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Baily’s beads


Baade–Wesselink method A method of determining the distance to pulsating stars, which can also be observed spectroscopically. One estimates the surface temperature and hence the surface brightness from the color index (B V color), based on simultaneous measurements of the blue and visual magnitude at bright and dim epochs in the star’s pulsation. One computes the square root of the ratio of the observed flux to the surface brightness for each of these epochs. This is an estimate of the angular diameter of the star. Spectroscopy yields the surface velocity of the star (via blue and red shifting of spectral lines), which leads to a determination of the total difference in radius of the star between the observations. The combination of these observations allows a determination of the physical size of the star, and thus of its absolute magnitude and distance. The method has also been applied to the expanding envelope of type II supernovae.

Babinet 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 20above the sun. See Arago point, Brewster point.

baby universe A theory regarding matter that falls into a black hole that subsequently evaporates. It states that this matter may go into a separate space-time, which could detach from the universe at one location and reattach elsewhere. This may not be particularly useful for space travel, but the existence of baby universes introduces a randomness so that even a complete unified theory would be able to predict much less than expected. However, averaging over ensembles of universes containing baby universes may lead to predictions via expected values of certain measured quantities, such as the cosmological constant.

backarc spreading




zones (ocean trenches)



of sea-floor

spreading occurs behind the subduction zone, thus creating new oceanic crust. The Sea of Japan is an example. The foundering oceanic plate pulls away from the adjacent continental margin, and backarc spreading fills the gap.

back scattering

Scattering through angles

greater than 90.



backscattering coefficient

The integral over

the hemisphere of backward directions of the volume scattering function.

backscattering fraction The ratio of the backscattering coefficient to the scattering coefficient.

backshore The relatively flat portion of a beach profile which lies between the steeper beachface and the dunes, cliffs, or structures behind the beach. Subaerial during non-storm conditions.

Backus effect A particular type of nonuniqueness that can occur in the inversion of geomagnetic data on a spherical surface, where instead of knowing the full vector magnetic field only the magnitude of the field B is known and not its orientation. Historically, early satellite measurements from platforms such as the POGOs are of this form, as it was difficult to obtain high quality measurements of satellite orientation. The effect occurs even if there is perfect knowledge of B on a spherical surface but can be alleviated by knowledge of B in a shell or by knowledge of the position of the magnetic equator. The source of the error is the existence of magnetic fields that are perpendicular to Earthlike fields everywhere on a spherical surface, and which, therefore, can be added or subtracted from the Earth’s field without changing B. As the Earth’s field is predominantly axial dipolar, the error terms associated by the Backus effect have strong sectoral variation in a band around the equator. See nonuniqueness.

Baily’s beads A phenomenon appearing at the onset and at the conclusion of a solar eclipse, in which the photosphere is almost totally eclipsed, except for a few locations on the limb of the moon, which allow view of the pho-

© 2001 by CRC Press LLC

Ballerina model

tosphere through lunar valleys. If only one bead is apparent, a “diamond ring effect” is produced.

Ballerina model Shape of the heliospheric current sheet as proposed by H. Alfvén in the early 1970s. The wavy neutral line on the source surface is carried outwards by the solar wind, resulting in a wavy heliospheric current sheet that resembles the skirt of a dancing ballerina. The waviness of this current sheet is described by the tilt angle. See heliospheric current sheet, source surface, tilt angle.

