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Dictionary of Geophysics, Astrophysic, and Astronomy.pdf

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radioisotopes

Radio Frequency Bands

Designation	Band	Frequency	Wavelength
Extremely Low Frequency	ELF	0.003 – 3 kHz	100,000 – 100 km
Very Low Frequency	VLF	3 – 30 kHz	100 – 10 km
Low Frequency	LF	30 – 300 kHz	10 – 1 km
Medium Frequency	MF	300 kHz – 3 MHz	1 km – 100 m
High Frequency	HF	3 – 30 MHz	100 – 10 m
Very High Frequency	VHF	30 – 300 MHz	10 – 1 m
Ultra High Frequency	UHF	300 MHz – 3GHz	1 m – 10 cm
Super High Frequency	SHF	3 – 30 GHz	10 – 1 cm
Extra High Frequency	EHF	30 – 300 GHz	1 cm – 1 mm

radioisotopes The isotopes of elements which are unstable and change into other elements via radioactive decay.

radio lobe Extended, often irregular and ﬁlamentary region of radio emission observed at the end of radio jets on opposite sides of the nucleus, in powerful radio galaxies and quasars. Radio lobes often extend beyond the optical image of a galaxy and typically reach end-to-end sizes of 50 kpc to 1 Mpc (the largest radio lobes known span 9 Mpc). The radio spectral energy distribution of lobes decreases sharply with increasing frequency; lobes are said to be steep spectrum sources in opposition to radio cores which show a ﬂat spectral speciﬁc ﬂux distribution. Emission is due to synchrotron processes, as in radio cores, but produced by electrons with lower energy. A prototypical lobe-dominated radio source is the elliptical galaxy Centaurus A (the brightest radio source in the Centaurus constellation), with two lobes extending far beyond the optical image of the galaxy, each 300 kpc in projected linear size.

radiometer An instrument used to measure radiant energy, as opposed to the number of photons.

radiometric dating A method of obtaining absolute ages of geological specimens by comparing relative concentrations of parents and daughter elements for a particular radioactive decay.

radiometry The science of the measurement of radiant energy.

radio stars Stars whose radio emission is strong enough to be detected from Earth. This is rather rare and generally associated with extreme youth (see stellar activity) or presence of a companion (see RS Canum Venaticorum stars). Radio stars are particularly important because they permit coordinate systems on the sky determined separately from radio and optical data to be combined.

radius of deformation A horizontal length scale deﬁned as r = c/f, where c is the phase speed of long gravity waves in the ocean or atmosphere, and f = 2 sin θ is the Coriolis parameter with being the angular velocity of Earth’s rotation and θ latitude. For motion of horizontal scales larger than the deformation radius, rotation effects are dominant, whereas for motion of smaller horizontal scales, rotation effects are less important. On the equator, f vanishes and the equatorial radius of deformation is deﬁned as rE = √c/β where β = 2 cos θ is the meridional gradient of the Coriolis parameter.

radon A radioactive colorless noble gas, Rn. Atomic number 86, natural atomic number 222. Melting temperature 202 K; boiling temperature 211.3 K. Radon exhibits an orange to yellow ﬂuorescense in the solid state. Radon is produced

as a daughter element in α− decay of radium. The longest-lived isotope is 222Rn which has a

half-life of 3.825 days, much longer than that of the other known isotopes (210Rn to 221 Rn). All

isotopes decay by α emission; 210Rn and 211Rn also have an electron capture branch, and 221Rn also has a β− decay branch.

Raychaudhuri equation

Recently radon buildup in buildings has been a concern because inhaling the element directly irradiates the lungs, potentiating lung cancer, especially in conjunction with smoking. U.S. standards recommend action if the air radon load exceeds four picoCuries per liter.

rain Liquid water precipitation that reaches the ground. Rain drops (water droplets) accumulate on condensation centers in clouds until they are too heavy to remain suspended and then fall earthward.

rainbow An arc that displays a spectrum of colors and appears opposite the sun when solar rays are refracted and reﬂected in raindrops, spray, or mist. Bright, primary rainbows have a color pattern ranging from blue on the inside at about 40◦ from the center of the arc, to red on the outside of the arc at about 42◦ from the center.

Raman scattering Inelastic photon scattering in which the energy of the scattered photon equals the energy of the incident photon plus or minus energy determined by the vibrational and rotational frequencies of the molecule; characterized by a volume scattering function that has forward-backward directional symmetry. See scattering cross-section.

random waves In oceanography, waves that include a variety of wave periods, as opposed to a single period, which would deﬁne a monochromatic sea. If the range in wave periods is small, a narrow-banded energy spectrum results. A wide range of periods will yield a broad-banded energy spectrum.

