An Etymological Dictionary of Astronomy and Astrophysics
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1) A type of instability occurring within a rapidly → rotating star where non-axisymmetric motions can separate surfaces of constant pressure from → equipotential surfaces.
2) A hydrodynamic instability associated with a baroclinic layer of the atmosphere. It arises from temperature variation along the pressure surfaces. Baroclinic instability is associated with the vertical → shear of the mean flow, which is related to the horizontal temperature gradient by the thermal wind equation. Instabilities in a baroclinic region grow by converting potential energy associated with the mean horizontal temperature gradient into kinetic energy through ascending warm air and descending cold air (Rasmussen & Turner (eds.), Polar Lows, Cambridge Univ. Press, 2003).

→ baroclinic; → instability.

A hydrodynamical instability that arises when the horizontal → shear gradient becomes very large. Barotropic instabilities grow by extracting kinetic energy from the mean flow field.

→ barotropic; → instability.

The condition in which a physical system is capable of assuming either of two stable states.

→ bi-; → stable.

An abrupt discontinuity in the → stellar wind properties of → hot stars near → effective temperatures about 21,000 K and 10,000 K, corresponding to O9.5-B3 supergiants (Castor et al. 1975, ApJ 195, 157; Lamers et al., 1995, ApJ 455, 269). At these temperatures the → terminal velocity of the wind drops steeply by about a factor two and the → mass loss rate increases steeply by about a factor three to five, when going from high to low temperatures. Bistability jump is related to the degree of ionization in the wind. With a little drop in the temperature, the dominant driving element (Fe) will recombine to lower ionization stages which produces a lower terminal velocity and a relatively high density in the wind. → wind momentum. Additional bistability jumps may occur at higher temperatures where CNO may provide the dominant line driving, especially for low metallicity stars (Vink et al. 2001, A&A 369, 574). However, a recent study using a larger sample finds that there is a gradual decline in the wind terminal velocities of early B supergiants and not a "jump" (Crowther et al. 2006, A&A 446, 279).

→ bistability; → jump.

The mechanism that accounts for the → bistability jump.

→ bistability; → mechanism.

Statics: The → energy that must be expended to permanently disturb a specific state of → equilibrium of a body.

→ degree; → stability.

1) General: The process by which an → accretion disk cools, causing it to fragment into self-gravitating → clumps.
2) A model of → planet formation in which a region of a → circumstellar disk becomes dense and cool enough to be unstable to → gravitational collapse, resulting in the formation of a gaseous → protoplanet. Disk instability has been put forward as a mechanism for forming massive → giant planets on short time-scales (1 Ky-1 My).
3) In models of galactic structure, a process that is thought to cause the formation of → pseudo-bulges.
4) → disk instability model (DIM).

→ disk; → instability.

A model describing → dwarf novae and → Soft X-ray Transient (SXT)s. Accordingly, these objects are triggered by an → accretion disk instability due to an abrupt change in opacities (→ opacity) at → temperatures at which hydrogen is partially ionized. All versions of the DIM have this ingredient. They differ in assumptions about → viscosity, and about what happens at the inner and outer disk radii. Basically, during → quiescence, material accumulates in the accretion disk until a critical point is reached. The disk then becomes unstable and is dumped onto the → compact object, releasing a burst of → X-rays. However, the greater duration of SXT bursts (months) and the time interval between bursts (decades) cannot be accounted for by the standard disk instability model used for dwarf novae, and additional factors such as X-ray illumination and irradiation of the accretion disk are required for the model to match the observed properties of SXTs (J-P Lasota and J-M Hameury, 1995).

→ disk; → instability; → model.

A type of instability that often occurs in fluids which are thermally stably stratified, but have an inhomogeneous composition. A well-known example, found in upper layers of the Earth's oceans, is → salt fingers. Similar fingering instabilities can occur in any other thermally stably stratified solution, provided the concentration of the slower-diffusing solute increases with height. The saturated state of this instability, → fingering convection, takes the form of tightly-packed, vertically-elongated plumes of sinking dense fluid and rising light fluid, and significantly enhances the vertical transport of both heat and chemical composition. The fingering instability occurs in stars within radiation zones that have an unstable mean → molecular weight  → gradient (μ gradient). This situation is often found as a result of material accretion onto a star by anything from a single or multiple planets, to material from a dust-enriched or debris accretion disk, or material from a more evolved companion. It also naturally arises in the vicinity of the → hydrogen shell burning in → red giant branch (RGB) stars, and in thin element-rich layers near the surface of intermediate-mass stars. The fingering instability initially takes the form of thin tubes, hence the name "finger," within which the fluid moves vertically. The tubes rapidly break down, however, as a result of parasitic shear instabilities that develop inbetween them, and the fingering instability eventually saturates into a state of homogeneous fingering convection where the typical aspect ratio of the eddies is closer to one (P. Garaud et al., 2015, arXiv:1505.07759).

