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Dictionary of Geophysics, Astrophysic, and Astronomy.pdf

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Bogomol’nyi bound The mass of a (magnetic) monopole depends on the constants that couple the Higgs ﬁeld with itself and with the gauge ﬁelds forming the monopole conﬁguration. The energy of a monopole conﬁguration can be calculated, albeit numerically, for any value of these constants. It can, however, be seen that the mass always exceeds a critical value, ﬁrst computed by E.B. Bogomol’nyi in 1976, which is

mM ≥ η/e ,

where η is the mass scale at which the monopole is formed, and e is the coupling of the Higgs ﬁeld to the gauge vectors Aaµ (a being a gauge index). The bound is saturated, i.e., equality holds, when the ratio of the coupling constants vanishes, a limit known as the Prasad– Sommerﬁeld limit. Since magnetic monopoles may be produced in the early universe, this limit is of relevance in cosmology. See cosmic topological defect, monopole, Prasad–Sommerﬁeld limit, t’Hooft–Polyakov monopole.

Bohr’s theory of atomic structure Theory of the atomic structure of hydrogen postulated by Neils Bohr (1885–1962). The theory is based upon three postulates: 1. The electrons rotate about the nucleus without radiating energy in the form of electromagnetic radiation. 2. The electron orbits are such that the angular momentum of the electron about the nucleus is an integer of h/2π, where h is Planck’s constant. 3. A jump of the electron from one orbit to another generates emission or absorption of a photon, whose energy is equal to the difference of energy between the two orbits. This theory has now been superseded by wave mechanics, which has shown that for the hydrogen atom spectrum, Bohr’s theory is a good approximation.

bolide A meteoroid that explodes or breaks up during its passage through the atmosphere as a meteor.

bolometric correction (B.C.) The correction to an observed magnitude (luminosity) in a particular wavelength region to obtain the bolometric magnitude (luminosity). This correction is to account for the stellar ﬂux that falls beyond the limits of the observed wavelength region.

bolometric magnitude/luminosity The luminosity of a star integrated over all wavelengths the star radiates. This is a measure of the total energy output of a star.

Boltzmann’s constant (k) Constant of proportionality between the entropy of a system

Sand the natural logarithm of the number of all possible microstates of the system 8, i.e.,

S= k ln(8). When one applies statistical mechanics to the ideal or perfect gas, one ﬁnds that Boltzmann’s constant is also the constant of proportionality of the equation of state of an ideal gas when the amount of gas is expressed in the number of molecules N rather

than the number of moles, i.e., P V = NkT . k = 1.3806503(24) × 10−23 J K−1. Named

after Ludwig Boltzmann (1844–1906).

Bondi mass In general relativity the function m(r, t) equal to the total energy contained inside the sphere of radius r at the time t. If there is no loss or gain of energy at r → +∞, and the space is asymptotically ﬂat, then

lim m(r, t) = MADM ,

r→+∞

where MADM is the ADM mass. See ADM mass, asymptotic ﬂatness.

Bonnor symmetry A stationary (i.e., rotating) axisymmetric vacuum space-time can be mapped to a static axisymmetric electrovacuum space-time. In this process, the twist potential must be extended in the complex plane. When the twist is proportional to a real parameter, the complex continuation of this parameter can be used to make the resulting twist potential real. See electrovacuum.

bore A steep wave that moves up narrowing channels, produced either by regular tidal events, or as the result of a tsunami. A bore of this type, generated by an earthquake off the coast of Chile, destroyed Hilo on the island of Hawaii on May 22, 1960.

borrow site A source of sediment for construction use. May be on land or offshore.

boson

boson An elementary particle of spin an integer multiple of the reduced Planck constant h¯. A quantum of light (a photon) is a boson.

boson star A theoretical construct in which the Klein–Gordon equation for a massive scalar

ﬁeld φ:

φ + m2φ = 0

is coupled to a description of gravity, either Newtonian gravity with φg the gravitational potential

2φg = 4πG1 ( φ)2

or General Relativistic gravitation:

Gµv = 8πGTµv(φ)

where Tµv(φ) is the scalar stress-energy tensor. In that case the wave operator applied to φ is the covariant one. φ = φα;α. Stable localized solutions, held together by gravity are called boson strings. Nonstationary and nonspherical boson stars may be found by numerical integration of the equations.

