Abbott, David C. Astrophysicist. In 1976, in collaboration with John I. Castor and Richard I. Klein, developed the theory of winds in early type stars (CAK theory). Through hydrodynamic models and atomic data, they showed that the total line-radiation pressure is the probable mechanism that drives the wind in these systems, being able to account for the observed wind speeds, wind mass-loss rates, and general form of the ultraviolet P-Cygni line proﬁles through which the wind was originally detected.

Abney’s law of additivity

Abelian Higgs model Perhaps the simplest example of a gauge theory, ﬁrst proposed by P.W. Higgs in 1964. The Lagrangian is similar to the one in the Goldstone model where the partial derivatives are now replaced by gauge covariants, ∂µ → ∂µ −ieAµ, where e is the gauge coupling constant between the Higgs ﬁeld φ and Aµ. There is also the square of the antisymmetric tensor Fµν = ∂µAν − ∂νAµ which yields a kinetic term for the massless gauge ﬁeld Aµ. Now the invariance of the Lagrangian is with re-

Abelian string Abelian strings form when, in the framework of a symmetry breaking scheme

aberration of stellar light Apparent displacement of the geometric direction of stellar light arising because of the terrestrial motion, discovered by J. Bradley in 1725. Classically, the angular position discrepancy can be explained by the law of vector composition: the apparent direction of light is the direction of the difference between the earth velocity vector and the velocity vector of light. A presently accepted explanation is provided by the special theory of relativity. Three components contribute to the aberration of stellar light with terms called diurnal, annual, and secular aberration, as the motion of the earth is due to diurnal rotation, to the orbital motion around the center of mass of the solar system, and to the motion of the solar system. Because of annual aberration, the apparent position of a star moves cyclically throughout the year in an elliptical pattern on the sky. The semi-major axis of the ellipse, which is equal to the ratio between the mean orbital velocity of earth and the speed of light, is called the aberration constant. Its adopted value is 20.49552 sec of arc.

A-boundary

absolute humidity One of the deﬁnitions for the moisture content of the atmosphere — the total mass of water vapor present per unit volume

absolute viscosity The ratio of shear to the rate of strain of a ﬂuid. Also referred to as molecular viscosity or dynamic viscosity. For a Newtonian ﬂuid, the shear stress within the ﬂuid, τ, is related to the rate of strain (velocity gradient), dudz , by the relation τ = µdudz . The coefﬁcient of proportionality, µ, is the absolute viscosity.

absolute zero The volume of an ideal gas at constant pressure is proportional to the absolute temperature of the gas (Charles’ Law). The temperature so deﬁned corresponds to the thermodynamic deﬁnition of temperature. Thus, as an ideal gas is cooled, the volume of the gas tends to zero. The temperature at which this occurs, which can be observed by extrapolation, is absolute zero. Real gases liquefy at temperatures near absolute zero and occupy a ﬁnite volume. However, starting with a dilute real gas, and extrapolating from temperatures at which it behaves in an almost ideal fashion, absolute zero can be determined.

absorbance The (base 10) logarithm of the ratio of the radiant power at a given wavelength incident on a volume to the sum of the scattered and directly transmitted radiant powers emerging from the volume; also called optical density.

absorptance The fraction of the incident power at a given wavelength that is absorbed within a volume.

absorption cross-section The cross-section- al area of a beam containing power equal to the power absorbed by a particle in the beam [m2].

absorption fading In radio communication, fading is caused by changes in absorption that cause changes in the received signal strength. A short-wave fadeout is an obvious example, and the fade, in this case, may last for an hour or more. See ionospheric absorption, short wave fadeout.

absorption line A dark line at a particular wavelength in the spectrum of electromagnetic radiation that has traversed an absorbing medium (typically a cool, tenuous gas between a hot radiating source and the observer). Absorption lines are produced by a quantum transition in matter that absorbs radiation at certain wavelengths and produces a decrease in the intensity around those wavelengths. See spectrum. Compare with emission line.

abstract index notation A notation of tensors in terms of their component index structure (introduced by R. Penrose). For example, the

abyssal circulation Currents in the ocean that reach the vicinity of the sea ﬂoor. While the general circulation of the oceans is primarily driven by winds, abyssal circulation is mainly

accretion disk

abyssal plain Deep old ocean ﬂoor covered with sediments so that it is smooth.

acceleration The rate of change of the velocity of an object per unit of time (in Newtonian physics) and per unit of proper time of the object (in relativity theory). In relativity, acceleration also has a geometric interpretation. An object that experiences only gravitational forces moves along a geodesic in a spacetime, and its acceleration is zero. If non-gravitational forces act as well (e.g., electromagnetic forces or pressure gradient in a gas or ﬂuid), then acceleration at point p in the spacetime measures the rate with which the trajectory C of the object curves off the geodesic that passes through p and is tangent to C at p. In metric units, acceleration has units cm/sec2 ; m/sec2.