→ finger; → -ing; → instability.

The process by which fluctuations in an infinite medium of size greater than a certain length scale (the Jeans length) grow by self-gravitation.

→ gravitational; → instability.

The condition for the stability of a → three-body system. Three-body systems exist widely in the → solar system and → extrasolar systems, including Sun-planet-moon systems, planets-star systems, and → triple star systems. This concept of stability was introduced by Hill (1878). He used the → Jacobi integral to construct bounds of motion for → conservative systems with time-independent → potentials, which was introduced to study the stability of the Moon in the Sun-Earth → restricted three-body problem. The stability is defined by the → zero-velocity surface based on the Jacobi integral. The concept of the Hill stability has been used by many researchers to study the stability of three-body systems. The studies include the Hill stability in the full → three-body problems, the hierarchical three body problems, and the restricted three body problems (See, e.g., S. Gong & J. Li, 2015, Astrophys Space Sci. 358,37).

Hill, G.W.: Researches in the lunar theory. Am. J. Math. 1(2), 129-147 (1878); → stability.

The condition of a system when it is disturbed by internal or external forces. The system continues to depart from the original condition, in contrast to a stable system, which will return to its previous condition when disturbed.

From → in- "not" + → stability

A narrow, almost vertical, band on the right hand side of the → main sequence in the → H-R diagram occupied by many different types of → pulsating stars (→ RR Lyrae, → Cepheids, → W Virginis, → ZZ Ceti). Stars traverse this region at least once after they leave the main sequence. The narrow temperature range of the instability strip corresponds to the stellar → effective temperature that can sustain → partial ionization zones, capable of maintaining stellar oscillations. The blue (hot) edge of the instability strip pertains to stars with surface temperatures hotter than ~ 7500 K. Because these stars have partial ionization zones too close to their surface, the pulsation mechanism is not active. The red (cooler) edge of the instability strip is determined by stars with a temperature lower than ~ 5500 K. In these stars convection prevents the build-up of heat pressure necessary to drive pulsations.

→ instability; → strip.

An instability that occurs in a → self-gravitating  → interstellar cloud which is in → hydrostatic equilibrium. Density fluctuations caused by a perturbation may condense the material leading to the domination of gravitational force and the cloud collapse. The advent of instability involves a threshold called the → Jeans length or the → Jeans mass.

→ Jeans; → instability.

An → instability raised when there is sufficient velocity difference across the interface between two uniformly moving → incompressible fluid layers, or when velocity → shear is present within a continuous fluid.

→ Kelvin-Helmholtz contraction; → instability.

An instability that can be described (to first-order accuracy) by linear (or tangent linear) equations.

→ linear; → instability.

An instability that arises from the action of a weak → poloidal magnetic field in a → differentially rotating system, such as a → Keplerian disk. The MRI provides a mechanism to account for the additional outward → angular momentum transport. To put it simply, the → frozen magnetic field line acts as a spring connecting two radially neighboring fluid parcels. In a Keplerian disk the inner fluid parcel orbits more rapidly than the outer, causing the spring to stretch. The magnetic tension forces the inner parcel to slow down reducing its angular momentum by moving it to a lower orbit. The outer fluid parcel is forced by the spring to speed up, increase its angular momentum, and therefore move to a higher orbit. The spring tension increases as the two fluid parcels grow further apart, and eventually the process runs away. The MRI was first noted in a non-astrophysical context by E. Velikhov in 1959 when considering the stability of → Couette flow of an ideal hydromagnetic fluid. His result was later generalized by S. Chandrasekhar in 1960. The MRI was rediscovered by Balbus and Hawley 1991 (ApJ 376, 214) who demonstrated that this instability does indeed manifest itself in → accretion disks, and could account for the turbulent mixing needed to explain the observed mass → accretion rates.

→ magneto-; → rotational; → instability.

The instability of a physical or mathematical system that arises from the nonlinear nature of relevant variables and their interactions within the system.

→ nonlinear; → instability.

An instability arising from the → pair production inside a → massive star leading to energetic → supernova explosions. The pair instability occurs when, late in the star's life, the core reaches a sufficiently high temperature after → carbon burning, a condition in which the pair production can take place. The pairs of electron and positron annihilate to form a neutrino and an anti-neutrino. Consequently, the pressure drops and the outer layers fall in onto the core. The temperature and pressure increase rapidly and eventually titanic nuclear burning causes an extraordinary explosion with energies higher than 10⁵¹ erg. See also → pair-instability supernova and → pulsational pair-instability supernova.

→ pair; → instability.

→ pair instability

→ pair; → instability.