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Dictionary of Geophysics, Astrophysic, and Astronomy.pdf

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Callan–Rubakov effect

cabbeling Mixing mechanism resulting in buoyancy effects due to the non-linear relation between temperature, salinity, and density. If mixing occurs between two water masses with the same potential density but different salinities S and temperatures , the resulting water will be denser than the original water masses due to variations of the thermal expansivity α and the saline contraction coefﬁcient β with and S. In the ﬁgure the two initial water types are represented by the labels A and B. The water type that results from mixing will have a density that lies on the straight line between A and B and, therefore, will be denser. The effect is particularly strong at low temperatures. Cabbeling leads to a diapycnal density (mass) ﬂux, although the original mixing may be purely isopycnal.

	4
	3
				.4
	2			27						.8
C]	2					.6				27
°					B
[
Temperature	1										28
	0	27	. 4						8
		27					27	.
					.6			.
Potential	1			27	.6
				27

	2									28
	2		A
			A
	3
	4		34.2		34.4		34.6			34.8	35
	34		34.2		34.4		34.6			34.8	35
					Salinity [0/				]
							00
Contours of potential density σθ as a function of salinity

and potential temperature.

cable A horizontal unit of length used in ocean navigation, equal to 100 fathoms, equal to 600 feet, equal to 182.88 meters; approximately one tenth of a Nautical mile. See nautical mile.

CAI C alcium-, a luminum-rich i nclusion found in chondritic meteorites. Usually of mil-

limeter or centimeter size and roughly spherical, they are depleted in volatiles relative to solar composition and display a melt rim, which apparently formed in an episode of intense heating followed by rapid quenching.

caldera The central crater of a volcano. The caldera is formed when magma from a chamber in or under the volcanic structure is removed, either by eruption onto the surface or by withdrawal to another underground location. This removal of the magma removes the method of support for the overlaying crust, and the surface collapses to create the caldera. Volcanos often display multiple overlapping calderas, indicating that several episodes of magma injection and withdrawal have occurred over the volcano’s history.

calendar A system of reckoning time in days and years enumerated according to cyclic patterns. Examples are the Julian calendar and the Gregorian calendar.

California current A cold ocean current ﬂowing southeastward down the west coast of the United States and Baja California.

California nebula NGC1499: Very large nebula in the constellation Perseus, approximately 3◦ in length; the site of substantial star formation with strong hydrogen emission.

Callan–Rubakov effect Baryon violating processes have a very low probability of occurring at ordinary energies, since they require the exchange of very massive (grand uniﬁcation scale) gauge particles. These particles are actually part of the structure of gauged monopoles, which therefore can act as seeds for enhancing processes such as baryogenesis.

For a monopole of mass mM , the interaction probability with a proton say, would be proportional to m−M2 which, for a grand uniﬁed model, is far too small to be cosmologically or astrophysically relevant. However, magnetic monopoles eventually exert an attractive force on all particles having a magnetic moment, and this enhances the interaction probability, as was discovered by C.G. Callan and V.A. Rubakov in the early 1980s. As it turns out, the result-

Callisto

ing probability is as high as that characteristic of strong interactions and could, therefore, have a signiﬁcant impact on cosmology. See cosmic topological defect, monopole, t’Hooft– Polyakov monopole.

Callisto Moon of Jupiter, also designated JIV. Discovered by Galileo in 1610, it is one of the four Galilean satellites. Its orbit has an eccentricity of 0.007, an inclination of 0.51◦, a precession of 0.643◦ yr−1, and a semimajor axis of

1.883 ×106 km. Its radius is 2400 km, its mass, 1.07 × 1023 kg, and its density 1.85 g cm−3. It

has a geometric albedo of 0.20 and orbits Jupiter once every 16.69 Earth days.

calorie The quantity of energy needed to raise the temperature of 1 g of water by 1◦C. The exact equivalence to energy depends on the temperature and pressure at which the measurement is made. The preferred “thermochemical” or “deﬁned” calorie is assigned a value of 4.1840 Joules.

Calypso Moon of Saturn, also designated SXIV. Discovered by Pascu, Smith, and colleagues in 1980, it orbits Saturn in the same orbit as Tethys but trailing it by 60◦. This is one of the two stable Lagrange points in the Saturn-Tethys system. Telesto orbits at the other. Its orbit has a semimajor axis of 2.95 × 105 km. Its size is 17 × 11 × 11 km, but its mass has not been measured. It has a geometric albedo of 0.6 and orbits Saturn once every 1.888 Earth days.

