An Etymological Dictionary of Astronomy and Astrophysics
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A standard or rule that can serve as basis for a judgment or decision.

From Gk. kriterion "means for judging, standard," from krites "judge," from krinein "to separate, distinguish, judge." L. cribrum "sieve" *krei- "to sieve, discriminate, distinguish."

Sanjidâr verbal noun from sanjid- past tense stem of sanjidan "to compare; to measure" (Mid.Pers. sanjidan "to weigh," from present tense stem sanj-, Av. θanj- "to draw, pull;" Proto-Iranian *θanj-) + suffix -âr.

An improvement of → Schwarzschild's criterion for convective instability, which includes effects of chemical composition of the gas. In the Ledoux criterion the gradient due to different molecular weights is added to the adiabatic temperature gradient.

After the Belgian astrophysicist Paul Ledoux (1914-1988), who studied problems of stellar stability and variable stars. He was awarded the Eddington Medal of the Royal Astronomical Society in 1972 (Ledoux et al. 1961 ApJ 133, 184); → criterion.

An approximate empirical criterion for the stability of a → galactic disk against its collapse to form a bar. The disk is stable if the following relation holds: T/|W| < 0.14, where T is the rotational → kinetic energy and |W| is the absolute value of the gravitational → potential energy. While the → Toomre criterion applies only to small linear perturbations, the Ostriker-Peebles criterion describes global modes.

Ostriker & Peebles, 1973, ApJ 186, 467; → criterion.

A criterion for the instability of a basic swirling flow with an arbitrary dependence of angular velocity Ω(r) on the distance r from the axis of rotation. This states that in → inviscid fluids: Ω(r) < 0 for instability, where Ω = (1/r³) (d/dr)(r⁴Ω⁴).

→ Rayleigh; → criterion.

A condition for the onset of → instability in multilayer fluids which compares the balance between the restoring force of → buoyancy and the destabilizing effect of the → shear.

Named after the British meteorologist Lewis Fry Richardson (1881-1953), who first arrived in 1920 to the dimensionless ratio now called → Richardson number. The first formal proof of the criterion, however, came four decades later for → incompressible flows (Miles, J. W. 1961, J. Fluid Mech., 10, 496; Howard, L. N., 1961, J. Fluid Mech., 10, 509). Its extension to → compressible flows was demonstrated subsequently (Chimonas 1970, J. Fluid Mech., 43, 833); → criterion.

An integral constraint used to quantify the uncertainty on the extent of → convective overshooting and its effect on models of stars.

Roxburgh, I. 1989, A&A, 211, 361; → criterion.

The condition in stellar interior under which → convection occurs. It is expressed as: |dT/dr|_ad < |dT/dr|rad, where the indices ad and rad stand for adiabatic and radiative respectively. This condition can also be expressed as: ∇_ad<∇_rad, where ∇ = d lnT / d lnP = P dT / T dP with T and P denoting temperature and pressure respectively. More explicitly, in order for convection to occur the adiabatic temperature gradient should be smaller than the actual temperature gradient of the surrounding gas, which is given by the radiative temperature gradient if convection does not occur. Suppose a hotter → convective cell or gas bubble rises accidentally by a small distance in height. It gets into a layer with a lower gas pressure and therefore expands. Without any heat exchange with the surrounding medium it expands and cools adiabatically. If during this rise and → adiabatic expansion the change in temperature is smaller than in the medium the gas bubble remains hotter than the medium. The expansion of the gas bubble, adjusting to the pressure of the medium, happens very fast, with the speed of sound. It is therefore assumed that the pressure in the gas bubble and in the surroundings is the same and therefore the higher temperature gas bubble will have a lower density than the surrounding gas. The → buoyancy force will therefore accelerate it upward. This always occurs if the adiabatic change of temperature during expansion is smaller than the change of temperature with gas pressure in the surroundings. It is assumed that the mean molecular weight is the same in the rising bubble and the medium. See also → Ledoux's criterion; → mixing length.

Named after Karl Schwarzschild (1873-1916), German mathematical physicist (1906 Göttinger Nachrichten No 1, 41); → criterion.

A criterion for → convective stability in → massive stars. The Solberg-Høiland stability criterion corresponds to the inclusion of the effect of → rotation (variation of → centrifugal force) in the convective stability criterion. It is a combination of → Ledoux's criterion (or possibly → Schwarzschild's criterion) and → Rayleigh's criterion. Both the dynamical shear and Solberg-Høiland instabilities occur in the case of a very large → angular velocity decrease outwards. Therefore, in a → rotating star the Ledoux or Schwarzschild criteria for convective instability should be replaced by the Solberg-Høiland criterion. More specifically, this criterion accounts for the difference of the centrifugal force for an adiabatically displaced fluid element. It is also known as the axisymmetric baroclinic instability. It arises when the net force (gravity + buoyancy + centrifugal force) applied to a fluid parcel in an adiabatical displacement has components only in the direction of the displacement (A. Maeder, Physics, Formation and Evolution of Rotating Stars, 2009, Springer).

E. Høiland, 1939, On the Interpretation and Application of the Circulation Theorems of V. Bjerknes. Archiv for mathematik og naturvidenskab. B. XLII. Nr. 5. Oslo.
H. Solberg, 1936 (reprint), Le mouvement d'inertie de l'atmosphere stable et son rôle dans la théorie des cyclones.
H. Solberg, 1941, On the Stability of the Circular Vortex. Avhandl. utg. av Det Norske Videnskaps-Akademi i Oslo. I. Mat-Naturv. Klasse. No. 11.
Wasiutynski, J. 1946, Astrophysica Norvegica, 4, 1.

A criterion for the stability of the disk of a → spiral galaxy. It is expressed by the → Toomre parameter.

→ Toomre criterion; → criterion.