Codex @codex  0

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.

The bright region where the stream from Roche-lobe overflow strikes an accretion disk. Dissipation of relative kinetic energy produces a localized source of light whose visibility changes around the orbital period.

The rate at which angular momentum crosses a surface, including advection and stresses. With positive inward mass accretion rate, the net inward flux in a steady accretion disk is $\dot{M}h-\mathcal{G}$.

Angular momentum transport moves angular momentum between locations through matter, stresses, waves, or fields. An accretion disk must transport angular momentum outward for most of its mass to move inward.

An astrophysical disk is a flattened, rotating distribution of matter. Examples include a young star's protoplanetary disk, an accretion disk around a compact object and a stellar galactic disk. For gas that can radiate away random-motion energy while retaining angular momentum, settling into a disk is easier than falling directly toward the center. Ordered orbital motion supplies radial support; pressure, random motions or magnetic forces determine the thickness. The same geometry therefore contains systems with very different heating and transport mechanisms.

Black-hole accretion is the inflow of matter onto a black hole, converting some of its gravitational binding energy into heat, electromagnetic radiation and outflows. Matter with substantial angular momentum generally forms an accretion disk; internal stresses transfer angular momentum outward so that matter can move inward. The released energy can be radiated before the material crosses the event horizon. In a thin-disk model the innermost stable circular orbit marks the transition toward rapid plunging motion, although the detailed inner flow depends on the accretion state.^[ref]

The relation $L=\eta \dot{M}{c}^2$ defines the radiative efficiency of black-hole accretion, where $L$ is emitted luminosity, $\dot{M}$ the mass accretion rate and $c$ the speed of light. A radiatively inefficient accretion flow carries much of its available energy inward or into outflows instead of emitting it, so luminosity alone need not measure the mass supply.

For the opposite internal torques on a black hole and its accretion disk, the total angular momentum ${\mathbf{J}}_t$ and the black-hole spin magnitude $J_h$ are constant. If $A=K_2|{\mathbf{J}}_h\times {\mathbf{J}}_d{|}^2$, then $d({\mathbf{J}}_h\cdot {\mathbf{J}}_t)/dt=A$ and $d{J}_d^2/dt=-2A$. The $K_1$ term produces precession; the positive $K_2$ term increases the alignment of the hole with the total vector while decreasing the disk angular-momentum magnitude. The exact direction equation is $\dot{c}=K_2{J}_h{J}_t(1-c^2)$ for $c=\cos \angle ({\mathbf{J}}_h,{\mathbf{J}}_t)$.

Charles F. Gammie studies accretion disks, black holes and computational approaches to their dynamics. His 2001 study used local, razor-thin models to investigate gravitational instability in a cooling astrophysical disk.

The models distinguish two outcomes. Sufficiently slow radiative cooling permits a fluctuating state in which dissipation of turbulence replaces the lost heat; faster cooling permits gravitational fragmentation. The reported transition depends on the local model and its assumptions. Its broader importance is the explicit link between an energy balance and whether a disk transports angular momentum or breaks into bound structures.^[ref]

For a vertically stratified accretion disk with surface density $\Sigma =\int \rho dz$, the density-weighted mean kinematic viscosity is $\bar{\nu }={\Sigma }^{-1}\int \rho \nu dz$. In an alpha disk with $\nu =\alpha p/(\rho \Omega )$, this becomes $\bar{\nu }=\alpha (\Sigma \Omega {)}^{-1}\int pdz$.

// Target: astrophysics.bigb

GRS 1915+105 is an X-ray binary containing an accreting stellar-mass black hole. Gas supplied by its companion forms an accretion disk; changes in that gas produce strong, variable X-ray emission. Its radio-emitting jets make it an example of a microquasar.

The thermal disk spectrum has been used to estimate the black-hole spin by fitting a relativistic disk model. The inference depends on quantities including mass, distance, inclination and the disk's physical state. It therefore illustrates how a bright spectrum constrains a compact object through a model, rather than providing a direct measurement of the event horizon.^[ref]

Jeffrey E. McClintock studies black holes through the X-rays emitted by their accreting gas. In work on GRS 1915+105, his team fitted a relativistic accretion disk model to the thermal continuum and inferred a rapidly rotating Kerr black hole.

The inference depends on connecting the fitted inner emitting scale to the black hole's spin. The study selected relatively low-luminosity thermal-state data, where a thin accretion disk was an appropriate approximation, and included changes between local emission and the measured radiation spectrum. It reported a dimensionless spin exceeding 0.98 within that modeling framework.^[ref]

John F. Hawley helped explain angular-momentum transport in accretion disks through the magnetorotational instability. With Steven A. Balbus, he showed in 1991 that even a weak magnetic field can destabilize differentially rotating disks whose angular velocity decreases outward.^[ref]

In the spring model of magnetorotational instability, magnetic tension couples displaced fluid elements and transfers angular momentum. This can amplify their separation despite stability under the corresponding unmagnetized rotational test.