Canary current A cool ocean current ﬂowing southward off the west coast of Portugal and along the northwest coast of Africa.

candela SI unit of luminous intensity. The luminous intensity of a source that emits monochromatic radiation of frequency 540 × 1012 Hz with a radiant intensity of 1/683 watt per steradian.

canonical momentum In classical mechanics, a generalized momentum in principle obtained from a Lagrangian, or if no Lagrangian exists, postulated as one of the independent phase space coordinates in a Hamiltonian system. The Lagrangian deﬁnition of the canonical

momentum pα conjugate to the particular coordinate xα is:

pα	=	∂L	α	=	1 . . . N

		α
		∂ dxdt

where t is the parameter describing the motion (typically the time).

If the Lagrangian is only a function of the parameter (time), the coordinates xα, and their parameter derivatives (time derivatives) dxβ /dt, the Lagrange equations are:

d ∂L			∂L	,

	α	=
dt ∂ dxdt		=	∂xα

which can be read:

dpα = ∂L . dt ∂xα

Notice that if the Lagrangian is quadratic in the velocities dxα/dt, then pα is linear in the dxβ /dt, and the relationship can be inverted to express dxβ /dt as a function of pα. Only if the Lagrangian is homogeneous of degree one in the velocities is such an inversion impossible. See Lagrangian.

canonical transformation	In classical me-
chanics, transformation of variables and of the
Hamiltonian, which preserves the form of the
Hamilton equations. The Hamilton equations
can be written

q˙i	=	∂H/∂pi
p˙j	=	−∂H/∂qj

where H = H (pi , qi , t) is the Hamiltonian. A canonical transformation introduces new coordinates (Qi , Pj ) on phase space and a new Hamiltonian K(Qi , Pj , t), such that the identical motion is described by

Qi	=	∂K/∂Pi
˙	=	∂K/∂Pi
P˙j	=	−∂K/∂Qj .

The standard method to obtain a canonical transformation is to choose a generating function F , which is a function of one class of “old” variable ({qj } or {pk}), one class of new variable ({Qk} or {Pm}), and time:

F = F qj , Pl , t .

carbon-14 dating

Here we mean that F is a function of all of the qi, all of the Pl, and of time.

The equations connecting the old and new descriptions are then

∂F pl = ∂ql

Qk = ∂F ∂Pk

K= H + ∂F .

∂t

Similar sets of equations can be derived by introducing different functions F . For instance,

F(pi , Ql , t) gives

qk = −∂F/∂pk ∂F

Pm = −∂Qm

K= H + ∂F .

∂t

For the remaining two possibilities, one has the following rules: K = H +∂F/∂t always holds; derivatives with respect to the variables always come with ﬁxed signs. That is, the other two sets of equations involve one of ∂F/∂ql or −∂F/∂pk and one of ∂F/∂Pm and −∂F/∂Ql (note the signs).

Solution of one of these sets or its equivalent provides the coordinate transformation. The solution proceeds as follows: If, for instance F = F(qk , Pj , t), then ∂F/∂ql is generally a function of qk , Pj , and t. Hence Pl = ∂F/∂ql can be inverted to solve for the new momenta Pl in terms of the old coordinates and momenta qk, pj , and t. Similarly, ∂F/∂Pk is a function of qk , Pl, and t. Substituting in the expression for Pl in terms of qk , pl , t already found gives an explicit expression for Qp in terms of ql , pk , t. Finally, the new Hamiltonian K must be expressed entirely in terms of the new variables Qk , Pl , t using the relationships just found. See Hamilton–Jacobi Theory.

Canopus -0.2 magnitude star, of spectral type FO at RA06h 23m 57.1s dec −52◦41’44”.

cap cloud An orographic stratocumulus cloud mass that forms closely over the top of a mountain, arising from the condensation of

water in air as it rises to the peak; a particular case of pileus.

CAPE (Convective Available Potential Energy) Provides a measure of the maximum possible kinetic energy that a statically unstable parcel can acquire, assuming that the parcel ascends without mixing with the environment and instantaneously adjusts to the local environmental pressure. See available potential energy.

