core-mantle coupling

radio axis and the line of sight form a larger angle in lobe-dominated objects. The jet onesidedness suggests that radiation is boosted by relativistic beaming: If the emitting particles are moving at a velocity close to the speed of light, the detection of the jet on the approaching side is strongly favored. In this case, a very large dynamical range is needed to detect the radiolobes, which, seen pole-on, may appear as a faint fuzz surrounding the core.

core flow Magnetic field may be generated in a conducting fluid by fluid flow, as described by the induction equation of magnetohydrodynamics. Such flow in the Earth’s core is thought to be the generating mechanism for the bulk of the Earth’s magnetic field. The motions and field within the core cannot be directly calculated from observations of the magnetic field at the Earth’s surface (although it may be possible to indirectly infer certain parts of the internal flow and field). However, observations of the surface field can be used to calculate the field at the core-mantle boundary by assuming that the electrical currents in the mantle are negligible, in which case the flow at the surface of the core is constrained using the radial component of the induction equation of magnetohydrodynamics in the frozen-flux limit (i.e., assuming that magnetic diffusion within the core may be neglected):

∂Br = H · (Br u) ∂t

where Br is the radial field and u the velocity vector. Since the flow does not penetrate the core-mantle boundary, there are two components of the velocity but only one constraining equation, which means that although the above equation can be used to invert time varying models of Br for possible flows, they will not be uniquely determined. Extra constraints on the flow have been used to alleviate the nonuniqueness. See nonuniqueness.

core-mantle boundary At around 3480 km from the center of the Earth, the material composition is thought to change from molten iron plus dissolved impurities (the outer core) to crystalline silicate rock (the mantle). This coremantle boundary is in terms of absolute den-

sity contrast the Earth’s major transition, with a jump from 5.6 g/cm3 at the base of the mantle to 9.9 g/cm3 at the top of the core. There is also a significant contrast in viscosity (although the viscosities of both sides are poorly constrained) and also, quite possibly, conductivity (although it has been proposed that the conductivity of the base of the mantle is highly elevated). The degree to which chemical exchange occurs across the core-mantle boundary is a frequent topic of study. Analysis of seismic data has indicated significant lateral variation in seismic wave speeds at the base of the mantle and also anisotropy, and there have also been claims of seismic observations of topography of the boundary itself. See core-mantle coupling.

core-mantle coupling This term may be used to refer either to the exchange of material across the core-mantle boundary (e.g., via chemical reaction), or the exchange of momentum between parts of the core and the mantle. The mechanism for the latter type of coupling is disputed, as is the degree to which the former type of coupling occurs at all. Changes in the rotation rate and direction of the Earth’s mantle on timescales of decades are usually attributed to momentum exchange between the core and the mantle, and there have been claims that the core is important on even shorter timescales, even though on subannual timescales the atmosphere is the predominant driving force for changes in Earth’s rotation. There are several possibilities for how momentum exchange may occur: viscous coupling, electromagnetic coupling, topographic coupling, and gravitational coupling. Viscous coupling is usually ruled out as the cause of the observed changes in Earth rotation because the viscosity of the core is usually regarded as very small. Electromagnetic coupling would occur via magnetic linkage between the liquid metal of the core and conductivity in the mantle, in which electrical currents would be induced by changes in the magnetic field. Topographic coupling would occur through the resistance of topography on the core-mantle boundary to flow at the top of the core, while gravitational coupling would happen if lateral variations in the density of the mantle and core are arranged so as to yield a torque between the two. See core-mantle boundary.

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Coriolis

Coriolis A term used to refer to the force or acceleration that results due to the rotation of a coordinate system, such as a system fixed to the rotating Earth. Increases in importance as angular velocity or length or time scale of the problem increase.

Coriolis effect (Coriolis force) A nonconservative effective inertial force contributing to the deviation from simple trajectories when a mechanical system is described in a rotating coordinate system. It affects the motion of bodies on the Earth and in molecular spectroscopy leads to an important interaction between the rotational and vibrational motions. The effect is described by an additional term in the equations of motion, called the Coriolis force, Fcor = 2mω ×v, where ω is the angular velocity, and v is the velocity measured in the rotating frame. In meteorology, it is an apparent force acting on a moving mass of air that results from the Earth’s rotation. Coriolis force causes atmospheric currents to be deflected to the right in the northern hemisphere and to the left in the southern hemisphere. It is proportional to the speed and latitude of the wind currents, and, therefore, varies from zero at the equator to a maximum at the poles. Coriolis force is very important to large-scale dynamics. To a unit mass fluid, on Earth it is expressed as

f	= −	2I	× = −
			V	2 i(wIcosR
− vIsinR) +					+	−
			j(uIsinR)		k(		uIcosR)

where I is the angular velocity of Earth, R is latitude, and u, v, w are components of wind. Coriolis force is always perpendicular to the motion direction. Thus it affects only the direction of wind and never affects wind speed. (Gustave Coriolis, 1835.) See centrifugal force.