Bouguer correction A correction made to gravity survey data that removes the effect of the mass between the elevation of the observation point and a reference elevation, such as the mean sea level (or geoid). It is one of the several steps to reduce the data to a common reference level. In Bouguer correction, the mass in consideration is approximated by a slab of inﬁnite horizontal dimension with thickness h, which is the elevation of the observation point above the reference level, and average density ρ. The slab’s gravitational force to be subtracted from the measured gravity value is then g = 2πGρh, where G is the gravitational constant.

Bouguer gravity anomaly Much of the point-to-point variation in the Earth’s gravity ﬁeld can be attributed to the attractions of the mass in mountains and to the lack of attraction of the missing mass in valleys. When the attraction of near surface masses (topography) is used to correct the “free-air” gravity measurements, the result is a Bouguer-gravity map. However, major mountain belts (with widths greater than about 400 km) are “compensated”. Bouguer gravity anomalies are caused by inhomogeneous

lateral density distribution below the reference level, such as the sealevel, and are particularly useful in studying the internal mass distributions. Thus, the primary signal in Bouguer gravity maps is the negative density and the negative gravity anomalies of the crustal roots of mountain belts.

Bouguer–Lambert law (Bouguer’s law)

See Beer’s law.

bounce motion The back-and-forth motion of an ion or electron trapped in the Earth’s magnetic ﬁeld, between its mirror points. This motion is associated with the second periodicity of trapped particle motion (“bounce period”) and with the longitudinal adiabatic invariant.

boundary conditions Values or relations among the values of physical quantities that have to be speciﬁed at the boundary of a domain, in order to solve differential or difference equations throughout the domain. For instance, solving Laplace’s equation φ = 0 in a 3- dimensional volume requires specifying a priori known boundary values for φ or relations among boundary values of φ, such as speciﬁcation of the normal derivative.

boundary layer pumping	Ekman pumping.
Boussinesq approximation	In the equation

of motion, the density variation is neglected except in the gravity force.

Boussinesq assumption The Boussinesq assumption is employed in the study of open channel ﬂow and shallow water waves. It involves assumption of a linearly varying vertical velocity, zero at the channel bottom and maximum at the free surface.

Boussinesq equation The general ﬂow equation for two-dimensional unconﬁned ﬂow in an aquifer is:

∂x	h∂x		+	∂y	h ∂y	=	K ∂t
∂		∂h		∂	∂h		Sy ∂h

where Sy is speciﬁc yield, K is the hydraulic conductivity, h is the saturated thickness of the aquifer, and t is the time interval. This equation

Brans–Dicke theory

is non-linear and difﬁcult to solve analytically. If the drawdown in an aquifer is very small compared with the saturated thickness, then the saturated thickness h can be replaced with the average thickness b that is assumed to be constant over the aquifer, resulting in the linear equation

∂2h	+	∂2h		=	Sy ∂h
							.
∂x2			∂y2		Kb	∂t

Bowen’s ratio The ratio between rate of heat loss/gain through the sea surface by conduction and rate of heat loss/gain by evaporation/condensation.

Boyle’s law For a given temperature, the volume of a given amount of gas is inversely proportional to the pressure of the gas. True for an ideal gas. Named after Robert Boyle (1627– 1691).

Brackett series The set of spectral lines in the far infrared region of the hydrogen spectrum with frequency obeying

ν = cR 1/n2f − 1/n2i ,

where c is the speed of light, R is the Rydberg constant, and nf and ni are the ﬁnal and initial quantum numbers of the electron orbits, with nf = 4 deﬁning the frequencies of the spectral lines in the Brackett series. This frequency is associated with the energy differences of states in the hydrogen atom with different quantum numbers via ν = AE/h, where h is Planck’s constant and where the energy levels of the hydrogen atom are:

En = hcR/n2 .

Bragg angle Angle θ which relates the angle of maximum X-ray scattering from a particular set of parallel crystalline planes:

sin θ = nλ/(2d)

where n is a positive integer, λ is the wavelength of the radiation, and d is the normal separation of the planes. θ is measured from the plane (not the normal).

Bragg Crystal Spectrometer (BCS) Bragg Crystal Spectrometers have been ﬂown on a number of solar space missions including the Solar Maximum Mission (1980–1989). Such a spectrometer is currently one of the instruments on the Yohkoh spacecraft. This instrument consists of a number of bent crystals, each of which enables a selected range of wavelengths to be sampled simultaneously, thus providing spectroscopic temperature discrimination. Typical wavelengths sampled by these detectors lie in the soft X-ray range (1 to 10 Å).

braided river A river that includes several smaller, meandering channels within a broad main channel. The smaller channels intersect, yielding a braided appearance. Generally found at sites with steeper slopes.

