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DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY © 2001 by CRC Press LLC Abney’s law of additivity G→ H , the generators of the groupG com- mute. One example is the complete breakdown of the AbelianU(1)→1. The vacuum mani- fold of the phase transition is the quotient space, A and in this case, it is given by M∼U(1). The first homotopy group is thenπ (M)∼ Z, the 1 (Abelian) group of integers. Abbott, David C. Astrophysicist. In All strings formed correspond to elements 1976, in collaboration with John I. Castor and ofπ (except the identity element). Regarding 1 Richard I. Klein, developed the theory of winds the string network evolution, exchange of part- in early type stars (CAK theory). Through ners (through intercommutation) is only possi- hydrodynamic models and atomic data, they ble between strings corresponding to the same showed that the total line-radiation pressure is element of π (or its inverse). Strings from 1 the probable mechanism that drives the wind in different elements (which always commute for these systems, being able to account for the ob- Abelian π ) pass through each other without 1 served wind speeds, wind mass-loss rates, and intercommutation taking place. See Abelian general form of the ultraviolet P-Cygni line pro- Higgs model, homotopy group, intercommuta- files through which the wind was originally de- tion (cosmic string), Kibble mechanism, non- tected. Abelian string, spontaneous symmetry break- ing. Abelian Higgs model Perhaps the simplest example of a gauge theory, first proposed by aberration of stellar light Apparent dis- P.W. Higgs in 1964. The Lagrangian is simi- placement of the geometric direction of stel- lar to the one in the Goldstone model where the lar light arising because of the terrestrial mo- partial derivatives are now replaced by gauge co- tion, discovered by J. Bradley in 1725. Clas- variants,∂ →∂ −ieA , wheree is the gauge µ µ µ sically, the angular position discrepancy can be coupling constant between the Higgs fieldφ and explained by the law of vector composition: the A . There is also the square of the antisymmet- µ apparent direction of light is the direction of the ric tensor F = ∂ A −∂ A which yields µν µ ν ν µ difference between the earth velocity vector and a kinetic term for the massless gauge fieldA . µ the velocity vector of light. A presently accepted Now the invariance of the Lagrangian is with re- explanation is provided by the special theory of spect to the gaugeU(1) symmetry transforma- i (x) relativity. Three components contribute to the tionφ→ e φ and, in turn, the gauge field −1 aberration of stellar light with terms called di- transforms asA (x)→ A (x)+e ∂ (x), µ µ µ urnal, annual, and secular aberration, as the mo- with (x) being an arbitrary function of space tion of the earth is due to diurnal rotation, to the and time. It is possible to write down the La- orbital motion around the center of mass of the grangian of this model in the vicinity of the true solar system, and to the motion of the solar sys- vacuum of the theory as that of two fields, one tem. Because of annual aberration, the apparent of spin 1 and another of spin 0, both of them be- position of a star moves cyclically throughout ing massive (plus other higher order interaction the year in an elliptical pattern on the sky. The terms), in complete agreement with the Higgs semi-major axis of the ellipse, which is equal to mechanism. the ratio between the mean orbital velocity of Interestingly enough, a similar theory serves earth and the speed of light, is called the aberra- to model superconductors (whereφ would now tion constant. Its adopted value is 20.49552 sec be identified with the wave function for the of arc. Cooper pair) in the Ginzburg–Landau theory. See Goldstone model, Higgs mechanism, spon- taneous symmetry breaking. Abney’s law of additivity The luminous power of a source is the sum of the powers of Abelian string Abelian strings form when, in the components of any spectral decomposition the framework of a symmetry breaking scheme of the light. © 2001 by CRC Press LLC cA-boundary A-boundary (or atlas boundary) In relativ- absorptance The fraction of the incident ity, a notion of boundary points of the space- power at a given wavelength that is absorbed time manifold, constructed by the closure of the within a volume. open sets of an atlasA of coordinate maps. The transition functions of the coordinate maps are absorption coefficient The absorptance per extended to the boundary points. 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 absolute humidity One of the definitions for −1 becomes vanishingly small. Units: m . the moisture content of the atmosphere — the total mass of water vapor present per unit volume absorption cross-section The cross-section- of air, i.e., the density of water vapor. Unit is 3 al area of a beam containing power equal to the g/cm . 2 power absorbed by a particle in the beam m . absolute magnitude See magnitude. absorption efficiency factor The ratio of the absorption cross-section to the geometrical absolute space and time In Newtonian cross-section of the particle. Mechanics, it is implicitly assumed that the measurement of time and the measurement of absorption fading In radio communication, lengths of physical bodies are independent of fading is caused by changes in absorption that the reference system. cause changes in the received signal strength. A short-wave fadeout is an obvious example, and absolute viscosity The ratio of shear to the the fade, in this case, may last for an hour or rate of strain of a fluid. Also referred to as more. See ionospheric absorption, short wave molecular viscosity or dynamic viscosity. For fadeout. a Newtonian fluid, the shear stress within the fluid,τ, is related to the rate of strain (velocity absorption line A dark line at a particu- du du gradient), , by the relationτ = µ . The dz dz lar wavelength in the spectrum of electromag- coefficient of proportionality,µ , is the absolute netic radiation that has traversed an absorbing viscosity. medium (typically a cool, tenuous gas between a hot radiating source and the observer). Absorp- absolute zero The volume of an ideal gas tion lines are produced by a quantum transition at constant pressure is proportional to the abso- in matter that absorbs radiation at certain wave- lute temperature of the gas (Charles’ Law). The lengths and produces a decrease in the intensity temperature so defined corresponds to the ther- around those wavelengths. See spectrum. Com- modynamic definition of temperature. Thus, as pare with emission line. an ideal gas is cooled, the volume of the gas tends to zero. The temperature at which this oc- abstract index notation A notation of ten- curs, which can be observed by extrapolation, sors in terms of their component index structure is absolute zero. Real gases liquefy at tempera- (introduced by R. Penrose). For example, the b a tures near absolute zero and occupy a finite vol- tensorT(θ,θ) = T θ ⊗θ is written in the b a b ume. However, starting with a dilute real gas, abstract index notation asT , where the indices a and extrapolating from temperatures at which it signify the valence and should not be assigned behaves in an almost ideal fashion, absolute zero a numerical value. When components need to can be determined. be referred to, these may be enclosed in matrix a 1 2 brackets: (v )=(v ,v ). absorbance The (base 10) logarithm of the ratio of the radiant power at a given wavelength abyssal circulation Currents in the ocean incident on a volume to the sum of the scattered that reach the vicinity of the sea floor. While and directly transmitted radiant powers emerg- the general circulation of the oceans is primarily ing from the volume; also called optical density. driven by winds, abyssal circulation is mainly © 2001 by CRC Press LLC accretion disk driven by density differences caused by temper- compact bodies like neutron stars (R ∼ 10 km) ature and salinity variations, i.e., the thermoha- or black holes; in these cases, the efficiency can line circulation, and consequently is much more be higher than that of thermonuclear reactions. sluggish. Maximum efficiency can be achieved in the case of a rotating black hole; up to 30% of the rest abyssal plain Deep old ocean floor covered energy of the infalling matter can be converted with sediments so that it is smooth. into radiating energy. If the infalling matter has substantial angular momentum, then the process acceleration The rate of change of the veloc- of accretion progresses via the formation of an ity of an object per unit of time (in Newtonian accretion disk, where viscosity forces cause loss physics) and per unit of proper time of the object of angular momentum, and lets matter drift to- (in relativity theory). In relativity, acceleration ward the attracting body. also has a geometric interpretation. An object In planetary systems, the formation of large that experiences only gravitational forces moves bodies by the accumulation of smaller bodies. along a geodesic in a spacetime, and its accel- Most of the planets (and probably many of the eration is zero. If non-gravitational forces act larger moons) in our solar system are believed as well (e.g., electromagnetic forces or pressure to have formed by accretion (Jupiter and Sat- gradient in a gas or fluid), then acceleration at urn are exceptions). As small objects solidified