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celestial sphere

causal boundary (Geroch, Kronheimer and Penrose, 1972). A boundary construction using only the causal properties of a space-time.

causal curve In relativity, a time-like or null curve, i.e., one that can be the history of a particle moving no faster than the speed of light. See null vector, time-like vector.

causal future/past The causal future/past

J ±(S) of a set S is defined as the union of all points that can be reached from S by a future/past-directed causal curve. See causal curve.

causality relations A trip from point x to point y of a causal space is an oriented curve with past endpoint x and future endpoint y consisting of future-oriented time-like geodesic segments. A causal trip is similarly defined, with the time-like geodesic segments replaced by causal geodesic segments.

1.Point x chronologically precedes point y (i.e., x y) if and only if there exists a trip from x to y.

2.Point x causally precedes point y (i.e., x y) if and only if there exists a causal trip from x to

y. For an arbitrary point x of a space-time, the relation x x holds, since a causal trip may consist of a single point.

cavity, magnetic A region of weak magnetic field created by a relatively dense plasma expelling its field lines. Produced in some distant barium releases.

CCD Acronym of charge-coupled device, presently the most widely used detector in optical astronomy. The CCD is a two-dimensional detector, like a photographic film or plate. Each picture element (pixel) of a CCD is a photodiode where electrons, freed by the incoming radiation via photoelectric effect, are held in a positive potential for an arbitrary time (i.e., the exposure time). At readout time, an oscillating potential transfers the stored charges from pixel to pixel across each row of pixels to an output electrode where the charges are measured. Unlike photographic plates, CCD possess linearity of response (i.e., the number of electrons freed is proportional to the number of photons detected)

and detection quantum efficiency (i.e., the ratio between detected and incident photons) which is very high, close to 100% for red light. The pixel size can be as small as 15 µm × 15 µm; arrays of 2048×2048 pixels are among the largest available CCDs.

cD galaxies Luminous, large-size elliptical galaxies that are located at the center of dense clusters of galaxies. The notation “cD” indicates a cluster D galaxy in the Yerkes classification scheme. The photometric profile of a cD galaxy is different from that of other elliptical galaxies, since there is an excess of light at large radii over the prediction of the de Vaucouleurs law. cD galaxies possess a stellar halo that may extend up to 1 Mpc, exceptional mass and luminosity, and are thought to result from multiple merging of galaxies and from cannibalism of smaller galaxies belonging to the cluster. An example of a cD galaxy is Messier 87, located at the center of the Virgo cluster. See de Vaucouleurs’ law, Yerkes classification scheme of galaxies.

Celaeno Magnitude 5.4 type B7 star at RA 03h44m, dec +24.17’; one of the “seven sisters” of the Pleiades.

celerity Phase speed; the speed of a wave deduced from tracking individual wave crests.

celerity The translational speed of a wave crest. Given by C = L/T , where C is celerity in units of length per time, L is wavelength, and T is period.

celestial equator Extension to the celestial sphere of the plane of the Earth’s equator; the set of locations on the celestial sphere that can appear directly overhead at the Earth’s equator. See nutation, precession.

celestial poles The points on the celestial sphere that are directly overhead the Earth’s poles. See nutation, precession.

celestial sphere The imaginary sphere representing the appearance of the sky, in which all celestial objects are visualized at the same distance from the Earth and at different direc-

© 2001 by CRC Press LLC

Celsius, Anders

tions from the Earth. The celestial sphere thus surrounds the Earth, and locations on the sphere are given by the two angles necessary to define a given direction.

Celsius, Anders Astronomer (1701–1744). Proposed the Centigrade temperature scale.

Celsius scale Also called Centigrade Scale, scale for measuring temperature in which the melting point of ice is 0, and the boiling point of water is 100. This definition has been superseded by the International Temperature Scale 1968, which is expressed both in Kelvin and degrees Celsius. Named after Anders Celsius (1701–1744).

Centaur An “outer planet crosser.” A minor body whose heliocentric orbit is between Jupiter and Neptune and typically crosses the orbits of one of the other outer giant planets (Saturn, Uranus, Neptune). The orbits of the Centaurs are dynamically unstable due to interactions with the giant planets, so they must be transition objects from a larger reservoir of small bodies to potentially active inner solar system objects. The Kuiper belt is believed to be this source reservoir.