Brans–Dicke theory Or scalar-tensor theory of gravitation. A theory of gravitation (1961) which satisﬁes the weak equivalence principle but contains a gravitational coupling GN , which behaves as (the inverse of) a scalar ﬁeld φ. This φ ﬁeld satisﬁes a wave equation with source given by the trace of the energy momentum tensor of all the matter ﬁelds. Thus GN is not generally constant in space nor in time. The corresponding action for a space-time volume V can be written as

S = 1

16π

d4x√−g φR + ωφ−1∂µφ∂µφ + LM ,

where R is the scalar curvature associated to the metric tensor whose determinant is g, ω is a coupling constant, and LM is the matter Lagrangian density.

In the limit ω → ∞ the scalar ﬁeld decouples, and the theory tends to general relativity. For ω ﬁnite, instead, it predicts significant differences with respect to general relativity. However, from tests of the solar system dynamics, one deduces that ω > 500 and the theory can lead to observable predictions only at the level of cosmology. In the Brans–Dicke theory the strong equivalence principle is violated, in that objects with different fractional gravitational binding energy typically fall at different rates.

Brazil current

A generalization of Brans–Dicke theory is given by the dilaton gravity theories, in which the scalar ﬁeld φ is called the dilaton and couples directly to all matter ﬁelds, thus violating even the weak equivalence principle. See dilaton gravity.

Brazil current A warm ocean current that travels southwestward along the central coast of South America.

breaker zone The nearshore zone containing all breaking waves at a coast. Width of this zone will depend on the range of wave periods and heights in the wave train and on bathymetry.

breakwater A man-made structure, often of rubble mound construction, intended to shelter the area behind (landward of) it. May be used for erosion control or to shelter a harbor entrance channel or other facility.

breccias Composite rocks found on the moon, consisting of heterogeneous particles compacted and sintered together, typically of a light gray color.

Bremsstrahlung (German for braking radiation.) Radiation emitted by a charged particle under acceleration; in particular, radiation caused by decelerations when passing through the ﬁeld of atomic nuclei, as in X-ray tubes, where electrons with energies of tens of kilovolts are stopped in a metal anode. Bremsstrahlung is the most common source of solar ﬂare radiation, where it is generated by deceleration of electrons by the Coulomb ﬁelds of ions.

bremstrahlung [thermal] The emission of bremstrahlung radiation from an ionized gas at local thermodynamic equilibrium. The electrons are the primary radiators since the relative accelerations are inversely proportional to masses, and the charges are roughly equal. Applying Maxwell’s velocity distribution to the electrons, the amount of emitted radiation per time per volume per frequency is obtained for a given temperature and ionized gas density.

Brewster point One of three points on the sky in a vertical line through the sun at which

the polarization of skylight vanishes. Usually located at about 20◦ below the sun. See Arago point, Babinet point.

brightness The luminosity of a source [J/sec] in the bandpass of interest. (For instance, if referred to visual observations, there are corrections for the spectral response of the eye.) Apparent brightness of a stellar object depends on its absolute luminosity and on its distance. The ﬂux of energy through a unit area of detector (e.g., through a telescope objective) is F = L/4πr2 [J/sec/m2]. Stellar apparent magnitude gives a logarithmic measure of brightness: m = −2.5 log(F ) + K. The magnitude scale is calibrated by ﬁxing the constant K using a number of ﬁducial stars. Absolute magnitude is deﬁned as the apparent magnitude a source would have if seen at a distance of 10pc and is a measure of the absolute brightness of the source.

brightness temperature The temperature of an equivalent black body with a given intensity and long wavelengths where the Rayleigh– Jeans approximation is valid. This temperature is used in radio and submillimeter astronomy and is given by

= Iνc2 TB 2kν2

where h and k are the Planck and Boltzmann constants, respectively, ν is the frequency in Hertz, and I ν is the monochromatic speciﬁc intensity (i.e., the ﬂux per frequency interval per solid angle) in units of erg s−1 cm−2 Hz−1 sr−1. To relate an object’s brightness temperature to its ﬂux density in Janskys, the size of the source in stearadians (or the full width of the main beam of the radiotelescope) is used:

Sν = 2πkTB θ24ln2/λ2

which reduces to

Sν = 7.35 × 10−4θ2TB /λ2

where θ is the width of the telescope’s full beam at half maximum in arcseconds, TB is the brightness temperature in Kelvins, λ is the center wavelength in centimeters, and Sν is the ﬂux density in Janskys.