pointp in the spacetime measures the rate with from the solar nebula, they collided and occa- which the trajectoryC of the object curves off sionally stuck together, forming a more massive the geodesic that passes throughp and is tan- object with a larger amount of gravitational at- gent toC atp. In metric units, acceleration has traction. This stronger gravity allowed the ob- 2 2 units cm/sec ; m/sec . ject to pull in smaller objects, gradually build- ing the body up to a planetismal (a few kilo- acceleration due to gravity (g) The standard meters to a few tens of kilometers in diameter), 2 value(9.80665m/s ) of the acceleration experi- then a protoplanet (a few tens of kilometers up enced by a body in the Earth’s gravitational field. to 2000 kilometers in diameter), and finally a planet (over 2000 kilometers in diameter). See accreted terrain A terrain that has been ac- accretion disk, active galactic nuclei, black hole, creted to a continent. The margins of many con- quasi stellar object, solar system formation, star tinents, including the western U.S., are made up formation, X-ray source. of accreted terrains. If, due to continental drift, New Zealand collides with Australia, it would accretionary prism (accretionary wedge) be an accreted terrain. The wedge-shaped geological complex at the frontal portion of the upper plate of a subduction accretion The infall of matter onto a body, zone formed by sediments scraped off the top of such as a planet, a forming star, or a black hole, the subducting oceanic plate. The sediments un- occurring because of their mutual gravitational dergo a process of deformation, consolidation, attraction. Accretion is essential in the forma- diagenesis, and sometimes metamorphism. The tion of stars and planetary systems. It is thought wedge partially or completely fills the trench. to be an important factor in the evolution of stars The most frontal point is called the toe or defor- belonging to binary systems, since matter can be mation front. See trench. transferred from one star to another, and in active accretion disk A disk of gas orbiting a ce- galactic nuclei, where the extraction of gravita- lestial body, formed by inflowing or accreting tional potential energy from material which ac- matter. In binary systems, if the stars are suffi- cretes onto a massive black hole is reputed to be ciently close to each other so that one of the stars the source of energy. The efficiency at which is filling its Roche Lobe, mass will be transferred gravitational potential energy can be extracted to the companion star creating an accretion disk. decreases with the radius of the accreting body and increases with its mass. Accretion as an en- In active galactic nuclei, hot accretion disks ergy source is therefore most efficient for very surround a supermassive black hole, whose © 2001 by CRC Press LLC accretion, Eddington presence is part of the “standard model” of active accretion, hypercritical See accretion, galactic nuclei, and whose observational status Super-Eddington. is becoming secure. Active galactic nuclei are thought to be powered by the release of poten- accretion, Super-Eddington Mass accretion tial gravitational energy by accretion of matter at a rate above the Eddington accretion limit. onto a supermassive black hole. The accretion These rates can occur in a variety of accretion disk dissipates part of the gravitational poten- conditions such as: (a) in black hole accretion tial energy, and removes the angular momen- where the accretion energy is carried into the tum of the infalling gas. The gas drifts slowly black hole, (b) in disk accretion where luminos- toward the central black hole. During this pro- ity along the disk axis does not affect the accre- cess, the innermost annuli of the disk are heated tion, and (c) for high accretion rates that create to high temperature by viscous forces, and emit sufficiently high densities and temperatures that a “stretched thermal continuum”, i.e., the sum the potential energy is converted into neutrinos of thermal continua emitted by annuli at differ- rather than photons. In this latter case, due to ent temperatures. This view is probably valid the low neutrino cross-section, the neutrinos ra- only in active galactic nuclei radiating below the diate the energy without imparting momentum Eddington luminosity, i.e., low luminosity ac- onto the accreting material. (Syn. hypercritical tive galactic nuclei like Seyfert galaxies. If the accretion). accretion rate exceeds the Eddington limit, the disk may puff up and become a thick torus sup- ported by radiation pressure. The observational Achilles A Trojan asteroid orbiting at the L4 proof of the presence of accretion disks in ac- ◦ point in Jupiter’s orbit (60 ahead of Jupiter). tive galactic nuclei rests mainly on the detection of a thermal feature in the continuum spectrum (the big blue bump), roughly in agreement with achondrite A form of igneous stony mete- the predictions of accretion disk models. Since orite characterized by thermal processing and the disk size is probably less than 1 pc, the disk the absence of chondrules. Achondrites are gen- emitting region cannot be resolved with present- erally of basaltic composition and are further day instruments. See accretion, active galactic classified on the basis of abundance variations. nuclei, big blue bump, black hole, Eddington Diogenites contain mostly pyroxene, while eu- limit. crites are composed of plagioclase-pyroxene basalts. Ureilites have small diamond inclu- sions. Howardites appear to be a mixture of eu- crites and diogenites. Evidence from microme- accretion, Eddington As material accretes teorite craters, high energy particle tracks, and onto a compact object (neutron star, black hole, gas content indicates that they were formed on etc.), potential energy is released. The Edding- the surface of a meteorite parent body. ton rate is the critical accretion rate where the rate of energy released is equal to the Eddington ˙ luminosity: GM M /R = Eddington accretor accretor achromatic objective The compound objec- 4πcR accreting object ˙ L ⇒ M = tive lens (front lens) of a telescope or other op- Eddington accretion κ whereκ is the opacity of the material in units tical instrument which is specially designed to of area per unit mass. For spherically sym- minimize chromatic aberation. This objective metric accretion where all of the potential en- consists of two lenses, one converging and the ergy is converted into photons, this rate is the other diverging; either glued together with trans- maximum accretion rate allowed onto the com- parent glue (cemented doublet), or air-spaced. pact object (see Eddington luminosity). For The two lenses have different indices of refrac- ionized hydrogen accreting onto a neutron star tion, one high (Flint glass), and the other low (R = 10 kmM = 1.4M ), this rate is: (Crown glass). The chromatic aberrations of NS NS −8 −1 1.5 × 10 M yr . See also accretion, Super- the two lenses act in opposite senses, and tend Eddington. to cancel each other out in the final image. © 2001 by CRC Press LLC active fault achronal set (semispacelike set) A set of proceed. It is usually defined as the difference points S of a causal space such that there are between the internal energy (or enthalpy) of the no two points in S with timelike separation. transition state and the initial state. acoustic tomography An inverse method activation entropy (S ) The activation a which infers the state of an ocean region from entropy is defined as the difference between the measurements of the properties of sound waves entropy of the activated state and initial state, or passing through it. The properties of sound in the entropy change. From the statistical defini- the ocean are functions of temperature, water tion of entropy, it can be expressed as velocity, and salinity, and thus each can be ex- ω a ploited for acoustic tomography. The ocean S =R ln a ω is nearly transparent to low-frequency sound I waves, which allows signals to be transmitted whereω is the number of “complexions” as- a over hundreds to thousands of kilometers. sociated with the activated state, andω is the I number of “complexions” associated with the actinides The elements of atomic number 89 initial state. R is gas constant. The activation through 103, i.e., Ac, Th, Pa, U, Np, Pu, Am, entropy therefore includes changes in the con- Cm, Bk, Cf, Es, Fm, Md, No, Lr. figuration, electronic, and vibration entropy. action In mechanics the integral of the La- activation volume (V ) The activation vol- grangian along a path through endpoint events ume is defined as the volume difference between with given endpoint conditions: initial and final state in an activation process, j  t ,x   b which is expressed as b i i I = L x,dx /dt,t dt j t ,x ,C a a ∂G V = (or, if appropriate, the Lagrangian may con- ∂P tain higher time derivatives of the point- whereG is the Gibbs energy of the activation coordinates). Extremization of the action over process andP is the pressure. The activation paths with the same endpoint conditions leads volume reflects the dependence of process on to a differential equation. If the Lagrangian is pressure between the volume of the activated a simpleL=T −V , whereT is quadratic in state and initial state, or entropy change. the velocity andV is a function of coordinates of the point particle, then this variation leads to active continental margin A continental Newton’s second law: margin where an oceanic plate is subducting be- 2 i d x ∂V neath the continent. =− ,i = 1, 2, 3. 