Centaurus A (Cen A) Active galaxy at RA13h25m28s, dec 4301 11 in constellation Centaurus. Also classified as NGC5128. Distance approximately 3.4Mpc. Large, elliptical galaxy with strong dust lanes seen in the visible and infrared, strong jets seen in radio (double lobed) and in the X-ray (single lobed). Also visible in the gamma ray range.

center of figure To a first approximation the earth is a sphere. However, the rotation of the earth creates a flattening at the poles and an equatorial bulge. The shape of the earth can be represented as an oblate spheroid with equatorial radius larger than the polar radius by about a factor of 1/300. The center of the best fit spheroid to the actual shape of the earth is the center of figure. There is an offset between the center of figure and the center of mass of a few kilometers.

center of mass In Newtonian mechanics, the “average” location X of the mass, given in com-

ponents by

 

 

m(i)xa

 

Xa =

m(i)(i)

, a = 1, 2, 3 ,

 

 

 

where the sums indicated by 9 are over all the masses, labeled (i). In relativistic mechanics there are many inequivalent formulations which all reproduce this nonrelativistic result in the limit of small velocities.

Centigrade scale

See Celsius scale.

centimeter burst A transient solar emission of radiation at radio wavelengths 1 to 10 cm. Centimeter bursts provide a powerful diagnostic of energetic electrons in the solar atmosphere, especially during solar flares. The production mechanisms include thermal bremsstrahlung, gyrosynchrotron radiation, and collective plasma processes.

central meridian passage The passage of a solar feature across the longitude meridian that passes through the apparent center of the solar disk. Useful for identifying a characteristic time during the transit of a solar feature (e.g., an active region) across the solar disk.

central peak A mound of deformed and fractured rock found in the center of many impact craters. This material originally existed under the crater floor and was uplifted by the stresses associated with the impact event. Central peaks are believed to form by hydrodynamic flow during crater collapse. The target material behaves as a Bingham fluid, which displays properties of viscous fluids yet has a definite plastic yield stress. As the crater formed in this target material collapses, shear stresses cause material to be jetted up in the center of the crater. When the shear stresses fall below the cohesion of the target material, the motion of this central jet ceases, and the material freezes into a central peak. Central peaks are common features of complex craters but are associated with the smaller complex craters. As crater size increases, central peaks tend to be replaced first by craters with a ring of central peaks (called a peak ring), then by a combination of central peaks surrounded by a peak ring, and finally a multiple-ring basin.

© 2001 by CRC Press LLC

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Cerenkov radiation

central pit A depression found in the center of many impact craters. Central pits are particularly common on bodies where ice is (or believed to be) a major component of the upper crust, such as Jupiter’s icy moons of Ganymede and Callisto and on Mars. The formation of central pits is not well understood but is believed to be related to the vaporization of crustal ice during crater formation.

centrifugal force The conservative force that arises when Newton’s equations are applied in a rotating frame; the apparent force acting on a body of mass m that is rotating in a circle around a central point when observed from a reference system that is rotating with the body:

F = m ω × × r)

where ω is the angular velocity vector, and r is the radius vector from the origin. The magnitude of the force can also be expressed in terms of the distance d from the axis and the velocity v in a circle or orthogonal to the axis: F = mv2/d; the direction of this force is perpendicularly outward from the axis. These terms appear in dynamical equations when they are expressed in a rotating reference system or when they are expressed in cylindrical or spherical coordinates rather than Cartesian coordinates. These terms are generally treated as if they were actual forces.

centroid moment tensor (CMT) In seismology, a moment tensor obtained when a point source is put at a centroid of a source region. Dziewonski et al. began to determine CMT routinely in 1981 for earthquakes with Ms 5.5. Recently, CMT has been used to estimate seismic moment and force systems on a source region of an earthquake, replacing a fault plane solution determined from polarity of P- and S- waves. Six independent components of the moment tensor and four point-source hypocentral parameters can be determined simultaneously through iterative inversion of a very long period (T > 40 s) body wave train between the P-wave arrival and the onset of the fundamental modes and mantle waves (T > 135 s). Not assuming a deviatoric source, some focal mechanisms have been found to have large non-double couple components.

Cepheid variable A giant or supergiant star crossing the instability strip in the HR diagram at spectral type F-G. The stars can be crossing either from blue to red as they first leave the main sequence or from red to blue in later evolutionary phases. In either case, the stars are unstable to radial pulsation because hydrogen at their surfaces is partially ionized on average and acts like a tap or faucet that turns the flow of outward radiation up or down, depending on its exact temperature. As a result, the stars change their size, brightness, and color (temperature) in very regular, periodic patterns 1 to 50 days, and with a change of 0.5 to 1 magnitude. Because the counterbalancing force is gravity, the pulsation period, P , is roughly equal to (Gρ)1/2, where ρ is the star’s average density and G is Newton’s constant of gravity. This, in turn, means that there is a relationship between period, luminosity, and color for whole populations of Cepheids. Thus, if you measure the period and color of a Cepheid, you know its real brightness and can, in turn, learn its distance from its apparent brightness. Cepheids can be singled out only in relatively nearby galaxies, and with the Hubble Space Telescope, they have been measured out to galaxies in the Virgo Cluster. Classical Cepheids are population I stars that are massive young objects. The W Virginis Cepheids belong to the older population II stars. The prototype star, δ Cephei, was discovered to vary in 1784. This period-luminosity relation was originally discovered for the Cepheids in the Large Magellanic Cloud by Henrietta S. Leavitt in the first decade of the 20th century. Once an independent measure of the distance to a few nearby Cepheids was accomplished (through spectroscopy and other methods), a period-luminosity relation was defined. The calibration of the period-luminosity relation is the underpinning of our distance measurements to the nearest galaxies (within 400 Mpc), which then calibrates the Hubble constant, the proportionality constant that relates red shift of distant galaxies to the expansion of the universe.

