alpha disk model
model-e gerdé âlfâ, ~ disk ~
Fr.: modèle disque alpha
A simple → accretion disk model in which the → angular momentum is transported outward by action of some kind of → viscosity. In this model, first proposed by Shakura & Sunyaev (1973), the turbulent kinematic viscosity is given by ν = α cs H, where α is a parameter, cs the sound speed in the medium, and H → scale height. The α parameter controls the amount of → turbulence in the medium whose H and cs are upper limits for → mixing length and turbulent speed, respectively. Values of α = 10-3 to 10-2 yield evolution → time scales that are broadly consistent with the ages inferred for → T Tauri stars. A weak point of this model is the arbitrariness of the choice of the parameter α, which reflects the lack of a rigorous theory of turbulence.
anisotropic homogeneous cosmological model
model-e keyhânšenâxti-ye hamgen o nâ-izogard
Fr.: modèle cosmiologique homogène mais anisotrope
Fr.: modèle bayésien
A mathematical framework described by the prior distribution of a random parameter and by the likelihood of the observations. In this framework, all information on the random parameter based on the observations is included in the posterior distribution which can be obtained using → Bayes' theorem (see, e.g., Andrieu et al., 2001, "An Introduction to Monte Carlo Methods for Bayesian Data Analysis," in Nonlinear Dynamics and Statistics, ed. A. I. Mees, Boston: Birkhäuser).
Bayesian model averaging (BMA)
miyângin-giri-ye Bayesi-e model
An approach to model selection in which one bases inference on an average of all possible models instead of a single best model. The BMA is largely used in various branches of knowledge to properly account for model uncertainty in performing predictions.
Bianchi cosmological model
model-e keyhânšenâxti-ye Bianchi
Fr.: modèle cosmologique de Bianchi
A cosmological model based on the theory of → general relativity, which is homogeneous but → anisotropic. There are actually ten dinstinct Bianchi types, classified according to the particular kinds of symmetry they posses.
Big Bang model
model-e Meh Bâng, ~ Big Bang
Fr.: modèle du big bang
Fr.: modèle à effet de couverture
Fr.: modèle d'ampoule
Fr.: modèle de Bohr
A model suggested in 1913 to explain the stability of atoms which classical electrodynamics was unable to account for. According to the classical view of the atom, the energy of an electron moving around a nucleus must continually diminish until the electron falls onto the nucleus. The Bohr model solves this paradox with the aid of three postulates (→ Bohr's first postulate, → Bohr's second postulate, → Bohr's third postulate). On the whole, an atom has stable orbits such that an electron moving in them does not radiate electromagnetic waves. An electron radiates only when making a transition from an orbit of higher energy to one with lower energy. The frequency of this radiation is related to the difference between the energies of the electron in these two orbits, as expressed by the equation hν = ε1 - ε2, where h is → Planck's constant and ν the radiation frequency. The electron needs to gain energy to jump to a higher orbit. It gets that extra energy by absorbing a quantum of light (→ photon), which excites the jump. The electron does not remain on the higher orbit and returns to its lower energy orbit releasing the extra energy as radiation. Bohr's model answered many scientific questions in its time though the model itself is oversimplified and, in the strictest sense, incorrect. Electrons do not orbit the nucleus like a planet orbiting the Sun; rather, they behave as → standing waves. Same as → Bohr atom.
Fr.: modèle CAK
The standard model of → radiation-driven winds in which the acceleration of → stellar wind is provided by the → absorption and → scattering of ultraviolet photons in ions of abundant elements (→ CNO, → iron peak) in the → Lyman continuum. The model was developed by Castor et al. (1975), who assumed that the forces due to the radiative lines and the pressure gradients are functions of local velocity gradient, and used a large number (~ 105) of lines which have a statistical distribution in line strengths. The model led to predictions of → mass loss rates (M_dot) and terminal velocities as a function of stellar properties and the line statistics parameters. With the modifications by Friend and Abbott (1986), Pauldrach et al. (1986), and Kudritzki et al. (1989), CAK multi-line theory gives good agreement with observationally derived values of mass loss rate and → terminal velocity (v∞). CAK wind solutions predict the terminal velocity to be proportional to the → escape velocity and the mass loss rate to depend strongly on the stellar → luminosity. Observations over the past decades have shown that these main wind parameters, M_dot and v∞, indeed behave as predicted by CAK. This basic agreement between observations and theory provides strong evidence that the winds from → massive stars are driven by → radiation pressure and this has favored the CAK formalism. See also → multiple scattering. See the review by J. Puls et al. 2008, Astron. Astrophys. Rev. 16, 209.
CAK, the initials of the researchers who developed the model: J.I. Castor, D.C. Abbott, and R.I. Klein(1975, Radiation-driven winds in Of stars, ApJ 195, 157); → model.
negare-ye mâdde-ye sard-e târik
Fr.: théorie de la matière noire froide
A → cosmological model that attributes the formation of structures in the → early Universe to an exotic particle (→ cold dark matter) which was → non-relativistic at the time of → decoupling. According to this model, CDM began clumping together soon after the → Big Bang, while the → baryonic matter was still coupled with the → photons, and prevented to condense. Smaller → clumps of dark matter merged to form larger and larger clumps, and when the normal visible matter had decoupled from the photons, at the → recombination era (380,000 years after the Big Bang), it collapsed onto these dark matter clumps. In this way, the dark matter clumps acted as seeds for galaxy formation.
