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red line

primary energy source is hydrogen burning (by the CNO cycle), in a thin shell around an inert helium core (more massive analogs are called red supergiants). The star is about 10 times as bright as it was on the main sequence (see HR diagram), and as the core grows, the star leaves the main sequence track of the Hertzsprung–Russell diagram and ascends the red giant branch, gaining in luminosity (on the order of 103 L ) yet decreasing in surface temperature (near 3800 K). The phase lasts about 10% of the main sequence lifetime and is terminated by the ignition of helium burning. As the star eventually depletes its core supply of He, hydrogen fusion begins again in a thin shell around the core. Eventually, the core becomes inert C and O with separate, concentric shells where He-fusion and H fusion continues. At this stage, the star is considered to be in the asymptotic giant branch stage of evolution and has achieved a luminosity of 104 L or greater and a surface temperature of 1800 to 3500 K. The sun will become a red giant about 5 billion years in the future, increasing the surface temperature of the Earth to about 900 K, where some metals melt and sulfur boils.

red line A coronal line observed at 6374 Å resulting from a forbidden transition in highly ionized iron atoms (Fe X). Important for study of coronal structures at temperatures of order 1 MK.

redshift A displacement of a spectral line toward longer wavelengths. This can occur through the Doppler effect or, as described by general relativity, from the effects of a star’s gravitational field or in the light from distant galaxies. The relative displacement toward longer wavelength (or equivalently, of lower energy) of light is measured from spectral features like emission or absorption of lines and is defined as

z = (λ − λ0) /λ0 ,

where λ0 is the rest wavelength of a spectral feature. The displacement toward a longer wavelength is conventionally termed a redshift even if the photons are not in the visible spectral range. Galaxies and quasars, with the only exceptions of several galaxies very close to the Milky Way, invariably show all their spectral lines shifted to

the red, with redshift increasing with distance according to Hubble’s Law. Redshifts up to z ≈ 5 have been (in 1998) observed for quasars.

Red Spot A feature in Jupiter’s atmosphere, some 10,000 by 50,000 km in extant. It was probably first observed by Hooke in 1664, but a continuous record of observations only goes back to the end of 1831. Its position is roughly fixed, with some drift relative to the average position. Although a number of suggestions have been forwarded to explain this feature, the most likely is an atmospheric disturbance, similar to a hurricane. Scaling arguments indicate that such a disturbance would be much longer lived on Jupiter than on Earth.

reduced gravity Reduced gravity g is defined by g = g(ρ2 − ρ1)/ρ2 where ρ1 and ρ2 are the density of the upper and lower layer.

reduced gravity model A model treating the ocean thermocline as an infinitesimally thin interface separating a warm upper layer and an infinitely deep abyssal. In such a model, the motion in the abyssal is negligible, and the upper layer motion is described by a set of shallow water equations with the gravitational acceleration g replaced by a reduced gravity g = g(ρ1−ρ2)/ρ2, where ρ1 and ρ2 are water density in the upper layer and abyssal, respectively. The reduced gravity model is particularly useful in modeling the longest wavelength internal mode in the tropical oceans where the thermocline is tight and shallow.

reef A ridge of coral or rock which lies at or near the surface of the sea.

reference frame A standard of reference used for physical systems, which is in principle equivalent to observations by a real observer, via measurements using the observer’s clock and a local set of Euclidean measurement axes with a length standard. The reference frame is expressed in terms of a set of basis vectors e(a). In principle another set e(b ) of basis vectors can be defined by a nonsingular (not necessarily constant) linear combination

e(b ) = Ab ae(a) .

© 2001 by CRC Press LLC

refractive index

General vectors can be written as a linear combination of the basis vectors:

A = Aae(a) .

See summation convention.

In Newtonian mechanics, global inertial frames are always possible, but not necessary. From the viewpoint of a non-inertial (accelerated and rotating) observer, fictitious (inertial), e.g., the centrifugal and Coriolis, forces appear to act on bodies and particles. This description proved to be of great use in application to the study of mechanics. In general relativity (curved, thus inhomogeneous spacetimes), there exist no global inertial frames. Since general relativity embraces not only mechanics, but the theory of all physical fields as well, their field theoretical counterparts appear alongside the relativistic inertial forces as well. Even in general relativity, to a local freely falling observer inertial forces do not appear, only physically arising forces, e.g., via Coulomb’s law.

reflecting telescope A telescope that is constructed using a mirror as the primary optical element, and which forms a focus by reflection, in contrast to a refracting telescope, where the primary optical element is a lens.

reflection Any wave or particle phenomenon in which an incoming flux strikes a layer and is returned obeying the law: 6n = 6i, where the incident and excident angles 6i, 6r are measured from the normal to the layer. In geophysics, seismic waves are reflected by discontinuities in seismic velocities within the Earth. Important reflections are the Earth’s core, inner core, and Moho. Unconformities in the sedimentary column act as reflecting boundaries and provide data on sedimentary structures, which is important for geophysical exploration.

reflection coefficient In any essentially 1-dimensional wave phenomenon, a typically complex dimensionless number giving the amplitude and phase of a reflected wave compared to the incident wave. In some cases, the term is used to mean the magnitude of this quantity (ignoring the phase). For instance, for water waves it is defined as the ratio of the reflected wave height to the incident wave height.

