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eccentricity

 

Magnitude

 

 

 

 

distance (km)

Felt

Intensity

Damage

 

2

0

I

Not felt

 

 

 

II

Felt by a few people

 

3

15

III

Hanging objects sway

 

 

 

IV

Windows and doors rattle

 

4

80

V

Sleepers awaken

 

5

150

VI

Windows and glassware broken

 

 

 

VII

Difficult to stand

 

6

220

VIII

Branches broken from trees

 

7

400

IX

Cracks in ground – general panic

 

 

 

X

Large landslides – most masonry structures destroyed

 

8

600

XI

Nearly total destruction

 

 

 

 

 

east-west effect An east-west anisotropy in the arrival of cosmic ray particles. At equal inclinations to the vertical, a higher flux of particles is observed from the west than from the east because of an asymmetry in the distribution of trapped orbits (see cutoff energy). The direction of the asymmetry (more from west than from east) shows that primary cosmic ray particles have a positive electric charge.

easy access region Prior to the observations of the spacecraft Ulysses, the topology of the heliosphere was assumed to be similar to the one of the magnetosphere. In particular, above the solar poles cusp-like regions were expected where the cosmic radiation should have an easy access to the inner heliosphere, leading to higher fluxes over the poles compared to the ones at the same radial distance in the equatorial plane. Although Ulysses’ findings show an increase in the intensity of the galactic cosmic radiation over the sun’s poles, this increase is much smaller than the one expected in the picture of an easy access.

Two physical mechanisms seem to contribute to this lack of easy access: (a) an unexpected high level of magnetic field turbulence, leading to an enhanced scattering and thus preventing a relatively large number of particles from penetrating deep into the heliosphere, and (b) a more peanut-like shape of the heliosphere with a wider extent over the poles owing to the fast solar wind flowing out of the polar coronal holes.

ebb current The tidal current that results when the water in bays and estuaries is higher

than that in the adjoining sea. The opposite is referred to as a flood current.

ebb delta A deposit of sediments immediately offshore a tidal inlet.

ebb shoal See ebb delta.

ebb tide Used essentially interchangeably with ebb current.

eccentric Not centered, or not circular. Refers to elliptical orbits, where eccentricity is defined as the distance between the foci divided by the major axis, or equivalently

2 = 1 − b 2 , a

where is the eccentricity, a is the semimajor axis, and b is the semiminor axis. The eccentricity of a circle is zero. For parabolas eccentricity = 1; for hyperbolic orbits, eccentricity exceeds 1. See eccentricity.

eccentric dipole An approximation to the internal magnetic field of the Earth. It replaces that field with the field of a magnetic dipole, suitably oriented, but achieves additional accuracy by displacing that dipole from the center of the Earth in such a way that the quadrupole harmonic terms (terms which diminish as 1/r4) are reduced as much as possible.

eccentricity A characterization of conic sections, which are also solutions to the Newtonian equations of motion for a mass in the field of

© 2001 by CRC Press LLC

echelle spectrograph

a central mass, thus applicable to planetary orbits. Eccentricity = zero for circles, eccentricity < 1 corresponds to an ellipse, = 1 to a parabola, and > 1 to a hyperbola. See conic section, Kepler’s laws.

echelle spectrograph A grating spectrograph designed to achieve high spectral resolution, employed as an analyzer of optical and UV radiation. To increase resolution, the echelle spectrograph works with high diffraction orders (10 to 100). The light diffracted by the echelle grating is made of several high order spectra, covering adjacent narrow spectral ranges. They would overlap spatially if they were not separated by a cross-disperser, i.e., a grating with the grooves aligned perpendicularly to those of the echelle grating. The final echelle spectrum is a sequence of spatially displaced spectra of increasing order, and must be recorded on a twodimensional detector, such as a CCD or a photographic plate. With echelle spectrographs, a spectral resolving power of several 104 can be achieved with a compact design. See diffraction grating, grating spectrograph.

echo sounder A device that sends an acoustic signal into a water column and records the travel time for the sound to be reflected off of an object and returned to the sender. Generally used from a boat to measure water depth to the seafloor.

eclipse The obscuration of one astronomical body by another which moves between the first body and the observer.

eclipse year About 346.62 days; because of the precession of the nodes of the moon’s orbit (the moon must be near the node for a solar eclipse to occur) alignment of the nodal line with the Earth-sun direction recurs every eclipse year.