2 i dt ∂x active fault A fault that has repeated dis- By extension, the word action is also applied to placements in Quaternary or late Quaternary pe- field theories, where it is defined: riod. Its fault trace appears on the Earth’s sur- j  t ,x face, and the fault has a potential to reactivate b  b n I = L gd x, in the future. Hence, naturally, a fault which j t ,x a a had displacements associated with a large earth- quake in recent years is an active fault. The de- whereL is a function of the fields (which de- gree of activity of an active fault is represented pend on the spacetime coordinates), and of the by average displacement rate, which is deduced gradients of these fields. Heren is the dimen- from geology, topography, and trench excava- sion of spacetime. See Lagrangian, variational tion. The higher the activity, the shorter the re- principle. currence time of large earthquakes. There are activation energy (H ) That energy re- some cases where large earthquakes take place a quired before a given reaction or process can on an active fault with low activity. © 2001 by CRC Press LLC active front active front An active anafront or an active margins have major earthquakes and volcanism; katafront. An active anafront is a warm front at examples include the “ring of fire” around the which there is upward movement of the warm Pacific. sector air. This is due to the velocity component active region A localized volume of the solar crossing the frontal line of the warm air being atmosphere in which the magnetic fields are ex- larger than the velocity component of the cold tremely strong. Active regions are characterized air. This upward movement of the warm air usu- as bright complexes of loops at ultraviolet and ally produces clouds and precipitation. In gen- X-ray wavelengths. The solar gas is confined eral, most warm fronts and stationary fronts are by the strong magnetic fields forming loop-like active anafronts. An active katafront is a weak structures and is heated to millions of degrees cold frontal condition, in which the warm sec- Kelvin, and are typically the locations of sev- tor air sinks relative to the colder air. The upper eral solar phenomena such as plages, sunspots, trough of active katafront locates the frontal line faculae, and flares. The structures evolve and or prefrontal line. An active katafront moves change during the lifetime of the active region. faster than a general cold front. Active regions may last for more than one solar rotation and there is some evidence of them re- active galactic nuclei (AGN) Luminous nu- curring in common locations on the sun. Active clei of galaxies in which emission of radiation regions, like sunspots, vary in frequency dur- ranges from radio frequencies to hard-X or, in ing the solar cycle, there being more near solar the case of blazars, toγ rays and is most likely maximum and none visible at solar minimum. due to non-stellar processes related to accretion The photospheric component of active regions of matter onto a supermassive black hole. Active are more familiar as sunspots, which form at the galactic nuclei cover a large range in luminosity 42 47 −1 center of active regions. (∼ 10 −10 ergs s ) and include, at the low luminosity end, LINERs and Seyfert-2 galax- adiabat Temperature vs. pressure in a sys- ies, and at the high luminosity end, the most tem isolated from addition or removal of ther- energetic sources known in the universe, like mal energy. The temperature may change, how- quasi-stellar objects and the most powerful ra- ever, because of compression. The temperature dio galaxies. Nearby AGN can be distinguished in the convecting mantle of the Earth is closely from normal galaxies because of their bright nu- approximated by an adiabat. cleus; their identification, however, requires the detection of strong emission lines in the optical adiabatic atmosphere A simplified atmo- and UV spectrum. Radio-loud AGN, a minority sphere model with no radiation process, water (10 to 15%) of all AGN, have comparable opti- phase changing process, or turbulent heat trans- cal and radio luminosity; radio quiet AGN are fer. All processes in adiabatic atmosphere are not radio silent, but the power they emit in the isentropic processes. It is a good approximation radio is a tiny fraction of the optical luminosity. for short-term, large scale atmospheric motions. The reason for the existence of such dichotomy In an adiabatic atmosphere, the relation between is as yet unclear. Currently debated explana- temperature and pressure is tions involve the spin of the supermassive black  AR hole (i.e., a rapidly spinning black hole could C p T p help form a relativistic jet) or the morphology = T p 0 0 of the active nucleus host galaxy, since in spiral galaxies the interstellar medium would quench whereT is temperature, p is pressure, T and 0 a relativistic jet. See black hole, QSO, Seyfert p are the original states ofT andp before adi- 0 galaxies. abatic processes,A is the mechanical equivalent of heat,R is the gas constant, andC is the spe- p active margins The boundaries between the cific heat at constant pressure. oceans and the continents are of two types, ac- tive and passive. Active margins are also plate adiabatic condensation point The height boundaries, usually subduction zones. Active point at which air becomes saturated when it © 2001 by CRC Press LLC ADM form of the Einstein–Hilbert action is lifted adiabatically. It can be determined by adiabatic invariant A quantity in a mechan- the adiabatic chart. ical or field system that changes arbitrarily little even when the system parameter changes sub- adiabatic cooling In an adiabatic atmo- stantially but arbitrarily slowly. Examples in- sphere, when an air parcel ascends to upper clude the magnetic flux included in a cyclotron lower pressure height level, it undergoes expan- orbit of a plasma particle. Thus, in a variable sion and requires the expenditure of energy and magnetic field, the size of the orbit changes as consequently leading to a depletion of internal the particle dufts along a guiding flux line. An- heat. other example is the angular momentum of an orbit in a spherical system, which is changed if adiabatic deceleration Deceleration of en- the spherical force law is slowly changed. Adia- ergetic particles during the solar wind expan- batic invariants can be expressed as the surface sion: energetic particles are scattered at mag- area of a closed orbit in phase space. They are netic field fluctuations frozen into the solar wind the objects that are quantized (=mh) in the Bohr plasma. During the expansion of the solar wind, model of the atom. this “cosmic ray gas” also expands, resulting in a cooling of the gas which is equivalent to a decel- adiabatic lapse rate Temperature vertical eration of the energetic particles. In a transport change rate when an air parcel moves vertically equation, adiabatic deceleration is described by with no exchange of heat with surroundings. In a term the special case of an ideal atmosphere, the adi- ∇· v ∂ ◦ sowi abatic lapse rate is 10 per km. (αTU) 3 ∂T ADM form of the Einstein–Hilbert action with T being the particle’s energy, T its rest o In general relativity, by introducing the ADM energy,U the phase space density, v the solar sowi (Arnowitt, Deser, Misner) decomposition of wind speed, andα=(T + 2T )/(T+T ). o o the metric, the Einstein–Hilbert action for pure Adiabatic deceleration formally is also gravity takes the general form equivalent to a betatron effect due to the reduc- tion of the interplanetary magnetic field strength 1 with increasing radial distance. S = EH 16πG    4 1/2 ij 2 (3) adiabatic dislocation Displacement of a vir- d xαγ K K −K + R ij tual fluid parcel without exchange of heat with  1 1 3 1/2 the ambient fluid. See potential temperature. − d xγ K+ 8πG 8πG t a a   adiabatic equilibrium An equilibrium sta-   2 1/2 i ij dt d xγ Kβ −γ α , tus when a system has no heat flux across its ,j i x b b boundary, or the incoming heat equals the out- going heat. That is,dU=−dW , from the first where the first term on the r.h.s. is the vol- law of thermodynamics without the heat term, in ume contribution, the second comes from pos- whichdU is variation of the internal energy,dW sible space-like boundaries 4 of the space- t a is work. Adiabatic equilibrium can be found, for time manifold parametrized by t = t , and a instance, in dry adiabatic ascending movements the third contains contributions from time-like of air parcels; and in the closed systems in which i i boundaries x = x . The surface terms must b two or three phases of water exist together and be included in order to obtain the correct equa- reach an equilibrium state. tions of motion upon variation of the variables γ which vanish on the borders but have non- ij adiabatic index Ratio of specific heats: vanishing normal derivatives therein. C /C where C is the specific heat at con- p V p In the above, stant pressure, and C is the specific heat at V constant volume. For ideal gases, equal to 1 K = β +β −γ ij ij ji ij,0 (2+degrees of freedom )/(degrees of freedom). 