solid population concentrated by settling, growth and drift. Its composition is set jointly by the original elemental inventory, local condensation conditions and transport.

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.

inside-out collapse of a singular isothermal sphere starts from an idealized static envelope,with constant isothermal sound speed $a_s$. Collapse begins centrally after formation of a central mass. An expansion wave moves outward through the initially static envelope at the sound speed:“Expansion” describes the outward-moving information front; the gas behind it moves inward. The exterior remains close to its original $r^{-2}$ equilibrium until the wave reaches it.

In the inner region, the central mass dominates and pressure becomes less important:The self-similar accretion scale is ${\dot{M}}_{\ast }=m_0{a}_s^3/G$, where the dimensionless coefficient $m_0$ follows from the dynamical similarity solution, not from counting material swept by the front. Indeed, the initial mass enclosed by the front grows at $2a_s^3/G$, and some of that material remains in the infalling envelope. For fixed mean particle mass, ${\dot{M}}_{\ast }\propto T^{3/2}$. The original similarity calculation establishes the static outer and free-fall inner regimes.^[ref]

The model assumes spherical symmetry, isothermality and negligible rotation or magnetic stresses. An asymmetric optically thick spectral line alone does not establish infall: an optically thin systemic-velocity tracer and spatial maps help distinguish inward motion from rotation, foreground absorption and outflow.