acceleration due to gravity (g) The standard value (9.80665m/s2) of the acceleration experienced by a body in the Earth’s gravitational ﬁeld.

accreted terrain A terrain that has been accreted to a continent. The margins of many continents, including the western U.S., are made up of accreted terrains. If, due to continental drift, New Zealand collides with Australia, it would be an accreted terrain.

accretion The infall of matter onto a body, such as a planet, a forming star, or a black hole, occurring because of their mutual gravitational attraction. Accretion is essential in the formation of stars and planetary systems. It is thought to be an important factor in the evolution of stars belonging to binary systems, since matter can be transferred from one star to another, and in active galactic nuclei, where the extraction of gravitational potential energy from material which accretes onto a massive black hole is reputed to be the source of energy. The efﬁciency at which gravitational potential energy can be extracted decreases with the radius of the accreting body and increases with its mass. Accretion as an energy source is therefore most efﬁcient for very

accretionary prism (accretionary wedge)

accretion, Eddington

Achilles A Trojan asteroid orbiting at the L4 point in Jupiter’s orbit (60◦ ahead of Jupiter).

achondrite A form of igneous stony meteorite characterized by thermal processing and the absence of chondrules. Achondrites are generally of basaltic composition and are further classiﬁed on the basis of abundance variations. Diogenites contain mostly pyroxene, while eucrites are composed of plagioclase-pyroxene basalts. Ureilites have small diamond inclusions. Howardites appear to be a mixture of eucrites and diogenites. Evidence from micrometeorite craters, high energy particle tracks, and gas content indicates that they were formed on the surface of a meteorite parent body.

achromatic objective The compound objective lens (front lens) of a telescope or other optical instrument which is specially designed to minimize chromatic aberation. This objective consists of two lenses, one converging and the other diverging; either glued together with transparent glue (cemented doublet), or air-spaced. The two lenses have different indices of refraction, one high (Flint glass), and the other low (Crown glass). The chromatic aberrations of the two lenses act in opposite senses, and tend to cancel each other out in the ﬁnal image.

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spect to the gauge U(1) symmetry transformation φ → ei (x)φ and, in turn, the gauge ﬁeld

transforms as Aµ(x) → Aµ(x) + e−1∂µ (x), with (x) being an arbitrary function of space and time. It is possible to write down the Lagrangian of this model in the vicinity of the true vacuum of the theory as that of two ﬁelds, one of spin 1 and another of spin 0, both of them being massive (plus other higher order interaction terms), in complete agreement with the Higgs mechanism.

Interestingly enough, a similar theory serves to model superconductors (where φ would now be identiﬁed with the wave function for the Cooper pair) in the Ginzburg–Landau theory. See Goldstone model, Higgs mechanism, spontaneous symmetry breaking.

G → H , the generators of the group G commute. One example is the complete breakdown of the Abelian U(1) → {1}. The vacuum manifold of the phase transition is the quotient space, and in this case, it is given by M U(1). The ﬁrst homotopy group is then π1(M) Z, the (Abelian) group of integers.

All strings formed correspond to elements of π1 (except the identity element). Regarding the string network evolution, exchange of partners (through intercommutation) is only possible between strings corresponding to the same element of π1 (or its inverse). Strings from different elements (which always commute for Abelian π1) pass through each other without intercommutation taking place. See Abelian Higgs model, homotopy group, intercommutation (cosmic string), Kibble mechanism, nonAbelian string, spontaneous symmetry breaking.

Abney’s law of additivity The luminous power of a source is the sum of the powers of the components of any spectral decomposition of the light.

A-boundary (or atlas boundary) In relativity, a notion of boundary points of the spacetime manifold, constructed by the closure of the open sets of an atlas A of coordinate maps. The transition functions of the coordinate maps are extended to the boundary points.

of air, i.e., the density of water vapor. Unit is g/cm3.

absolute magnitude	See magnitude.
absolute space and	time	In Newtonian

Mechanics, it is implicitly assumed that the measurement of time and the measurement of lengths of physical bodies are independent of the reference system.

absorption coefﬁcient The absorptance per unit distance of photon travel in a medium, i.e., the limit of the ratio of the spectral absorptance to the distance of photon travel as that distance becomes vanishingly small. Units: [m−1].

absorption efﬁciency factor The ratio of the absorption cross-section to the geometrical cross-section of the particle.