2α © 2001 by CRC Press LLC ADM mass is the extrinsic curvature tensor of the surfaces that are very nearly 0 and a semimajor axis of 5 of constant time4 , denotes covariant differ- 1.29 × 10 km. Its size is 12.5 × 10 × 7.5 km, t 16 entiation with respect to the three-dimensional its mass, 1.90 × 10 kg, and its density roughly ij (3) −3 metric γ ,K=K γ , and R is the intrinsic 4 gcm . It has a geometric albedo of 0.05 and ij scalar curvature of4 . From the above form of orbits Jupiter once every 0.298 Earth days. t i the action, it is apparent thatα andβ are not ADV (Acoustic Doppler Velocimeter) A de- dynamical variables (no time derivatives of the vice that measures fluid velocity by making use lapse and shifts functions appear). Further, the extrinsic curvature of4 enters in the action to of the Doppler Effect. Sound is emitted at a t build a sort of kinematical term, while the intrin- specific frequency, is reflected off of particles in sic curvature plays the role of a potential. See the fluid, and returns to the instrument with a Arnowitt–Deser–Misner (ADM) decomposition frequency shift if the fluid is moving. Speed of of the metric. the fluid (along the sound travel path) may be determined from the frequency shift. Multiple ADM mass According to general relativity, sender-receiver pairs are used to allow 3-D flow the motion of a particle of mass m located in measurements. a region of weak gravitational field, that is far away from any gravitational source, is well ap- advance of the perihelion In unperturbed proximated by Newton’s law with a force Newtonian dynamics, planetary orbits around a spherical sun are ellipses fixed in space. Many mM ADM perturbations in more realistic situations, for in- F=G , 2 r stance perturbations from other planets, con- tribute to a secular shift in orbits, including a wherer isa radial coordinate such that the metric rotation of the orbit in its plane, a precession of tensor g approaches the usual flat Minkowski the perihelion. General relativity predicts a spe- metric for large values ofr. The effective ADM cific advance of the perihelion of planets, equal massM is obtained by expanding the time- ADM to 43 sec of arc per century for Mercury, and time component of g in powers of 1/r, this is observationally verified. Other planets   have substantially smaller advance of their per- 2M 1 ADM g =−1 + +O . tt ihelion: for Venus the general relativity predic- 2 r r tion is 8.6 sec of arc per century, and for Earth the prediction is 3.8 sec of arc per century. These Intuitively, one can think of the ADM mass as are currently unmeasurable. the total (matter plus gravity) energy contained in the interior of space. As such it generally The binary pulsar (PSR 1913+16) has an ob- ◦ differs from the volume integral of the energy- servable periastron advance of 4.227 /year, con- momentum density of matter. It is conserved if sistent with the general relativity prediction. See no radial energy flow is present at larger. binary pulsar. More formally,M can be obtained by inte- advection The transport of a physical prop- gratinga surface term at larger in the ADM form erty by entrainment in a moving medium. Wind of the Einstein–Hilbert action, which then adds advects water vapor entrained in the air, for in- to the canonical Hamiltonian. This derivation stance. justifies the terminology. In the same way one can define other (conserved or not) asymptotical advection dominated accretion disks Ac- physical quantities like total electric charge and cretion disks in which the radial transport of gauge charges. See ADM form of the Einstein– heat becomes relevant to the disk structure. The Hilbert action, asymptotic flatness. advection-dominated disk differs from the stan- Adrastea Moon of Jupiter, also designated dard geometrically thin accretion disk model be- JXV. Discovered by Jewitt, Danielson, and Syn- cause the energy released by viscous dissipation nott in 1979, its orbit lies very close to that is not radiated locally, but rather advected to- of Metis, with an eccentricity and inclination ward the central star or black hole. As a conse- © 2001 by CRC Press LLC African waves quence, luminosity of the advection dominated affine connection A non-tensor object which disk can be much lower than that of a standard has to be introduced in order to construct the co- α thin accretion disk. Advection dominated disks variant derivatives of a tensor. Symbol: : . βγ are expected to form if the accretion rate is above Under the general coordinate transformation µ µ  µ µ the Eddington limit, or on the other end, if the x −→x =x +ξ (x) the affine connection accretion rate is very low. Low accretion rate, possesses the following transformation rule: advection dominated disks have been used to   α ν λ α 2 τ  ∂x ∂x ∂x ∂x ∂ x µ model the lowest luminosity active galactic nu- α : = : +       βγ νλ µ β γ τ β γ clei, the galactic center, and quiescent binary ∂x ∂x ∂x ∂x ∂x ∂x systems with a black hole candidate. See active µ ...µ A 1 l while for an arbitrary tensorT =T one ν ...ν 1 k galactic nuclei, black hole, Eddington limit. has α  α  ν 1 1 l ∂x ∂x ∂x α ...α advective heat transfer (or advective heat  l 1 T = ... β ...β   µ µ β  1 k 1 l 1 transport) Transfer of heat by mass move- ∂x ∂x ∂x ν k ment. Use of the term does not imply a par- ∂x µ ...µ 1 l ... T ν ...ν β 1 k ticular driving mechanism for the mass move- k ∂x ment such as thermal buoyancy. Relative to a The non-tensor form of the transformation of reference temperature T , the heat flux due to 0 affine connection guarantees that for an arbitrary material of temperatureT moving at speedv is αβ...γ tensorT its covariant derivative ρν...α q=vρc(T −T ), whereρ andc are density 0 and specific heat, respectively. αβ...γ αβ...γ α σβ...γ ∇ T = T +: T +... µ ρν...α ρν...α,µ σµ ρν...α σ αβ...γ −: T −... aeolian See eolian. ρµ σν...α is also a tensor. (Here the subscript “µ ” means aerosol Small size (0.01 to 10 µ m), rela- µ ∂/∂X .) Geometrically the affine connection tively stable suspended, colloidal material, ei- and the covariant derivative define the paral- ther natural or man-made, formed of solid par- lel displacement of the tensor along the given ticles or liquid droplets, organic and inorganic, smooth path. The above transformation rule and the gases of the atmosphere in which these leaves a great freedom in the definition of affine α particles float and disperse. Haze, most smokes, connection because one can safely add to: βγ and some types of fog and clouds are aerosols. any tensor. In particular, one can provide the Aerosols in the troposphere are usually removed α α symmetry of the affine connection: =: βγ γβ by precipitation. Their residence time order (which requires torsion tensor = 0) and also is from days to weeks. Tropospheric aerosols metricity of the covariant derivative∇ g = 0. µ αβ can affect radiation processes by absorbing, re- In this case, the affine connection is called the flecting, and scattering effects, and may act Cristoffel symbol and can be expressed in terms as Aitken nuclei. About 30% of tropospheric of the sole metric of the manifold as aerosols are created by human activities. In the 1 stratosphere, aerosols are mainly sulfate parti- α αλ : = g ∂ g +∂ g −∂ g β γλ γ βλ λ βγ βγ 2 cles resulting from volcanic eruptions and usu- ally remain there much longer. Aerosols in the See covariant derivative, metricity of covariant stratosphere may reduce insolation significantly, derivative, torsion. which is the main physics factor involved in climatic cooling associated with volcanic erup- African waves During the northern hemi- tions. sphere summer intense surface heating over the Sahara generates a strong positive temperature aesthenosphere Partially melted layer of the gradient in the lower troposphere between the ◦ Earth lying below the lithosphere at a depth of equator and about 25 N. The resulting easterly 80 to 100 km, and extending to approximately thermal wind creates a strong easterly jet core ◦ 200 km depth. near 650 mb centered near 16 N. African waves © 2001 by CRC Press LLC afternoon cloud (Mars) are the synoptic scale disturbances that are ob- airfoil probe A sensor to measure oceanic served to form and propagate westward in the turbulence in the dissipation range. The probe cyclonic shear zone to the south of this jet core. is an axi-symmetric airfoil of revolution that Occasionally African waves are progenitors of senses cross-stream velocity fluctuationsu = tropical storms and hurricanes in the western u of the free stream velocity vector W (see fig- Atlantic. The average wavelength of observed ure). Airfoil probes are often mounted on verti- African wave disturbance is about 2500 km and cally moving dissipation profilers. The probe’s the westward propagation speed is about 8 m/s. output is differentiated by analog electronic cir- cuits to produce voltage fluctuations that are pro- portional to the time rate of change ofu, namely afternoon cloud (Mars) Afternoon clouds ∂u(z)/∂t, where z is the vertical position. If appear at huge volcanos such as Elysium Mons, the profiler descends steadily, then by the Tayler Olympus Mons, and Tharsis Montes in spring transformation this time derivative equals veloc- to summer of the northern hemisphere. After- −1 ity shear ∂u/∂z= V ∂u(z)/∂t. This mi- noon clouds are bright, but their dimension is crostructure velocity shear is used to estimate small compared to morning and evening clouds. the dissipation rate of turbulent kinetic energy. In their most active period from late spring to early summer of the northern hemisphere, they airglow Widely distributed flux predomi- appear around 10h of Martian local time (MLT), nately from