J. R. Herrnstein led a 1999 determination of the Euclidean distance to NGC 4258 from maser emission in its nuclear accretion disk. Very-long-baseline interferometry resolved the changing angular positions of emitting regions orbiting the central black hole.

Combining those proper motions with measured acceleration and the orbital geometry gave a geometric Euclidean distance, rather than a distance obtained by assuming a standard candle's luminosity. The reported $7.2\pm 0.3\mathrm{Mpc}$ supplied an independent anchor for the cosmic distance ladder.^[ref]

Lense-Thirring precession is the rotation of orbital angular momentum caused by the gravitational field of a spinning mass. In the secular weak-field picture, the precession vector is parallel to the central spin. Thus an annulus has torque proportional to ${\mathbf{J}}_h\times \delta {\mathbf{J}}_d$, perpendicular to ${\mathbf{J}}_h$. Summing such torques preserves this orthogonality even if their radial coefficients differ. Dissipation and the internal response of a warped accretion disk can supplement precession with an alignment torque.

Lijun Gou coauthored an estimate of black-hole spin in Cygnus X-1 using the thermal spectrum of its accretion disk. The analysis combines independent constraints on mass, distance and inclination with a relativistic thin-disk model to infer an inner emitting radius and hence a spin parameter.^[ref]

This is a model-based inference rather than a direct image of the event horizon. Disk geometry, calibration and the relation between the spin and orbital axes are part of the interpretation.

In a low-mass X-ray binary, the donor star is relatively low mass. Roche-lobe overflow usually feeds an accretion disk around a neutron star or black hole. The low-mass label concerns the donor rather than the total binary mass. Accumulated fuel on a neutron star can produce a Type I X-ray burst.

The magnetorotational instability allows a weak magnetic field to destabilize some differentially rotating flows that are stable to axisymmetric hydrodynamic displacements. A useful picture connects two fluid elements by magnetic tension: the inner element loses angular momentum and moves inward, while the outer element gains angular momentum and moves outward. Decreasing angular velocity amplifies their separation. This makes the instability relevant to angular momentum transport in an accretion disk.

For a local, unstratified, incompressible ideal-MHD model with vertical magnetic field $B_z$, take an axisymmetric perturbation proportional to $e^{st+ikz}$. Let $v_A=|B_z|/\sqrt{{\mu }_0\rho }$ and $\kappa$ be the radial epicyclic frequency, withEliminating the horizontal velocity and magnetic perturbations givesFor a hydrodynamically stable background with ${\kappa }^2>0$, a growing root exists exactly whenIndeed, the constant term is then negative, so the quadratic in $s^2$ has one positive root. If the constant term is nonnegative, both roots are nonpositive: their sum is negative and their discriminant is ${\kappa }^4+16{\Omega }^2{k}^2{v}_A^2$. The vertical-field local limit follows from the original linear analysis.^[ref]

In a Keplerian disk, the unstable interval is $0<k^2{v}_A^2<3{\Omega }^2$. Maximizing the positive root gives $k^2{v}_A^2=15{\Omega }^2/16$ and growth rate $s_{\max }=3\Omega /4$. Strong tension stabilizes shorter wavelengths. In a finite disk the unstable wavelengths must also fit the vertical domain; magnetic diffusivity, viscosity and nonideal magnetic coupling can modify or suppress them. Thus a negative angular-velocity gradient alone is not a universal sufficient condition for every magnetized flow. Linear growth also does not by itself specify the eventual turbulent stress.

The inner radius at which a stellar magnetic dipole field disrupts a surrounding accretion disk. In a free fall pressure-balance estimate with fixed aspect ratio $ϵ=H/r$, $r_m\sim ({ϵ}^2{\mu }^4/(GM{\dot{M}}^2){)}^{1/7}$. Geometry and inflow structure change its numerical coefficient.

A multitemperature blackbody disk adds the radiation from annuli with different effective temperatures. For a steady, radiatively efficient accretion disk, the inner annuli are hotter and dominate higher photon frequencies, while cooler outer annuli contribute at lower frequencies. With $T(r)\propto r^{-3/4}$, integrating the Planck law produces the intermediate-frequency slope $F_{\nu }\propto {\nu }^{1/3}$. This slope applies between the outer thermal turnover and inner high-frequency cutoff, rather than across the entire spectrum.^[ref]

A neutrino-dominated accretion flow is a hot, dense accretion disk in which weak-interaction emission removes much of the dissipated energy. At extreme accretion rates, escaping photons can become inefficient at cooling the inner gas, while reactions involving nucleons and leptons emit neutrinos. Hyperaccreting black holes have therefore been investigated as engines for gamma-ray bursts. Whether cooling wins over inward energy transport depends on the flow parameters; the name describes a regime, not every rapidly accreting disk.^[ref]