eclipsing binary A pair of stars whose orbiting around each other is revealed because one periodically passes in front of (eclipses) the other from our point of view. This is probable only when the stars are quite close together or the stars are very large. The detailed shape of the light curve can be analyzed to reveal the physical sizes of the two stars, the ratio of their surface temperatures, and the angle the orbit plane

makes with our line of sight. The bigger the stars, the longer the eclipse lasts; the hotter the star in back, the deeper the eclipse; and angles different from 90◦ tend to round the corners of the dips in brightness (though illumination of one star by the other can have somewhat similar effects and the analysis can be complicated).

ecliptic The apparent path of the sun through (actually in front of) different stellar constellations as seen from the Earth; the extension on the celestial sphere of the plane of the orbit of the Earth. The orbits of the visible planets are close to the ecliptic (deviating by ≈ 7◦ for Mercury). This path crosses through the zodiac constellations. See celestial sphere.

Eddington approximation In radiative transfer, the approximation that the radiative flux is constant over direction in the upper hemisphere, and separately constant over the lower hemisphere.

Eddington limit The maximum luminosity, or accretion rate, beyond which the spherical infall of matter on a massive body stops because the infalling matter is pushed outward by radiation pressure. In the case of spherical accretion, i.e., matter falling radially and uniformly onto a body, the gravitational force

is given by: F gravity = GMf sourceM cloud/D2

where D is the distance of the cloud from the source. The radiation force is determined by assuming that the cloud is optically thin and the photons are traveling radially from an isotropic source. Then, each photon absorbed imparts its entire momentum to the cloud (pγ = Eγ /c). The radiation force is then given

by: F radiation = κM cloud L source where κ is the

4πD2c

opacity of the cloud. The Eddington luminosity is independent of distance: L Eddingtonsource =

4πGM sourcec/κ. Then the Eddington luminosity can be written as

LEdd = 1.3 × 1038(M/M )ergs s−1 ,

A consequence of the Eddington limit is that central black holes need to be very massive to radiate at L 1045 to 1047 erg, the typical luminosity of quasars. Since the accretion lu-

minosity can be written as = ˙ 2, i.e., as

L ηMc

© 2001 by CRC Press LLC

effective couplings

the fraction η of the rest mass falling onto the

black hole per unit time, ˙ , that is converted

(M)

into radiating energy, a limiting accretion rate is associated to the Eddington luminosity. See quasar.

Eddington luminosity See Eddington limit.

Eddington ratio The ratio between the bolometric luminosity of a source, and the Eddington luminosity. The Eddington ratio can be equivalently defined from the accretion rate. The Eddington ratio is a parameter expected to influence the structure and the radiating properties of an accretion disk in a fundamental way: If the Eddington ratio is < 1 a geometrically thin disk is expected to form, while if > 1 the accretion disk may inflate to form a torus whose thickness is supported by radiation pressure. See Eddington limit.

eddy A current that runs in a direction other than that of the main current; generally “spins off” from a larger flow and defines a circular path.

eddy correlation method Method to directly compute turbulent fluxes of scalars. Turbulent velocity fluctuations cause a net transport of scalar properties of the fluid. The turbulent flux is then given by the time or space averaged product v θ of the velocity v and the scalar θ, where the primes denote the fluctuations (see Reynolds decomposition) and the over-bar denotes the average. For example, the fluctuations of vertical velocity w and temperature T may be combined to give the vertical flux of heat, Cw T , where C is the specific heat.

eddy diffusivity An analog to molecular diffusivity, used to model diffusion in a turbulent flow.

eddy flux The flux of chemical properties, momentum, energy, heat, etc. via the eddies in turbulent motion.

eddy-resolving Eddy-resolving models are able to describe the turbulent flow down to a resolution including all scales on which viscosity is not dominant.

eddy viscosity An analog to molecular viscosity, used to describe shear stresses in a turbulent flow. A coefficient of proportionality to relate shear stress to rate of strain (velocity gradient) in turbulent flow.

edge wave Waves that are trapped at a coast by refraction. Waves strike the shore and some energy is reflected, and then turned by refraction. Depending on the incident angle and bathymetry, some of this energy will be trapped at the coast. The trapped wave moves in the longshore direction as a progressive wave.

effective charge A somewhat obsolete expression in field theory for the renormalized quantities which have logarithmic dependence of the scale parameter µ. “Effective charge” is sometimes used instead of the more common “effective coupling constant,” “effective mass,” “effective parameter,” etc. See effective couplings.