Krefl = Hr /Hi, where Krefl = reflection coefficient, Hr = height of reflected wave, and Hi = height of incident wave.

reflection nebula A part of the interstellar medium that reflects the light of nearby stars. Reflection nebulae are associated with stars that are not hot enough to ionize the gas.

reflectivity The fraction of incident energy in a particular bandpass reflected in one encounter with a reflecting surface. See emissivity.

refracting telescope A telescope that is constructed entirely using lenses and forms focused images by refraction, in contrast to a reflecting telescope, where the primary optical element is a mirror.

refraction Deflection of direction of propagation of a wave on passing from one region to another with different wave propagation speed. Applied, for instance, to lenses, where the phase speed of light is lower in the glass lens than in air (the glass has a higher refractive index), resulting in a deflection which can be arranged to bring parallel light rays to a focus. In geophysics, the bending of seismic body waves upwards to the Earth’s surface as they pass through the mantle. This bending occurs because the velocity of seismic wave propagation increases with depth. See refractive index.

refraction coefficient In oceanography, a non-dimensional coefficient that represents the increase or decrease in wave height due to

wave refraction for water waves. K = √ r

cosθ1/cosθ2, where Kr = refraction coefficient, θ1 = the angle that the wave crest makes with the bathymetric contours at a particular point 1, and θ2 = the angle between the wave crests and bathymetric contours at a point 2 that has a different depth.

refractive index The complex number for which the real part governs refraction (change of direction) at interfaces, and the imaginary part governs absorption; the real part is the ratio of the velocity of light in vacuum to the phase velocity in the medium (e.g., about 1.34 for seawater).

© 2001 by CRC Press LLC

refractory

refractory Material that resists heat, or in geology, elements or compounds with high melting or dissociation temperatures that remain in formations even after heating. See volatile.

region of anomalous seismic intensity A region where seismic intensity becomes markedly intense for the magnitude of an earthquake or for the epicentral distance. For instance, there are many cases showing that the Pacific coast from Hokkaido to Kanto districts in Japan is a region of anomalous seismic intensity for deep earthquakes beneath the Japan Sea and shallow earthquakes along the Pacific coast. This is thought to be because seismic waves, including shortperiod components, reach the region, passing through the subducted plate with low attenuation. In a more typical situation, seismic waves passing through a high attenuation region away from the subducted plate do not produce sensible ground motion. Recent research also suggests that the existence of a low velocity layer overlying the subducted plate plays an important role in producing a region of anomalous seismic intensity.

Regolith The fine powdery surface of an atmosphereless planet (e.g., the moon) which is produced by radiation and micrometeoric impacts on the surface.

Regulus 1.38 magnitude star of spectral type B7 at RA10h 08m 22.2s, dec +11◦58 02 .

Reissner–Nordström (RN) metric In general relativity, the unique, asymptotically flat metric describing the spherically symmetric gravitational and electric fields of an isolated mass M with electrical charge.

In spherical coordinates (t, r, θ, φ), the line element takes the form (in geometric units with speed of light c = 1, and Newton’s constant G = 1)

 

 

M

Q2

 

ds2

= − 1 −

2

+

 

dt2

r

r2

+ 1 − 2 M + Q2 −1 dr2 r r2

+ r2 dθ2 + sin2 θ dφ2 ,

The electric field is described by a potential φE

= Q/r.

For Q2 > M2 the Reissner–Nordström metric is regular everywhere except for the real (naked) singularity at r = 0. For Q2 ≤ M2, the Reissner-Nordström metric describes a black hole very similar to the Schwarzschild metric; there is an inner and an outer horizon r± =

M ± M2 − Q2 instead of just one horizon. Outside the outer horizon r+ (i.e., for r > r+) the solution has the expected properties of a mass and charged spherical mass (Region I). For r− < r < r+ (Region II) the coordinates switch meaning so that trajectories of worldlines have a spatial separation labeled by t, and evolve with a time parameter related to r. (This latter behavior is found for r < 2M in the uncharged, Schwarzschild, black hole.) The surface r = r+ is a future event horizon. For 0 < r < r−, r takes on again the meaning of a spatial coordinate (and t of time) (Region III). The timelike line r = 0 is a real singularity, visible to observers in Region III.