OH, oxygen, and neon at an altitude and their normal optical depths reach maximum of 85 to 95 km. Airglow has a brightness of in 14h to 15h MLT. Their brightness seen from order 14 magnitudes per square arcsec. Earth increases as they approach the evening limb. Afternoon clouds show a diurnal vari- air gun An artificial vibration source used ation. Sometimes afternoon clouds at Olym- for submarine seismic exploration and sonic pus Mons and Tharsis Montes form a W-shaped prospecting. The device emits high-pressured cloud together with evening clouds, in which the air in the oceanic water under electric control afternoon clouds are identified as bright spots. from an exploratory ship. The compressed air The altitude of afternoon clouds is higher than is conveyed from a compressor on the ship to the volcanos on which they appear. See evening a chamber which is dragged from the stern. cloud, morning cloud. A shock produced by expansion and contrac- tion of the air in the water becomes a seismic aftershocks Essentially all earthquakes are source. The source with its large capacity and followed by a sequence of “aftershocks”. In low-frequency signals is appropriate for investi- some cases aftershocks can approach the main gation of the deeper submarine structure. An air shock in strength. The decay in the number of gun is most widely used as an acoustic source aftershocks with time has a power-law depen- for multi-channel sonic wave prospecting. dence; this is known as Omori’s law. Airy compensation The mass of an elevated mountain range is “compensated” by a low den- ageostrophic flow The flow that is not sity crustal root. See Airy isostasy. geostrophic. See geostrophic approximation. Airy isostasy An idealized mechanism of agonic line A line of zero declination. See isostatic equilibrium proposed by G.B. Airy in declination. 1855, in which the crust consists of vertical rigid rock columns of identical uniform density ρ c air The mixture of gases near the Earth’s sur- independently floating on a fluid mantle of a face, composed of approximately 78% nitrogen, higher densityρ . If the reference crustal thick- m 21% oxygen, 1% argon, 0.035% carbon dioxide, ness is H , represented by a column of height variable amounts of water vapor, and traces of H , the extra mass of a “mountain” of heighth other noble gases, and of hydrogen, methane, must be compensated by a low-density “moun- nitrous oxide, ozone, and other compounds. tain root” of lengthb. The total height of the © 2001 by CRC Press LLC Alba Patera record of surface waves. An Airy phase appears at a transition between normal dispersion and re- verse dispersion. For continental paths an Airy phase with about a 20-sec period often occurs, while for oceanic paths an Airy phase with 10- to 15-sec period occurs, reflecting the thickness of the crust. Airy wave theory First-order wave theory for water waves. Also known as linear or first- order theory. Assumes gravity is the dominant restoring force (as opposed to surface tension). Named after Sir George Biddell Airy (1801– 1892). Aitken, John (1839–1919) Scottish physi- cist. In addition to his pioneering work on atmo- spheric aerosol, he investigated cyclones, color, and color sensations. Aitken nucleus count One of the oldest and most convenient techniques for measuring the concentrations of atmospheric aerosol. Satu- rated air is expanded rapidly so that it becomes supersaturated by several hundred percent with respect to water. At these high supersaturations water condenses onto virtually all of the aerosol to form a cloud of small water droplets. The concentration of droplets in the cloud can be de- termined by allowing the droplets to settle out onto a substrate, where they can be counted ei- ther under a microscope, or automatically by optical techniques. The aerosol measured with an Aitken nucleus counter is often referred to as the Aitken nucleus count. Generally, Aitken nu- cleus counts near the Earth’s surface range from 3 −3 average values on the order of 10 cm over Geometry of the airfoil probe,α is the angle of attack 4 −3 the oceans, to 10 cm over rural land areas, to of the oncoming flow. 5 −3 10 cm or higher in polluted air over cities. rock column representing the mountain area is Alba Patera A unique volcanic landform on thenh+H+b. Hydrostatic equilibrium below Mars that exists north of the Tharsis Province. the mountain root requires(ρ −ρ )b=ρ h. m c c It is less than 3 km high above the surround- ing plains, the slopes of its flanks are less than Airy phase When a dispersive seismic wave a quarter of a degree, it has a diameter of propagates, the decrease of amplitude with ≈ 1600 km, and it is surrounded by an addi- increasing propagation distance for a period tional 500 km diameter annulus of grabens. Its whose group velocity has a local minimum is size makes it questionable that it can properly be smaller than that for other periods. The wave called a volcano, a name that conjures up an im- corresponding to the local minimum is referred age of a distinct conical structure. Indeed from to as an Airy phase and has large amplitude on a the ground on Mars it would not be discernible © 2001 by CRC Press LLC albedo because the horizontal dimensions are so large. cosmic ray ions with particles of the upper at- Nevertheless, it is interpreted asa volcanic struc- mosphere. See neutron albedo. ture on the basis that it possesses two very large albedo of a surface For a body of water, summit craters from which huge volumes of lava the ratio of the plane irradiance leaving a water have erupted from the late Noachian until the body to the plane irradiance incident on it; it is early Amazonian epoch; hence, it might be the the ratio of upward irradiance to the downward largest volcanic feature on the entire planet. The irradiance just above the surface. exact origin is unclear. Possible explanations include deep seated crustal fractures produced albedo of single scattering The probability at the antipodes of the Hellas Basin might have of a photon surviving an interaction equals the subsequently provided a conduit for magma to ratio of the scattering coefficient to the beam reach the surface; or it formed in multiple stages attenuation coefficient. of volcanic activity, beginning with the emplace- ment of a volatile rich ash layer, followed by Alcyone Magnitude 3 type B7 star at RA more basaltic lava flows, related to hotspot vol- ◦  03h47m, dec +24 06 ; one of the “seven sisters” canism. of the Pleiades. albedo Reflectivity of a surface, given by Aldebaran Magnitude 1.1 star at RA I/F , whereI is the reflected intensity, andπF ◦  04h25m, dec +16 31 . is the incident flux. The Bond albedo is the frac- tion of light reflected by a body in all directions. Alfvénic fluctuation Large amplitude fluc- The bolometric Bond albedo is the reflectivity tuations in the solar wind are termed Alfvénic integrated over all wavelengths. The geomet- fluctuations if their properties resemble those ric albedo is the ratio of the light reflected by a of Alfvén waves (constant density and pres- body (at a particular wavelength) at zero phase sure, alignment of velocity fluctuations with the angle to that reflected by a perfectly diffusing magnetic-field fluctuations; see Alfvén wave). disk with the same radius as the body. Albedo In particular, the fluctuationsδv in the solar sowi ranges between 0 (for a completely black body wind velocity andδB in magnetic field obey the which absorbs all the radiation falling on it) to relation 1 (for a perfectly reflecting body). δB δv =±√ sowi 4πC The Earth’s albedo varies widely based on the status and colors of earth surface, plant cov- with C being the solar wind density. Note ers, soil types, and the angle and wavelength of that in the definition of Alfvénic fluctuations or the incident radiation. Albedo of the earth atmo- Alfvénicity, the changes in magnetic field and sphere system, averaging about 30%, is the com- solar wind speeds are vector quantities and not bination of reflectivity of earth surface, cloud, the scalar quantities used in the definition of the and each component of atmosphere. The value Alfvén speed. for green grass and forest is 8 to 27%; over 30% Obviously, in a real measurement it will be for yellowing deciduous forest in autumn; 12 to impossible to find fluctuations that exactly fulfill 18% for cities and rock surfaces; over 40% for the above relation. Thus fluctuations are clas- light colored rock and buildings; 40% for sand; sified as Alfvénic if the correlation coefficient up to 90% for fresh flat snow surface; for calm betweenδv andδB is larger than 0.6. The sowi ocean, only 2% in the case of vertically inci- magnetic field and velocity are nearly always dent radiation but can be up to 78% for lower observed to be aligned in a sense corresponding incident angle radiation; 55% average for cloud to outward propagation from the sun. layers except for thick stratocumulus, which can be up to 80%. Alfvénicity See Alfvénic fluctuation. albedo neutrons Secondary neutrons ejected Alfvén layer Term introduced in 1969 by (along with other particles) in the collision of Schield, Dessler, and Freeman to describe the © 2001 by CRC Press LLC Algol system region in the nightside magnetosphere where ory, without requiring linearization of the the- region 2 Birkeland currents apparently origi- ory. nate. Magnetospheric plasma must be (to a high In magnetohydrodynamics, the characteris- degree of