effective couplings The values of the coupling constants in quantum field theory depend on the dimensional parameter µ, which measures the typical scale of the energy of the interaction. This dependence is governed by the renormalization group and it has, in general, logarithmic form. Thus, instead of constant coupling, one finds some function of µ. For example, in quantum electrodynamics (QED) the charge of the electron is running (in the one-loop approximation) as

e(µ)

= 1 −

2 e2

µ

 

−1

 

 

 

 

ln

 

 

e

3

(4π)2

µ0

 

where e = e(µ0) and µ0 corresponds to some fixed scale. The minus sign in the bracket indicates the lack of asymptotic freedom in QED. This leads to the well-known formal problem (problem of charge zero, or Landau zero) because for some µ corresponding to a very high energy the bracket becomes zero and the effective coupling infinite. This in turn makes the perturbation theory inapplicable and addresses serious questions about the fundamental validity of the theory. Indeed, the resolution of this problem is beyond the scope of QED. It is supposed that at these very high energies QED is not an

© 2001 by CRC Press LLC

effective pressure

independent theory but part of some nonabelian unified (Grand Unification) theory in which the asymptotic freedom (or finiteness) takes place. At the energies comparable to the Planck energy the local quantum field theory should be (presumably) abandoned and instead one has to consider a more fundamental string or superstring theory. See effective charge.

effective pressure The pressure term of effective stress in a porous medium. If p is the total pressure, the effective pressure is defined as p = p − αpf , where pf is the pore fluid pressure. The parameter α is defined as α = 1 − K/Ks, where K and Ks are the bulk moduli of the matrix frame and the solid grains that constitute the matrix. In most practical cases, Ks K and α = 1. See effective stress.

effective stress In a porous medium, the pressure term of the total stress σij is partially sustained by the pore fluid. The stress tensor with the effect of pore fluid subtracted is called the effective stress. It is the effective stress that determines the deformation and failure of the solid component of the porous medium. The effective stress is defined as

σij = σij − αpf δij

where pf is the pore fluid pressure. The parameter α is defined as α = 1 − K/Ks, where K and Ks are the bulk moduli of the matrix frame and the solid grains that constitute the matrix. In most practical cases, Ks K and α = 1.

effective temperature The effective temperature of a blackbody is that temperature which characterizes the energy flux (total power output) at the surface of an object. The energy per second emitted by an object at a given frequency over a unit area is called the surface flux. It is found by integrating the blackbody equation over all solid angles and all frequencies. The surface integral gives

Fν = Bν(ν, T ) cos θ dφ dθ = πBν(ν, T )

in units of erg cm−2 s−1 Hz−1, where θ is the angle between the normal to the surface and the path of an emitted photon, φ is the azimuthal

angle, and Bν is the Planck blackbody intensity in units of erg s−1 cm−2 Hz−1 sr−1. The total energy emitted per second per unit area is the surface flux (above) integrated over all frequencies:

F =

 

2π5k4

πBν(ν, T )dν =

 

Teff4 = σTeff4

15h3c3

where σ is the Stefan–Boltzmann constant. The total energy flux of a blackbody is related to its luminosity by,

F = L/4πr2 = σTeff4 .

In astronomy, one computes the effective temperature of a star (or the sum) from its luminosity by this formula. The effective temperature then, is the characteristic temperature that relates a star’s total output power to its size.

effluent Something that is discharged; commonly used to refer to the discharge from a sewer or factory outfall lying in a river or coastal waters.

eigenray The integral curve of a principal direction of the Killing bivector [aKb]. By the Killing equation, the symmetrized derivative of the Killing vector K vanishes. In a spinorial notation, the null eigendirection is given

by the solution αA of the eigenvalue problem φAB αB = λαA where φAB is the spinor rep-

resentation of the Killing bivector. See Killing vector.

eigenvalue An allowed value of the constant a in the equation Au = au, where A is an operator acting on a function u (which is called an eigenfunction). Also called characteristic value.

eikonal approximation The approximation to a wave equation which assumes the wave function is of the form exp[iωt + ikx] where ω and k are large. This replaces the second order derivatives of the wave function by terms proportional to the square of ω or of k.

einstein One mole of photons (6.023 × 1023 photons).

Einstein–Cartan gravity An important particular case of gravity with torsion. The action

© 2001 by CRC Press LLC

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