The Reissner–Nordström metric can be analytically extended by transforming to Kruskallike coordinates so as to cover a larger manifold which contains an infinite chain of asymptotically flat regions of type I connected by regions II and III, the latter being bounded by time-like real singularities. In this case timelike curves exist which thread from regions I (“our universe outside the black hole”) through the hole to another region I. At face value it appears possible to fall into such a hole, and later emerge (elsewhere). However, the sensitivity of the solutions to small perturbations may prevent this possibility. The maximal analytic extension was obtained by Graves and Brill. See ADM mass, black hole, Cauchy singularity, domain of outer communication, future/past event horizon, Kruskal extension, real singularity, Schwarzschild metric.

relative depth A non-dimensional measure of water depth, used in the study of water waves. Defined as the ratio of water depth to wavelength, h/L.

relative humidity The ratio of the amount of moisture in a given volume of space to the amount which that volume would contain in a

© 2001 by CRC Press LLC

residence time (replacement time or average transit time) (TR)

state of saturation, i.e., the ratio of the actual vapor pressure (e) to the saturation vapor pressure (E). The relative humidity f is (as a percentage)

f = e × 100% . E

Relative humidity expresses the saturation status of air. Generally the relative humidity decreases during the daytime as temperature increases, and increases at night as the temperature falls.

relativistic jets Collimated ejection of matter at a velocity close to the speed of light, giving rise to highly elongated, often knotted structures in radio-loud active galactic nuclei, for example, radio quasars and powerful radio galaxies. Radio jets usually originate from an unresolved core and physically connect, or point, to extended lobes. Linear sizes of jets mapped at radio frequencies in external galaxies range from several kpc or tens of kpc, down to the minimum size resolvable with very long baseline interferometers ( 1 parsec). Parsec-size jets show several indications of relativistic motion, including apparent superluminal motion, and jet one-sidedness ascribed to relativistic beaming of radiation. It is less clear whether jets observed at scales of several kiloparsecs are still relativistic. It is thought that only the most powerful radio galaxies, class II according to Fanaroff and Riley, and quasars may sustain a relativistic flow along kiloparsec-sized jets. Jets emit radiation over a wide range of frequencies. This suggests that the radio emission is electron synchrotron radiation. Galactic objects, like the evolved binary system SS 433, and galactic superluminal sources are also believed to harbor relativistic jets. See superluminal source.

relativistic time delay The elongation of the travel-time of an electromagnetic signal, caused by the signal’s passing through a gravitational field. This typically occurs when a radar signal is sent from the Earth, reflected back from another planet to be received at the Earth, perhaps passing near the sun on the way. When the path of the signal does not come near the sun, the time-lapse between the emission of the signal and its reception on the Earth is almost the same as calculated from Newton’s theory. However, if the signal passes near the sun, the distance cov-

ered by the signal becomes longer because the sun curves the spacetime in its neighborhood. When the planet and the Earth are on opposite sides of the sun, and the path of the signal just grazes the sun’s surface, one finds for the relativistic time delay +t:

+t =

GM

4RERp/d2 ,

c3 ln

where M is the mass of the sun, RE is the distance from the sun to the Earth, Rp is the distance from the sun to the planet, and d is the radius of the sun. Here G is Newton’s gravitational constant, and c is the speed of light. The planets used in the measurement are Mercury, Venus, the artificial satellites Mariner 6 and 7, and Mars (where artificial satellites orbiting Mars or landed on Mars were used as reflectors). The value of +t predicted by Einstein’s relativity theory for the situation described above is 240 ms (Shapiro, 1964). This is now one of the standard experimental tests of the relativity theory (along with perihelion shift, light deflection, and the gravitational redshift).

relativity See general relativity, special relativity.

relaxation time Characteristic time to represent rate of relaxation phenomena. For instance, for a viscoelastic body which is characterized by Maxwell model, stress decreases exponentially with time when a deformation is applied at a time and is subsequently kept constant. The time that stress becomes 1/e (e is base of natural logarithms) of the initial value is called relaxation time. Each material has its own relaxation time.

rem An obsolete unit of radiation dose equivalent, equal to 100 ergs per gram.

remote sensing reflectance In oceanography, the ratio of the “water-leaving” radiance in air to the downward plane irradiance incident onto the sea surface [sr−1].

residence time (replacement time or average transit time) (TR) The average length of time that a parcel of water spends in a hydrologic reservoir; the minimum period required for all

© 2001 by CRC Press LLC

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