approximation) charge neutral, with tic propagation speed is the Alfvén speedC = A √ equal densities of positive ion charge and neg- B/ 4πρ (cgs units), whereB is the mean mag- ative electron charge. If such plasma convects netic field and ρ is the gas density. The ve- earthward under the influence of an electric field, locity and magnetic fluctuations are related by √ as long as the magnetic field stays constant (a fair δV = ∓δB/ 4πρ; the upper (lower) sign ap- approximation in the distant tail) charge neutral- plies to energy propagation parallel (antiparal- ity is preserved. lel) to the mean magnetic field. In collisionless kinetic theory, the equation for the characteristic Near Earth, however, the magnetic field be- propagation speed is generalized to gins to be dominated by the dipole-like form of the main field generated in the Earth’s core, and 4π 2 2 the combined drift due to both electric and mag- V =C 1 + P −P −E , ⊥  A A 2 B netic fields tends to separate ions from electrons, steering the former to the dusk side of Earth whereP andP are, respectively, the pressures ⊥  and the latter to the dawn side. This creates transverse and parallel to the mean magnetic Alfvén layers, regions where those motions fail field, to satisfy charge neutrality. Charge neutrality 1 2 E = ρ (V ) . α α is then restored by electrons drawn upwards as ρ α the downward region 2 current, and electrons ρ is the mass density of charge speciesα, and α dumped into the ionosphere (plus some ions V is its relative velocity of streaming rela- α drawn up) to create the corresponding upward tive to the plasma. Alfvén waves propagating currents. through a plasma exert a force on it, analogous to radiation pressure. In magnetohydrodynam- Alfvén shock See intermediate shock. 2 ics the force per unit volume is −∇δB /8π, 2 where δB is the mean-square magnetic fluc- Alfvén speed In magnetohydrodynamics, the tuation amplitude. It has been suggested that speed of propogation of transverse waves in a Alfvén wave radiation pressure may be impor- direction parallel to the magnetic field B. In SI √ tant in the acceleration of the solar wind, as well units,v =B/ (ρµ ) whereB is the magnitude A as in processes related to star formation, and in of the magnetic field tesla,ρ is the fluid density other astrophysical situations. 3 kg/meter , and µ is the magnetic permeability In the literature, one occasionally finds the Hz/meter. term “Alfvén wave” used in a looser sense, re- ferring to any mode of hydromagnetic wave. See Alfvén’s theorem See “frozen-in” magnetic hydromagnetic wave, magnetoacoustic wave. field. Algol system A binary star in which mass Alfvén wave A hydromagnetic wave mode transfer has turned the originally more massive in which the direction (but not the magnitude) of component into one less massive than its ac- the magnetic field varies, the density and pres- creting companion. Because the time scale of −2 sure are constant, and the velocity fluctuations stellar evolution scales asM , these systems, are perfectly aligned with the magnetic-field where the less massive star is the more evolved, fluctuations. In the rest frame of the plasma, were originally seen as a challenge to the theory. energy transport by an Alfvén wave is directed Mass transfer resolves the discrepancy. Many along the mean magnetic field, regardless of Algol systems are also eclipsing binaries, includ- the direction of phase propagation. Large- ing Algol itself, which is, however, complicated amplitude Alfvén waves are predicted both by by the presence of a third star in orbit around the equations of magnetohydrodynamics and the eclipsing pair. Mass transfer is proceeding the Vlasov–Maxwell collisionless kinetic the- on the slow or nuclear time scale. © 2001 by CRC Press LLC Allan Hills meteorite Allan Hills meteorite A meteorite found in magnetic field and fluid velocities are divided Antarctica in 1984. In August of 1996, McKay into mean parts which vary slowly if at all and et al. published an article in the journal Sci- fluctuating parts which represent rapid varia- ence, purporting to have found evidence of an- tions due to turbulence or similar effects. The cient biota within the Martian meteorite ALH fluctuating velocities and magnetic fields inter- 84001. These arguments are based upon chem- act in a way that may, on average, contribute to ically zoned carbonate blebs found on fracture the mean magnetic field, offsetting dissipation surfaces within a central brecciated zone. It has of the mean field by effects such as diffusion. been suggested that abundant magnetite grains This is parameterized as a relationship between in the carbonate phase of ALH 84001 resem- a mean electromotive forceGdue to this effect ble those produced by magnetotactic bacteria, and an expansion of the spatial derivatives of the in both size and shape. mean magnetic field B : 0 ∂B j 0 allowed orbits See Störmer orbits. G=α B +β +··· i ij 0j ijk ∂x k all sky camera A camera (photographic, or with the first term on the right-hand side, usually more recently, TV) viewing the reflection of the assumed to predominate, termed the “alpha ef- night sky in a convex mirror. The image is fect”, and the second term sometimes neglected. severely distorted, but encompasses the entire ∇× is then inserted into the induction equa- sky and is thus very useful for recording the dis- tion for the mean field. For simplicity,α is often tribution of auroral arcs in the sky. assumed to be a scalar rather than a tensor in mean-field dynamo simulations (i.e., =αB ). 0 alluvial Related to or composed of sediment For α to be non-zero, the fluctuating velocity deposited by flowing water (alluvium). field must, when averaged over time, lack cer- tain symmetries, in particular implying that the alluvial fan When a river emerges from a time-averaged helicity (u·∇× u) is non-zero. mountain range it carries sediments that cover Physically, helical fluid motion can twist loops the adjacent plain. These sediments are de- into the magnetic field, which in the geodynamo posited on the plain, creating an alluvial fan. is thought to allow a poloidal magnetic field to be created from a toroidal magnetic field (the op- alongshore sediment transport Transport posite primarily occurring through theω effect). of sediment in a direction parallel to a coast. See magnetohydrodynamics. Generally refers to sediment transported by waves breaking in a surf zone but could include 4 alpha particle The nucleus of a He atom, other processes such as tidal currents. composed of two neutrons and two protons. Alpha Centauri A double star (α-Centauri Altair Magnitude 0.76 class A7 star at RA h m s ◦  A, B), at RA 6 45 9 , declination 19h50.7m, dec+8 51 . ◦   −16 42 58 , with visual magnitude −0.27. Both stars are of type G2. The distance toα- alternate depths Two water depths, one sub- Centauri is approximately 1.326 pc. In addition critical and one supercritical, that have the same there is a third, M type, star (Proxima Centauri) specific energy for a given flow rate per unit of magnitude 11.7, which is apparently bound width. to the system (period approximately 1.5 million years), which at present is slightly closer to Earth altitude The altitude of a point (such as a than the other two (distance = 1.307 pc). star) is the angle from a horizontal plane to that ◦ point, measured positive upwards. Altitude 90 ◦ α effect A theoretical concept to describe is called the zenith (q.v.), 0 the horizontal, and ◦ a mechanism by which fluid flow in a dynamo −90 the nadir. The word “altitude” can also such as that in the Earth’s core maintains a mag- be used to refer to a height, or distance above netic field. In mean-field dynamo theory, the or below the Earth’s surface. For this usage, see © 2001 by CRC Press LLC Am star elevation. Altitude is normally one coordinate trality in the ionosphere, in the region above the of the three in the topocentric system of coordi- E-layer where collisions are rare. If that field did nates. See also azimuth and zenith angle. not exist, ions and electrons would each set their own scale height — small for the ions (mostly + Amalthea Moon of Jupiter, also designated O ), large for the fast electrons — and densities JV. Discovered by E. Barnard in 1892, its or- of positive and negative charge would not match. bit has an eccentricity of 0.003, an inclination The ambipolar field pulls electrons down and ◦ ◦ −1 of 0.4 , a precession of 914.6 yr , and a ions up, assuring charge neutrality by forcing 5 semimajor axis of 1.81× 10 km. Its size is both scale heights to be equal. 