tensor T (θ, θ)	=	a	b b	is written in the
tensor T (θ, θ)		T bθa	θ	is written in the

abstract index notation as Ta , where the indices signify the valence and should not be assigned a numerical value. When components need to be referred to, these may be enclosed in matrix brackets: (va) = (v1, v2).

driven by density differences caused by temperature and salinity variations, i.e., the thermohaline circulation, and consequently is much more sluggish.

compact bodies like neutron stars (R 10 km) or black holes; in these cases, the efﬁciency can be higher than that of thermonuclear reactions. Maximum efﬁciency can be achieved in the case of a rotating black hole; up to 30% of the rest energy of the infalling matter can be converted into radiating energy. If the infalling matter has substantial angular momentum, then the process of accretion progresses via the formation of an accretion disk, where viscosity forces cause loss of angular momentum, and lets matter drift toward the attracting body.

In planetary systems, the formation of large bodies by the accumulation of smaller bodies. Most of the planets (and probably many of the larger moons) in our solar system are believed to have formed by accretion (Jupiter and Saturn are exceptions). As small objects solidiﬁed from the solar nebula, they collided and occasionally stuck together, forming a more massive object with a larger amount of gravitational attraction. This stronger gravity allowed the object to pull in smaller objects, gradually building the body up to a planetismal (a few kilometers to a few tens of kilometers in diameter), then a protoplanet (a few tens of kilometers up to 2000 kilometers in diameter), and ﬁnally a planet (over 2000 kilometers in diameter). See accretion disk, active galactic nuclei, black hole, quasi stellar object, solar system formation, star formation, X-ray source.

The wedge-shaped geological complex at the frontal portion of the upper plate of a subduction zone formed by sediments scraped off the top of the subducting oceanic plate. The sediments undergo a process of deformation, consolidation, diagenesis, and sometimes metamorphism. The wedge partially or completely ﬁlls the trench. The most frontal point is called the toe or deformation front. See trench.

accretion disk A disk of gas orbiting a celestial body, formed by inﬂowing or accreting matter. In binary systems, if the stars are sufﬁciently close to each other so that one of the stars is ﬁlling its Roche Lobe, mass will be transferred to the companion star creating an accretion disk.

In active galactic nuclei, hot accretion disks surround a supermassive black hole, whose

presence is part of the “standard model” of active galactic nuclei, and whose observational status is becoming secure. Active galactic nuclei are thought to be powered by the release of potential gravitational energy by accretion of matter onto a supermassive black hole. The accretion disk dissipates part of the gravitational potential energy, and removes the angular momentum of the infalling gas. The gas drifts slowly toward the central black hole. During this process, the innermost annuli of the disk are heated to high temperature by viscous forces, and emit a “stretched thermal continuum”, i.e., the sum of thermal continua emitted by annuli at different temperatures. This view is probably valid only in active galactic nuclei radiating below the Eddington luminosity, i.e., low luminosity active galactic nuclei like Seyfert galaxies. If the accretion rate exceeds the Eddington limit, the disk may puff up and become a thick torus supported by radiation pressure. The observational proof of the presence of accretion disks in active galactic nuclei rests mainly on the detection of a thermal feature in the continuum spectrum (the big blue bump), roughly in agreement with the predictions of accretion disk models. Since the disk size is probably less than 1 pc, the disk emitting region cannot be resolved with presentday instruments. See accretion, active galactic nuclei, big blue bump, black hole, Eddington limit.

accretion, Eddington As material accretes onto a compact object (neutron star, black hole, etc.), potential energy is released. The Eddington rate is the critical accretion rate where the rate of energy released is equal to the Eddington

where κ is the opacity of the material in units of area per unit mass. For spherically symmetric accretion where all of the potential energy is converted into photons, this rate is the maximum accretion rate allowed onto the compact object (see Eddington luminosity). For ionized hydrogen accreting onto a neutron star (R NS = 10 km M NS = 1.4M ), this rate is: 1.5 × 10−8M yr−1. See also accretion, SuperEddington.

accretion, hypercritical	See accretion,
Super-Eddington.
accretion, Super-Eddington	Mass accretion

at a rate above the Eddington accretion limit. These rates can occur in a variety of accretion conditions such as: (a) in black hole accretion where the accretion energy is carried into the black hole, (b) in disk accretion where luminosity along the disk axis does not affect the accretion, and (c) for high accretion rates that create sufﬁciently high densities and temperatures that the potential energy is converted into neutrinos rather than photons. In this latter case, due to the low neutrino cross-section, the neutrinos radiate the energy without imparting momentum onto the accreting material. (Syn. hypercritical accretion).

luminosity:

˙ EddingtonMaccretor/Raccretor =

LEddington

4πcRaccreting object

˙ accretion