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Cerenkov radiation The Cerenkov effect (in

Russia: Vavilov–Cerenkovˇ

effect ) was first ob-

 

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served with the naked eye by P.A. Cerenkov in

1934 as a “feeble visible radiation” from fast electrons (Vavilov’s interpretation, 1934) due to

© 2001 by CRC Press LLC

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Cerenkov radiation

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γ -rays in pure water. In 1937 Cerenkov confirmed the theoretical prediction by Frank and Tamm about the sharp angular dependence of this radiation: Frank and Tamm earlier in the same year had given a complete classical ex-

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planation of the Cerenkov effect. Its quantum theory was given by Ginsburg in 1940. In 1958

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Cerenkov, Tamm, and Frank were awarded the Nobel Prize.

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Cerenkov radiation occurs when a charged particle is moving in a transparent medium with a velocity greater than that of light in this medium. This radiation is emitted with a conical front, the direction of motion of the particle being its axis making the angle θ with the cone’s generatrix, while cos θ = v/u. Here v is the velocity of light in the medium and u, the velocity of the charged particle (u > v). This picture is very similar to that of waves on the surface of water when a boat is moving faster than the

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waves propagate. In the theory of Cerenkov’s radiation, an important role is played by the medium’s dispersion (the frequency dependence of the electric and magnetic properties of the medium, hence of its refraction index).

In fact, the classical theory of what we now

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call Cerenkov radiation, as well as of some similar phenomena involving the superluminal (in a vacuum or in refractive media), was developed as early as 1888 by Heaviside: the first publication in the Electrician, with subsequent publications in 1889 and 1892, and especially in 1912 (comprising more than 200 pages of the third volume of his Electromagnetic Theory). In 1904 and 1905 Sommerfeld published four papers on the same effect, though only in a vacuum; there he mentioned, at least once, the previous work of Heaviside, as did Th. des Coudres in 1900. Subsequently this early development was lost until 1979, when the references were again cited.

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The Cerenkov effect is the basis of Cerenkov counters of ultrarelativistic charged particles which essentially consist of a (usually Plexiglas) transparent dielectric cylinder and some

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Cerenkov then was a student of S.I. Vavilov, performing a research in fluorescence as a part of his Ph.D. thesis under Vavilov’s supervision.

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photomultipliers to detect the Cerenkov radiation emitted in the dielectric by these particles.

Ceres The first observed asteroid, discovered by Giuseppe Piazzi in 1801. It has a diameter of 913 km. It orbits in the main asteroid belt. Its average distance to the sun agrees with the distance of the “missing planet” predicted by Bode’s Law.

CGS (Centimeter-Gram-Second) The system of measurement that uses these units for distance, mass, and time. This system incorporates the use of electrostatic units (esu) or electromagnetic units (emu) in the description of electromagnetic phenomena. The magnetic permeability (µ) and dielectric constant (=) are dimensionless in the CGS system.

chalcophile Elements that display an affinity for sulfur are called chalcophile elements. Such elements are readily soluble in iron monosulfide melts and tend to be found concentrated in sulfide ores.

Challenger Deep Deepest part of the Marianas Trench, deepest ocean water. Located at approximately 14215 E, 1120 N off the coast of Guam. Bottom depth approximately 11,000 m (36,100 ft); various “deepest” measurements range within 100 m of this value.

Chandler wobble Although the Earth’s pole of rotation (i.e., the axis about which the Earth is spinning) lies close to the axis of the solid Earth’s largest principle moment of inertia, they are generally not quite coincident because the solid Earth has a small amount of angular momentum ?L oriented perpendicular to the axis of the largest principle moment of inertia. There is a small angle between the two axes, and the action of ?L as viewed by an observer on the planet is to cause the axis of rotation to swivel around the axis of the maximum moment of inertia. This is the free precession of the planet, as opposed to the forced precession associated with tidal couples due to the moon and sun, and is called the Chandler wobble. The theory of the rotation of solid bodies suggests that the period of the wobble should be approximately 300 days, but in fact the period is around 435 days.

© 2001 by CRC Press LLC

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