18 135× 83× 75 km, its mass, 7.18× 10 kg, and −3 its density 1.8 g cm . It has a geometric albedo Amor asteroid One of a family of minor of 0.06 and orbits Jupiter once every 0.498 Earth planets with Mars-crossing orbits, in contrast to days. Its surface seems to be composed of rock most asteroids which orbit between Mars and and sulfur. Jupiter. There are 231 known members of the Amor class. Amazonian Geophysical epoch on the planet Mars, 0 to 1.8 Gy BP. Channels on Mars give ampere Unit of electric current which, if evidence of large volumes of water flow at the maintained in two straight parallel conductors end of the Hesperian and the beginning of the of infinite length, of negligible circular cross- Amazonian epoch. section, and placed 1 m apart in vacuum, pro- duces between these conductors a force equal to −7 Ambartsumian, Viktor Amazaspovich 2× 10 N/m of length. (1908–1996) Soviet and Armenian astrophysi- cist, founder and director of Byurakan As- Ampere’s law If the electromagnetic fields trophysical Observatory. Ambartsumian was are time independent within a given region, then born in Tbilisi, Georgia, and educated at the within the region it holds that the integral of the Leningrad State University. His early work magnetic field over a closed path is proportional was in theoretical physics, in collaboration with to the total current passing through the surface D.D. Ivanenko. Together they showed that limited by the closed path. In CGS units the con- atomic nuclei cannot consist of protons and elec- stant of proportionality is equal to 4π divided trons, which became an early indication of the by the speed of light. Named after A.M. Ampere existence of neutrons. The two physicists also (1775–1836). constructed an early model of discrete space- time. amphidrome (amphidromic point) A sta- tionary point around which tides rotate in a coun- Ambartsumian’s achievements in astrophys- ics include the discovery and development of terclockwise (clockwise) sense in the northern invariance principles in the theory of radiative (southern) hemisphere. The amplitude of a transfer, and advancement of the empirical ap- tide increases with distance away from the am- proach in astrophysics, based on analysis and phidrome, with the amphidrome itself the point interpretation of observational data. Ambart- where the tide vanishes nearly to zero. sumian was the first to argue that T Tauri stars are very young, and in 1947, he discovered stel- Am star A star of spectral typeA as deter- lar associations, large groups of hot young stars. mined by its color but with strong heavy metal He showed that the stars in associations were lines (copper, zinc, strontium, yttrium, barium, born together, and that the associations them- rare earths atomic number = 57 to 71) in its selves were gravitationally unstable and were spectrum. These stars appear to be slow ro- expanding. This established that stars are still tators. Many or most occur in close binaries forming in the present epoch. which could cause slow rotaton by tidal locking. This slow rotation suppresses convection and al- ambipolar field An electric field amounting lows chemical diffusion to be effective, produc- to several volts/meter, maintaining charge neu- ing stratification and differentiation in the outer © 2001 by CRC Press LLC anabatic wind layers of the star, the currently accepted expla- (retardation strain), and part of it becomes per- nation for their strange appearance. manent strain (inelastic strain). Anelastic defor- mation is usually controlled by stress, pressure, anabatic wind A wind that is created by air temperature, and the defect nature of solids. flowing uphill, caused by the day heating of the Two examples of anelastic deformation are the mountain tops or of a valley slope. The opposite attenuation of seismic waves with distance and of a katabatic wind. the post-glacial rebound. analemma The pattern traced out by the po- anemometer An instrument that measures sition of the sun on successive days at the same windspeed and direction. Rotation anemome- local time each day. Because the sun is more ters use rotating cups, or occasionally pro- northerly in the Northern summer than in North- pellers, and indicate wind speed by measuring ern winter, the pattern is elongated North-South. rotation rate. Pressure-type anemometers in- It is also elongated East-West by the fact that clude devices in which the angle to the verti- civil time is based on the mean solar day. How- cal made by a suspended plane in the wind- ever, because the Earth’s orbit is elliptical, the stream is an indication of the velocity. Hot wire true position of the sun advances or lags be- anemometers use the efficiency of convective hind the expected (mean) position. Hence, the cooling to measure wind speed by detecting tem- pattern made in the sky resembles a figure “8”, perature differences between wires placed in the with the crossing point of the “8” occurring near, wind and shielded from the wind. Ultrasonic but not at, the equinoxes. The sun’s position is anemometers detect the phase shifting of sound “early” in November and May, “late” in January reflected from moving air molecules, and a simi- and August. The relation of the true to mean mo- lar principle applies to laser anemometers which tion of the sun is called the equation of time. See measure infrared light reemitted from moving equation of time, mean solar day. air molecules. Ananke Moon of Jupiter, also designated angle of repose The maximum angle at JXII. Discovered by S. Nicholson in 1951, its which a pile of a given sediment can rest. Typi- orbit has an eccentricity of 0.169, an inclination cally denoted byφ in geotechnical and sediment ◦ 7 of 147 , and a semimajor axis of 2.12×10 km. transport studies. Its radius is approximately 15 km, its mass, 16 −3 3.8× 10 kg, and its density 2.7 g cm . Its angle-redshift test A procedure to determine geometric albedo is not well determined, and it the curvature of the universe by measuring the orbits Jupiter (retrograde) once every 631 Earth angle subtended by galaxies of approximately days. equal size as a function of redshift. A galaxy of sizeD, placed at redshiftz will subtend an angle Andromeda galaxy Spiral galaxy (Messier object M31), the nearest large neighbor galaxy, 2 2 DI (1+z) o approximately 750 kpc distant, centered at RA θ = −1 h m ◦  2cH 00 42.7 , dec+41 16 , Visual magnitude 3.4 , o ◦ ◦    −1 angular size approximately 3 by 1 . 1/2 I z+(I − 2) (I z+ 1) − 1 , o o o anelastic deformation Solids creep when a sufficiently high stress is applied, and the strain in a universe with mean densityI and no cos- o is a function of time. Generally, the response of mological constant. In models with cosmolog- a solid to a stress can be split into two parts: elas- ical constant, the angle also varies in a defined tic part or instantaneous part, and anelastic part manner but cannot be expressed in a closed form. or time-dependent part. The strain contributed However, since galaxies are not “standard rods” by the anelastic part is called anelastic deforma- and evolve with redshift, this test has not been tion. Part of the anelastic deformation can be successful in determining cosmological param- recovered with time after the stress is removed eters. © 2001 by CRC Press LLC anomalistic month Ångström (Å) A unit of length used in spec- anisotropic turbulence See isotropic turbu- troscopy, crystallography, and molecular struc- lence. −10 ture, equal to 10 m. anisotropic universe A universe that ex- angular diameter distance Distance of a pands at different rates in different directions. galaxy or any extended astronomical object es- The simplest example is Kasner’s model (1921) timated by comparing its physical size to the an- which describes a space that has an ellipsoidal gle subtended in the sky: ifD is the diameter of rate of expansion at any moment in time. More- the galaxy andδ the angle measured in the sky, over, the degree of ellipticity changes with time. thend = D/ tanδ D/δ. For a Friedmann A The generic Kasner universe expands only along model with density I in units of the critical o two perpendicular axes and contracts along the density, and zero cosmological constant, the an- third axis. gular diameterd of an object at redshiftz can A be given in closed form: anisotropy The opposite of isotropy (invari- ance under rotation), i.e., variation of properties −1 2cH o d = under rotation. For example, if a rock has a fab- A 2 2 I (1 +z) o ric such as layering with a particular orientation,    1/2 then phases of seismic waves may travel at dif- I z+(I − 2) (I z+ 1) − 1 . o o o ferent speeds in different directions through the rock, according to their alignment with the fab- Other operational definitions of distance can be ric. The wave speed along an axis varies when made (see luminosity distance) depending on the axis is rotated through the rock with respect the intrinsic (assumed to be known) and the ob- to the fabric, i.e., it is anisotropic. In terms of served properties to be compared. the material properties of the rock, this would be associated with an elasticity tensor that varies angular momentum L = r × p, where × under rotation. This occurs in the real Earth: for indicates the vector cross product, r is the radius example, wave speeds are observed to be faster vector from an origin to the particle, and p is the in the upper mantle under the ocean in the di- momentum of the particle. L is a pseudovector rection perpendicular to the mid-ocean ridges. whose direction is given by r, p via the right- The Earth’s inner core has been determined to hand rule, and whose magnitude is be anisotropic, with (to a first approximation) L=rp sinθ, faster wave speeds parallel to the Earth’s ro- tation axis than in directions perpendicular to whereθ is the angle between r and p. For a body it. Many other physical properties may also be or system of particles, the total angular momen- anisotropic, such as magnetic susceptibility, dif- tum is the vectorial sum of all its particles. In fusivity, and turbulence. this case the position is generally measured from the center of mass of the given body. See pseu- annual flood The maximum discharge peak dovector, right-hand rule, vector cross product. flow during a given water year (October 1 through September 30) or annual