Rankine–Hugoniot relations Relations describing the conservation of mass, momentum, energy, and the electromagnetic ﬁeld across the shock front. With the abbreviation [X] = Xu − Xd describing the change of a property X from the upstream to the downstream medium, the

Rankine–Hugoniot relations are: Conservation of mass:

[mvn] = [!vn] = 0 .

Momentum balance, with the last two terms describing the magnetic pressure perpendicular

and normal to the shock front:			4π	=0 .
!u(un) +	p + 8π n −
		B2	(Bn)B

Energy balance, containing ﬂow, internal and electromagnetic energy:

un	!u		γ		B2
		+		p +
	2		γ − 1		4π

−(Bn)(Bu) = 0 .

4π

Continuity of the normal component of the magnetic ﬁeld (this is a direct consequence of Gauss’ law of the magnetic ﬁeld, · B = 0):

[B · n] = 0 .

Continuity of the tangential component of the electric ﬁeld:

[n × (v × B)] = 0 .

In the above relations v is the plasma ﬂow speed, B the magnetic ﬁeld, n the shock normal, ! the density, p gas-dynamic pressure, and γ the speciﬁc heat ratio.

In purely gas-dynamic shocks, all terms containing the electromagnetic ﬁeld vanish, the Rankine–Hugoniot relations then are limited to the conservation of mass, momentum, and energy.

rare earth elements The elements Sc, Y, and the lanthanides (La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Hy, Ho, Er, Tm, Yb, Lu).

Raychaudhuri equation An equation relating the local expansion, rotation, and shear of a set of nearby trajectories of either material particles, or photons representing speed-of-light matter:

θ˙ = −1 θ2 −σ σ ij +ω ωij −R uαuβ +aα .

ij ij αβ ;α

(We sum over repeated indices.)

The dot indicates a time derivative associated with proper time for a central particle or with afﬁne parameter for a photon. Here θ is the expansion, deﬁned as the time rate of change of the local volume containing the matter (hence

Rayleigh distribution

θ = −ρ/ρ˙ , where ρ is the density of the points being followed.) θ can also be deﬁned in terms of the local velocity ﬁeld uµ : θ = uµ;µ, the divergence is taken using the 4-velocity and 4- metric. The “;” is the metric covariant derivative.

Similarly the shear, σij is the 3-tensor deﬁning non-spherical motion

σij =	uα;β + uβ;α − 3 gαβ θ PiαPjβ
	1

and Piβ is a projection into the 3-space associated with the central particle. The quantity aα

is the acceleration of the velocity uα : aα =

uα;β uβ .

Finally

ωij = uα,β − uβ,α PiαPjβ

is the rotation 3-tensor. The appearance of the Ricci tensor Rαβ in the Raychaudhuri equation can be related via Einstein’s equations to the gravitational focusing power of matter. It can be seen that θ and σij act to decrease the expansion, ωij acts to increase it. See summation convention.

Rayleigh distribution A probability density function. It has non-zero skewness and describes the distribution of certain non-negative parameters (such as wave height in deep water).

Rayleigh–Jeans approximation An approximation to Planck’s blackbody equation for monochromatic speciﬁc intensity at long wavelengths. For long wavelengths, we can make the approximation hν << kT, where h is Planck’s constant, ν is the frequency of the radiation in Hertz, k is Boltzmann’s constant, and T is the excitation temperature; then a Taylor expansion in temperature of the Planck equation gives:

2kT Iν = ν2c2

where Iν is the intensity of the radiation in units of erg s−1 cm−2 Hz−1 sr−1. The Rayleigh– Jeans approximation is useful to describe blackbody radiation in the domain of submillimeter and radio astronomy. If the intensity is in units of wavelength, then the approximation becomes

2ckT

Iλ = λ4 .

See Planck’s law.

Rayleigh number Fluid, heavier by +ρ/ρ on top of lighter ﬂuid may remain laminar despite the static instability (see stability), as long as the

Rayleigh number Ra < 1700±50. Ra is deﬁned as the ratio of (inertial time scale)2/ (thermal diffusive time scale × viscous diffusive time scale) or explicitly in terms of the relevant parameters Ra = g(+ρ/ρ)H3/(νDT), where +ρ/ρ is density difference between top and bottom, g is gravitational acceleration, H is thickness of the unstable layer, ν is kinematic viscosity, and DT is thermal diffusivity. Critical Rayleigh numbers, allowing the ﬂuid to become unstable can be achieved in laboratory applications. Natural convective systems (such as atmosphere, ocean, lakes) show very large Ra and always turn turbulent under unstable conditions (see convective turbulence).