Capella 0.08 magnitude binary star of spec-

tral types G8+ FO at RA05h16m41.3s, dec +45◦51 53 .

capillarity correction Due to the fact that mercury does not wet glass, in glass/mercury barometers the top surface of the mercury is convex. A correction for the curvature of the surface must be made; the mercury height is slightly less than the expected height for a given air pressure. The corrections are slight, on the order of 2 mm or less.

capillary fringe The zone directly above the water table that is saturated (soil wetness = 1) and under tension (pressure < 0). The height of the capillary fringe (hcr ) is inversely proportional to the radius of the soil grains (r) and directly proportional to the surface tension (σ ) and the cosine of the contact angle (θc):

hcr = 2σ cos θc

ρgr

where ρg is the ﬂuid weight density.

capillary wave A water wave in which the primary restoring force is surface tension; waves with wavelength <1.7 cm are considered capillary waves.

carbon-14 dating A method to date a carbonaceous object by measuring the radioactivity of its carbon-14 content; this will determine how long ago the specimen was separated from equilibrium with the atmosphere-plant-animal cycle (“died”). Carbon-14 is continuously produced in the atmosphere by cosmic-ray bombardment and decays with a half-life typically described as 5568 years; dating is accomplished by comparing the carbon-14 activity per unit mass of

carbonaceous chondrite

the object with that in a contemporary sample. Estimates are fairly accurate, out to about 50,000 years.

carbonaceous chondrite A chondritic meteorite that contains carbon and organic compounds in addition to the rocky minerals. They also contain water-bearing minerals, taken to be evidence of water moving slowly through their interiors not long after formation, and evidence of metamorphism of the meteorite by water and of possible cometary origin. It is believed that carbonaceous chondrites are the most primitive meteorites and that minerals they contain were the ﬁrst minerals to crystallize during the formation of the solar system.

carbon burning The set of nuclear reactions that convert carbon to oxygen, neon, and other heavier elements. Carbon burning occurs in hydrostatic equilibrium in the evolution of stars of more than about 10 solar masses (between helium burning and neon burning). It can also be ignited in degenerate matter, in which case the burning is explosive. This may happen in the cores of stars of about 8 solar masses. It definitely happens at the onset of a supernova of type Ia. Oxygen burning can also be either hydrostatic or explosive.

carbon cycle a series of nuclear reactions that occur in the interior of stars, and in which carbon 12 acts as a sort of catalyst, not being consumed

in the reaction. The chain is 12C → 13N →

14O → 14N → 15O → 15N → 12C + 4He.

The two oxygen to nitrogen steps are beta decays and emit neutrinos. The energy release is 26.7MeV, of which 1.7MeV is in neutrinos. This cycle represents about 2% of the energy production in the sun (which is mostly the p-p cycle); however, its temperature dependence is approximately T 15, so it dominates in more massive stars.

carbon dioxide Colorless, odorless trace component gas of the Earth’s atmosphere (approximately 370 parts per million), CO2. Over 99% of the Earth’s carbon dioxide is found in oceans. Carbon dioxide is evolved in volcanos, and is also perhaps carried to Earth in cometary cores. Carbon dioxide is a major re-

action product in combustion involving fossil fuels, all of which is hydrocarbon based. Coal, essentially pure carbon, produces much more CO2 than does natural gas (CH4) per unit of energy evolved. Carbon dioxide concentrations have been rising in the Earth’s atmosphere throughout the last century. Carbon dioxide is a greenhouse gas, transparent in the visible, opaque in infrared. It is estimated to contribute more than half the current greenhouse warming of the Earth. Carbon dioxide is evolved by animals and sequestered into complex organic compounds by plants.

carbon monoxide Colorless, odorless, and very toxic trace constituent of the air, CO. Formed in the incomplete combustion of carbon; also apparently produced by near surface ocean-biologic sources. A very tightly bound molecule, as a result of which it is the most common (apart from H2) in the interstellar medium and, in the atmospheres of cool stars, it generally uses up all of the available C or O, whichever is less abundant, leaving only the other one to form additional detectable molecules.

carbon star Cool, evolved star of relatively low mass in which sufﬁcient carbon has been mixed to the surface for the carbon-oxygen ratio to exceed unity. As a result, carbon monoxide formation does not use up all the carbon, and other molecules, including CH, CN, and C2, will appear in the star’s spectrum. The stars are generally on the asymptotic giant branch and are seen at somewhat lower luminosity than might be expected from standard theories of convection and mixing. Other chemical peculiarities are common, and there are many subtypes. See asymptotic giant branch star.

Caribbean current An extension of the North Equatorial current that ﬂows northwestward into the Caribbean past the Yucatan peninsula and exits the Caribbean basin westward past the southern tip of Florida.

Carme Moon of Jupiter, also designated JXI. Discovered by S. Nicholson in 1938, its orbit has an eccentricity of 0.207, an inclination of 164◦, and a semimajor axis of 2.26×107 km. Its radius is approximately 20 km, its mass 9.5 × 1016 kg,

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