year. angular velocity (ω) The angle through which a body rotates per unit time; a pseudovec- annular eclipse A solar eclipse in which the tor with direction along the axis given by the angular size of the moon is slightly too small right-hand rule from the rotation. to obscure the entire solar photosphere. As a result, a ring (“annulus”) of visible photosphere anisotropic A material whose properties surrounds the dark central shadow of the moon. (such as intrinsic permeability) vary according Annular eclipse occurs when the moon is near to the direction of flow. apogee, giving it a smaller angular size. anisotropic scattering Scattering that is not spherically symmetric. anomalistic month See month. © 2001 by CRC Press LLC anomalistic year anomalistic year See year. body and rose through the crust in a semi-molten state. Anorthosites are rare on Earth, but appear anomalous resistivity For a fully ionized to be more common on the moon. See igneous. collision-dominated plasma, such as the solar corona, the extremely low value of the classical anoxia The condition arising from insuffi- resistivity ensures that the rate of energy release cient ambient oxygen to support biological res- is negligible since the field lines are prevented piration, or the effect of such lack. from diffusing through the plasma. In a tur- ◦  bulent plasma, the resistivity can be enhanced Antarctic circle The latitude 66 32S. South via the correlation of particles over length scales of this line the sun does not rise on the southern much larger than the usual plasma length scale, winter solstice and does not set on the day of the the Debye length. This increases the colli- southern summer solstice. sion frequency and, consequently, the resistivity. This turbulently enhanced resistivity is known as antarctic circumpolar current South Ocean anomalous resistivity. current circling the Antarctic continent east- ward. The largest oceanic current in terms of anomaly See mean anomaly, true anomaly. volume. Also called the West Wind Drift. Spans ◦ ◦ 40 to 60 South. Very close to the Antarctic anomaly, South Atlantic The region above continent is the East Wind Drift, driven by pre- the southern Atlantic Ocean, in which the radi- vailing easterly winds near the continent. ation belt descends to heights lower than else- where, so that near-earth satellites, nominally Antarctic ozone depletion A rapid and ac- below the radiation belt, are likely to encounter celerating decrease in the ozone over Antarc- peak radiation levels there. tica each September and October, as the so- The “anomaly” is caused by the non-dipole called “ozone hole”, which is due to the chem- components of the main magnetic field of the ical activity of the chlorine atoms contained in earth, which create a region of abnormally weak the chlorofluorocarbons (CFCs or “Freons”). It magnetic field there (in the eccentric dipole was first reported on May 16, 1985, by J.C. Far- model of the Earth’s field, the dipole is furthest man et al. from the British Antarctic Survey pub- away from that region). lished in the British journal Nature. Field cam- Each ion or electron trapped along a field line paigns incorporating remote sensing, in situ and satellite observations, have now clearly demon- in the Earth’s field has a mirroring field intensity strated that man-made CFCs and some other B at which its motion along the line is turned m halogenated industrial compounds are responsi- around. Such particles also drift, moving from ble for this dramatic loss of ozone. These chemi- one field line to the next, all the way around the cals are released into the atmosphere where their Earth. If in this drift motion the mirror point long lifetimes (50 to 100 years) allow them to where the particle is turned back (and where the be transported to the middle and upper strato- field intensity equalsB ) passes above the South m Atlantic anomaly, it probably reaches an altitude sphere, where they can be decomposed by short- lower there than anywhere else. The radiation wave solar radiation to release their chlorine belt thus extends lower in this region than else- and bromine atoms. These free radicals are ex- where, and the loss of belt particles by collisions tremely reactive and can destroy ozone readily, with atmospheric molecules is likely to occur but in most parts of the atmosphere they react to there. form harmless “reservoir” compounds. In the Antarctic, however, very low temperatures in anorthosite Mafic igneous rock type that the late winter and early spring stratosphere per- consists predominantly of the mineral plagio- mit the formation of natural Polar Stratospheric clase (silicates of feldspar group) that seems to Cloud (PSC) particles, which provide sites for have differentiated at high temperature at the surface reactions in which the reservoir halogens crust-mantle boundary, where plagioclase crys- revert to ozone-destroying radicals with the help tallized before separating from the main magma of sunlight. The severity of the ozone loss is © 2001 by CRC Press LLC anticyclone also due, in part, to the special meteorology of from observations restricted to a small sample, it the Antarctic winter stratosphere, which isolates is essential to know whether the sample should the ozone hole, preventing the replenishment of be considered to be biased and, if so, how. The ozone and the dilution of ozone destroying com- anthropic principle provides guidelines for tak- pounds. Thus, the ozone hole results from the ing account of the kind of bias that arises from combination of a range of special local and sea- the observer’s own particular situation in the sonal conditions with man-made pollution; its world. For instance, the Weak Anthropic Prin- appearance in recent years simply corresponds ciple states that as we exist, we occupy a special to the build-up of anthropogenic halogenated place of the universe. Since life as we know it re- gases in the atmosphere. quires the existence of heavy elements such as C and O, which are synthesized by stars, we could The production of CFCs and some other com- not have evolved in a time less than or of the or- pounds potentially damaging to ozone is now der of the main sequence lifetime of a star. This limited by the Montreal Protocol and its amend- principle can be invoked to explain why the age ments. However, the lifetimes of these gases of astronomical objects is similar to the Hubble are long, and although it is thought that strato- time. This time scale would represent the lapse spheric chlorine levels will peak in the next few of time necessary for life to have evolved since years, recovery of the ozone hole may not be the Big Bang. On the other hand, in the Steady detectable for a number of years, and full recov- State Cosmology, where the universe has no ori- ery, to pre-ozone hole conditions, may not occur gin in time, the coincidence mentioned above until the middle of the twenty-first century. has no “natural” explanation. Antarctic ozone hole A large annual de- In the more controversial strong version, crease in the ozone content of the ozone layer the relevant anthropic probability distribution over the Antarctic region during the southern is supposed to be extended over an ensemble hemisphere spring. Discovered in 1985, the of cosmological models that are set up with a ozone hole presumably appeared in the early range of different values of what, in a particular 1980s and continued to increase in severity, size, model, are usually postulated to be fundamen- and duration through the 1990s. In recent years, tal constants (such as the well-known example up to two-thirds of the total amount of ozone of the fine structure constant). The observed has been lost by mid-October, largely as a result values of such constants might be thereby ex- of losses of over 90% in the layer between 14 plicable if it could be shown that other values and 22 km where a large fraction of the ozone is were unfavorable to the existence of anthropic normally found. The onset of the ozone losses observers. occurs in September, and the ozone hole usually Thus the Strong Anthropic Principle states recovers by the end of November. that the physical properties of the universe are as they are because they permit the emergence Antarctic Zone In oceanography, the region of life. This teleological argument tries to ex- in the Southern Ocean northward of the Con- plain why some physical properties of matter tinental Zone (which lies near the continent). seem so fine tuned as to permit the existence of It is separated from the Continental Zone by a life. Slight variations in nuclear cross-sections distinct oceanographic front called the Southern could have inhibited the formation of heavy el- Antarctic Circumpolar Current front. ements in stars. A different fine-structure con- stant would lead to a different chemistry and Antares 0.96 magnitude star, of spectral type ◦   presumably life would not exist. M1, at RA 16h 29m 24.3, dec−26 25 55 . anthropic principle The observation that hu- anticyclone A wind that blows around a high mankind (or other sentient beings) can observe pressure area, in the opposite sense as the Earth’s the universe only if certain conditions hold to al- rotation. This results in a clockwise rotation in low human (or other sentient) existence. When- the Northern Hemisphere and counterclockwise ever one wishes to draw general conclusions in the Southern Hemisphere. © 2001 by CRC Press LLC