Coriolis, Gaspard Gustave de Physicist (1792–1843). Presented mathematical studies on the effects of Earth’s rotations on atmospheric motions.

Coriolis parameter The local vertical (or radial) component of twice the Earth’s angular velocity, that is,

f = 2I sin( )

where is the geographical latitude (equator:= 0; poles: = π/2), and I is the Earth’s angular frequency (I = 2π/86 00 s−1). It expresses the Coriolis force by the momentum equation ∂v/∂t = −fu and ∂u/∂t = fv. The current components u, v are directed towards east and north, respectively.

corner frequency On Fourier amplitude spectrum for seismic displacement waveforms, amplitudes are almost constant on the lower frequency side of a frequency, whereas amplitudes become small with increasing frequency on the higher frequency side. The border frequency between them is called the corner frequency. The larger an earthquake is and the slower the rupture associated with an earthquake is, the lower the corner frequency becomes. From a finite line source model with unilateral rupture propagation, it is expected that the corner frequency is related to finiteness concerning apparent duration time of rupture in the direction of the length of the fault plane and finiteness concerning rise time of source time function, resulting in amplitude decrease on the higher frequency side, inversely proportional to the square of frequency. The flat amplitudes on the lower frequency side represent a pulse area of displacement waveforms.

corona In astronomy, the tenuous outer atmosphere of the sun or other star, characterized by low densities and high temperatures (> 106K). Its structure is controlled by solar magnetic fields, which form the corona into features called coronal streamers. The solar corona has a total visible brightness about equal to a full moon. Hence, since it is near the sun ( 2 to 4 solar radii), it is normally invisible, but can be observed with a coronagraph or during a total solar eclipse. This visible portion of the corona consists of two components: the F-corona, the portion which is caused by sunlight scattered or reflected by solid particles (dust), and the K- corona, which is caused by sunlight scattered by electrons in the extended hot outer atmosphere of the sun. Stellar coronae are sources of X-rays and radio emission, and their intensity varies with the period of the stellar activity cycle, about 11 years for the sun.

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coronal hole

In planetary physics, a corona is a large structure of combined volcanic and tectonic origin. Most coronae are found on Venus, although the term is also used to describe tectonic features on the Uranian moon of Miranda. The Venusian coronae typically consist of an inner circular plateau surrounded first by a raised ridge and then an annulus of troughs. Most of the interior features of the corona are typical volcanic structures, including calderas, small shield volcanos, and lava flows. Coronae tend to be very large structures, often 300 km or more in diameter. Planetary scientists believe they form when a large blob of hot magma from Venus’s interior rises close to the surface, causing the crust to bulge and crack. The magma then sinks back into the interior, causing the dome to collapse and leaving the ring. Rising and collapsing diapirs of material have also been proposed to explain the coronae on Miranda.

coronagraph A telescope designed to observe the outer portions of the solar atmosphere. The bright emission of the solar disk is blocked out in coronagraphs by means of an occulting disk, bringing the faint outer corona into view. Coronagraphs typically view the corona in white light, though filters can be used to achieve specific wavelength observations. Because of the need for an occulting disk, they only observe the corona above the solar limb, projected onto the plane of the sky. Modern coronagraphs, such as the one on the SOHO spacecraft, can observe the corona between 1.1 and 30 solar radii. Coronagraphs can also be operated from the ground as long as the air column above the coronagraph is thin enough to reduce atmospheric scattering sufficiently. The first coronagraph was operated by B. Lyot from the Pic du Midi in the Pyrenees at an altitude above 2900 m. Coronagraphs provide the most startling observations of coronal mass ejections, helmet streamers, and prominences.

Coronal Diagnostic Spectrometer (CDS) A Wolter II grazing incidence telescope equipped with both a normal incidence and a grazing incidence spectrometer flown on board the SOHO spacecraft. This instrument is designed to measure absolute and relative intensities of selected

EUV lines (150 to 800 Å) to determine temperatures and densities of various coronal structures.

coronal dimming During an eruptive event such as coronal mass ejection or a long duration flare, a large mass of plasma is ejected from the solar corona. When observed in soft X-ray wavelengths, the expulsion of million degree plasma is called coronal dimming. This coronal dimming relates the removal of hot material from the low corona to the higher, cooler material commonly associated with a coronal mass ejection, as seen in white light.