Fr.: modèle de coalescence
A scenario for building up → massive stars through merging of → intermediate-mass protostars. It occurs in the cores of dense stellar clusters that have undergone core contraction due to rapid → accretion of gas with low → specific angular momentum. The required densities are, however, very high, 108 stars pc-3, which are extremely rare (Bonnell et al. 1998, MNRAS 298, 93).
collect and collapse model
model-e anbâšt va rombeš
Fr.: modèle d'accumulation et d'effondrement
A → sequential star formation model involving → massive stars and → H II regions. The energetic ultraviolet photons from a massive star born in a → molecular cloud drive a spherical → ionization front radially outward from the star at a velocity much higher than the → sound speed in the cold neutral gas. The supersonic expansion of the H II region through the surrounding neutral gas creates a → shock front, sweeping up an increasingly massive and dense shell of cool neutral gas. This is the collect phase of the process in which the H II region simply acts like a snowplough. If the expansion of the H II region continues for long enough, the surface density of the shell increases to the point where the shell becomes self-gravitating. The shell is then expected to collapse and fragment. Individual fragments may then enter a non-linear collapse phase, possibly forming massive stars. This model was first proposed by Elmegreen & Lada (1977, ApJ 214, 725), who used a one-dimensional analysis. Whitworth et al. (1994, MNRAS, 268, 291) developed an analytical model for the collect and collapse process which predicts the fragmentation time, the size, number, and mass of the fragments (see also Elmegreen 1998, in ASP Conf. Ser. 148, Origins, eds. Woodward et al., p. 150 and references therein). → stimulated star formation, → triggered star formation.
competitive accretion model
model-e farbâl-e piši-juyâné
Fr.: modèle d'accrétion compétitive
A scenario for → massive star formation whereby developing → protostars in their natal → molecular clouds compete with each other to gather mass. The protostars → accrete mass with a rate which depends on their location within the protocluster. They use the same reservoir of gas to grow. Therefore those protostars nearest the center, where the potential well is deep, and gas densities are higher, have the highest → accretion rates. The competitive accretion model explains the observational fact that the most massive stars are generally found in cluster cores. It accounts also for the distribution of stellar masses. In this model the accretion process depends on the content of the cluster. In clusters where gas dominates the potential (e.g. at initial stages of cluster formation), the accretion process is better modeled by using the → tidal radius as the accretion radius. In contrast, when the stars dominate the cluster potential and are virialized, the accretion is better modeled by → Bondi-Hoyle accretion (Bonnell et al. 1997, MNRAS 285, 201; 2001, MNRAS 323, 785).
Fr.: modèle de concordance
The currently most commonly used cosmological model that describes the Universe as a flat infinite space in eternal expansion, accelerated under the effect of a repulsive → dark energy. The Universe is 13.7 billion years old and made up of 4% baryonic matter, 23% dark matter and 73% dark energy; the Hubble constant is 71 km/s/Mpc and the density of the Universe is very close to the critical value for re-collapse. These values were derived from → WMAP satellite observations of the → cosmic microwave background radiation.
M.E. concordaunce, from O.Fr. concordance, from L. concordantia, from → concord + -ance a suffix used to form nouns either from adjectives in -ant or from verbs.
Hamsâzgâni, from hamsâz, → concord, + -gân relation and multiplicity suffix + -i suffix that forms noun from adjectives.
Fr.: modèle copernicien, ~ de Copernic
A model of the Solar System proposed by Copernicus in which the Sun lies at the center with the planets orbiting around it. In this model, the Earth is a planet, and the Moon is in orbit around the Earth, not the Sun. The stars are distant objects that do not revolve around the Sun. Instead, the Earth is assumed to rotate once in 24 hours, causing the stars to appear to revolve around the Earth in the opposite direction. This model readily explained both the varying brightness of the planets and the → retrograde motion. In the Copernican model the planets executed uniform circular motion about the Sun. As a consequence, the model could not explain all the details of planetary motions on the celestial sphere without → epicycles of the → Ptolemaic system. However, the Copernican system required many fewer epicycles than its predecessor because it moved the Sun to the center. Hence, Copernicus borrowed elements from variants of the Ptolemaic system developed by Middle Eastern astronomers, mainly the Iranian Nasireddin Tusi (1201-1274) and the Damascene Ibn al-Shatir (1304-1375), which Copernicus apparently knew about.
Nicolaus Copernicus (1473-1543), the L. rendition of the Polish original name Mikołaj Kopernik, author of the epoch making work De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres), published in 1543, in which he exposed his heliocentric system; → model.
model-e keyhânšenâsik, ~ keyhânšenâxti
Fr.: modèle cosmologique
A mathematical description of the Universe, based on observation, which tries to explain its current aspect, and to describe its evolution during time.
Fr.: modèle de Cowling
A model of the internal structure of → massive stars in which a → convective core is surrounded by a large → radiative envelope. However, recent studies point to the presence of a thin → convection zone in the outer envelope of hot massive stars, beneath the → photosphere, which is caused by opacity peaks associated with iron and helium ionization. See also → iron convection zone.
After Thomas Cowling (1906-1990), a British astronomer, who put forward the model; → model.
Fr.: modèle de données
An abstract entity that describes the structure of → database by including the formal description of the information system used in the database.
model-e Debye (#)
Fr.: modèle de Debye
An extension of the → Einstein model accounting for → specific heats, based on the concept of → elastic waves in → crystals. In this model specific heat is given by: CV = 9R[(4/x2)∫ y2/(ey - 1)dy - x/(ex - 1)], integrating from 0 to x, where R is the → gas constant, k is → Boltzmann's constant, x = hνmax/k, and y = hν/k. The parameter TD = hνmax/k is the characteristic → Debye temperature of the crystal. At low temperatures the specific heat prediction by this model is in good agreement with observations (→ Debye law), in contrast to Einstein's model.