Rayleigh scattering The scattering of light by a body small compared to the wavelength of the light. For a given refractive index, the scattering cross-section varies like the wavelength to the inverse fourth power. The light is scattered symmetrically forward and backwards, with the percentage of light scattered to a cone at an angle θ from the forward direction being proportional to cos2θ.

Rayleigh wave A seismic surface wave resulting from the coupling of the P wave and the vertically polarized shear wave (SV) near the free surface. The speed of the Rayleigh wave is less than that of the shear (S) wave. In Rayleigh wave propagation, the particle motion forms a retrograde ellipse with the major axis vertical and the minor axis in the direction of wave propagation. For this reason, the Rayleigh wave is also called “ground roll” in exploration seismology. Rayleigh waves along the surface of a layered crust are dispersive. See dispersion.

ray parameter A geometrical quantity that is preserved by a seismic wave as it is refracted through a medium with a variable wave speed. In particular for a spherically symmetric stratiﬁed Earth, the ray parameter p is deﬁned by:

= r sin θi

red giant

where r is the distance from the center of the Earth, v is the local appropriate wave speed, and θi is the angle that the direction of phase propagation makes with a radial vector from the center of the Earth. It can be shown that

p = dT d+

where T is the travel time of the ray from source to receiver, and + is the angle between lines from the two to the center of the Earth. In a horizontally stratiﬁed situation (which is approximately true near the Earth’s surface, where variations in r can be neglected to ﬁrst order) the ray parameter simpliﬁes to p = R sin θi/v. If v is known as a function of radius or depth, then it is easy to use p to calculate the path taken by a ray emitted from a seismic source at a particular angle θi.

ray tracing Determining the path of a wave propogation by the use of the laws of reﬂection and refraction, ignoring diffraction.

ray tracing: wave packet approximation

The method by which the dominant wave behavior of light or other waves is taken into account, in which the central motion of approximately described wave packets determines the ray paths.

R Coronae Borealis stars Highly evolved, asymptotic giant branch stars that have shed (or burned) all of their hydrogen, leaving an atmosphere made mostly of helium and carbon. The carbon sporadically condenses into dust, veiling the visible light from the stars, so that they fade by many magnitudes in a few weeks. The dust is gradually blown away, and the stars brighten back to normal, only to fade again in a few years. Most are also pulsationally unstable (see instability strip) and show rather subtle periodic changes in size and brightness with periods of one to a few months.

RE See Earth radius.

real singularity In general relativity a region in space-time where some invariant geometrical quantities diverge, or where extension of ﬁnite acceleration curves is impossible.

Examples are the centers of black holes and white holes (e.g., see Schwarzschild metric).

Singularities can be space-like (occurring everywhere “simultaneously”) or time-like (occurring over a period of time). See black hole, white hole.

recombination (in atomic and molecular physics) Any of a number of processes in which an atom or molecule with positive charge reacts with another species or particle of negative charge. The different types of recombination can be represented:

X+ + e− → X + hν (radiative)

X+ + e− → X → X + hν (dielectronic)

XY + + e− → X + Y (dissociative)

X+ + Y − + M → Z + M (three–body)

X+ + Y − → X + Y (mutual neutralization)

where hν represents a photon released in the process, e− an electron, Y represents an excited state of species Y , M is a third particle that can absorb the energy released, and Z can be X, Y , or a new resulting species.

recombination line An emission line produced by the quantum transition between two states of an atom or molecule, in which the energetically higher state was produced by the recombination of an atom or molecule with an electron either directly or by other transitions following the recombination event. See emission line, recombination.

reconnection A process in a magnetized plasma, such as the solar magnetosphere, wherby diffusion of the ions allows adjacent oppositely directed ﬂux lines to merge and cancel, lowering the total energy of the ﬁeld. See also intercommutation (cosmic string).

recurrent novae Ordinary novae of the sort involving a nuclear explosion on the surface of a white dwarf, but where the hydrogen to be burned collects fast enough again that more than one event has been seen in historic times. Only about six examples are known, and particular systems are often added to or subtracted from the inventory as we learn more about them.

red giant The evolutionary phase of a star of 0.8 to about 5 solar masses during which the

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