coronal heating The temperature of the solar atmosphere increases dramatically from the photosphere, through the chromosphere and transition region, to the corona with temperatures in the corona varying from 2 to 3 million degrees Kelvin in the quiet diffuse corona to as much as 5 to 6 million degrees in active regions. The reason why the corona is so hot remains a mystery although it is now clear that the sun’s magnetic field plays a crucial role in the transport and dissipation of the energy required to heat the corona. The total energy losses in the corona by radiation, conduction, and advection are approximately 3 × 1021 J or about 500 W m−2. Balancing these losses requires only about 1 part in 100,000 of the sun’s total energy output.

coronal hole A low density extended region of the corona associated with unipolar magnetic field regions in the photosphere, appearing dark at X-ray and ultraviolet wavelengths. The magnetic field lines in a coronal hole extend high into the corona, where they couple to the solar wind and are advected into space. The corona, the outermost gravitationally bound layer of the solar atmosphere, is a very hot plasma (temperatures in the range of 1 to 2×106 K). The largescale structure of the coronal gas consists of relatively dense regions whose magnetic field lines are “closed” (anchored at two points in the photosphere) and lower-density regions (the coronal holes), whose magnetic field lines are “open” (anchored at a single point in the photosphere and extending outward indefinitely). The solar wind emerges along these open field lines.

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coronal lines

Except possibly for the periods of highest solar activity, the largest coronal holes are located at relatively high heliographic latitude, often with irregularly shaped extensions to lower latitude, sometimes into the opposite hemisphere. During maximum activity periods, equatorial coronal holes can appear and last for several solar rotations.

coronal lines Forbidden spectral emission lines emitted from highly ionized atomic species, in a high temperature, dilute medium where collision between ions and electrons dominates excitation and ionization, as in the solar corona. In such plasma the temperature (1 to 2×106 K in the solar corona) and hence the kinetic energy of ions and electrons is so high that collisions have sufficient energy to ionize atoms. The first coronal emission line was identified at 530.3 nm during the total solar eclipse of 1869. Only in the 1940s were most of the coronal lines identified as forbidden transitions from elements such as iron, nickel, and calcium in very high ionization stages. Ratios of coronal line fluxes, similarly to ratios of nebular lines, are used as diagnostics of temperature and density. See forbidden lines, nebular lines.

coronal loops The solar corona is comprised primarily of magnetic loop-like structures which are evident at all scales in the corona and are thought to trace out the magnetic field. Loops are seen at soft X-ray, EUV, and optical wavelengths. Typical configurations of loops occur in active regions, where many bright compact loop structures are associated with strong surface magnetic fields, and in arcades spanning a magnetic neutral line and often overlaying a filament or filament channel. The interaction and reconfiguration of these structures often accompany the dynamic eruptive phenomena on small scales in solar flares and very large scales in coronal mass ejections.

coronal mass ejection (CME) An ejection of material from the sun into interplanetary space, as a result of an eruption in the lower corona. This material may sometimes have higher speeds, densities, and magnetic field strengths relative to the background solar wind and may produce shocks in the plasma. The

fastest CMEs can have speeds of 2000 km s−1 compared with normal solar wind speeds closer to 400 km s−1. CMEs are more common at solar maximum, when three per day can be seen, than solar minimum, when one may be seen in five days. If the material is directed towards the earth, then the CME may cause a disturbance to the Earth’s geomagnetic field and ionosphere. See solar wind.

coronal rain Cool plasma flowing down along curved paths at the solar free-fall speed of 50 to 100 km s−1; material condensing in the corona and falling under gravity to the chromosphere. Typically observed in Hα at the solar limb above strong sunspots.

coronal transients A general term for short- time-scale changes in the corona but principally used to describe outward-moving plasma clouds. Erupting prominences are accompanied by coronal transients, which represent outward moving loops or clouds originating in the low corona above the prominence. As many as one coronal transient per day is observed to occur during the declining phase of the solar cycle and are most commonly associated with erupting filaments.

coronal trap The region of the corona in which charged particles are trapped between two areas of converging magnetic field, i.e., a magnetic bottle. The converging field causes a strengthening of the field and consequently a strengthening of the Lorentz force felt by a charge particle of velocity v. The particle’s pitch-angle, θ = cos−1(vz/v) where z is the direction parallel to the field direction, increases as the particle moves into the region of increasing field strength until all of the particle’s momentum is converted into transverse momentum (θ = 90◦). This location is known as the mirroring point because the particles cannot pass into a region of greater field strength and therefore become trapped. When collisions and waveparticle interactions are ignored, the conditions for a particle to be trapped are defined by the equation sinθ/B = sinθ0/B0 where θ0 is the particle’s initial pitch angle and B0 is the coronal field. Note that for a prescribed field convergence B/B0, particles with initial pitch angles

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