Balmer series The series of lines in the spectrum of the hydrogen atom which corresponds to transitions between the state with principal quantum number n = 2 and successive

higher states. The wavelengths are given by 1= RH (1/4 1/n2), where n = 3, 4, . . .

and RH is the Rydberg constant for hydrogen. The first member of the series (n = 2 3), which is often called the Hα line, falls at a wavelength of 6563 Å. See Rydberg constant.

banner cloud An altocumulus lenticularis cloud, (lenticular cloud) which forms on the lee side of the top of a mountain and remains a stationary feature with one edge attached to the ridge of the mountain.

bar A unit of pressure, defined as 106 dyne/cm2 (105 N/m2). The bar is commonly divided into 1000 mb. The pressure of atmosphere at sea level is about 1013 hPa = 1.013 bar.

bar detectors Solid bars, made of metallic alloys, for detecting gravitational waves. The technology was pioneered by J. Weber. The sensitivity of h = 1018 (relative strain) has been reached in second-generation cryogenic detectors. At this level of sensitivity, no gravitational wave event has yet been reliably detected. See LIGO.

barium release An experimental procedure near-Earth space physics, in which barium is evaporated by a thermite charge, usually in a sunlit region above the (denser) atmosphere, creating a greenish cloud. Barium atoms are rapidly ionized (within 10 sec or so), and the ions form a purple cloud, which responds to

magnetic and electric fields and therefore often drifts away from the neutral one.

The technique was pioneered by Gerhard Haerendel in Germany, and many releases have been conducted from rockets above the atmosphere, often with the barium squirted out by a shaped explosive charge. Typically releases are made after sunset or before sunrise, so that the rocket rises into sunlight but the clouds are seen against a dark sky. Effects of electric fields have been observed, striations like those of the aurora, even abrupt accelerations along field lines. Some releases have taken place in more distant space, notably an artificial comet in the solar wind, produced in 1984 by the AMPTE mission.

Barnard’s star Star of spectral type M3.8, 5.9ly distant with magnitude m = 9.5 and absolute magnitude M = 13.2; located at Right Ascension 17h58m, declination +0441 . Discovered in 1916 by E.E. Bernard, it has the largest known proper motion: 10.29 arcsec/year. Measurements by van de Kamp had suggested that there were perturbations of the motion corresponding to an associated planet, but recent observations using the Hubble space telescope have not confirmed this claim.

baroclinic atmosphere or ocean An atmosphere or ocean in which the density depends on both the temperature and the pressure. In a baroclinic atmosphere or ocean, the geostrophic wind or current generally has vertical shear, and this shear is related to the horizontal temperature or density gradient by the thermal wind relation.

baroclinic instability A wave instability that is associated with vertical shear of the mean flow and that grows by converting potential energy associated with the mean horizontal temperature or density gradient.

baroclinic wave Wave in the baroclinic flow.

barotropic atmosphere or ocean An atmosphere (or ocean) in which the density depends only on the pressure. In the barotropic atmosphere or ocean, the geostrophic wind or current is independent of height.

© 2001 by CRC Press LLC


barotropic instability A wave instability associated with the horizontal shear in a jet-like current and that grows by extracting kinetic energy from the mean flow field.

barotropy ln fluid mechanics, the situation in which there is no vertical motion, and the gradients of the density and pressure field are proportional, and the vorticity (as measured in an inertial frame) is conserved.

barred galaxies Disk galaxies showing a prominent, elongated feature, often streaked by absorption lanes due to interstellar dust. Prominent bars are observed in about 13 of disk galaxies; approximately 23 of galaxies do, however, show some bar-like feature. A bar can contribute to a substantial part, up to 13 , of the total luminosity of a galaxy. The bar photometric profile is quite different from the photometric profile of galaxies: the surface brightness along the bar major axis is nearly constant but decreases rapidly along the minor axis. The bar occupies the inner part of the galaxy rotation curve where the angular speed is constant; bars are therefore supposed to be rotating end over end, like rigid bodies.

barrier island An elongated island separated from a coast by a shallow bay or lagoon. Generally much longer in the longshore direction than cross-shore direction. The Outer Banks of North Carolina and much of the east coast of Florida provide good examples.

barriers When an earthquake is caused by a rupture on a fault, inversions of seismic waves indicate some portions of the fault do not rupture; these are barriers.

Barycentric Coordinate Time (TCB) Barycentric Dynamical Time has been deemed by the International Astronomical Union (IAU) to be an inferior measure of time in one sense: Its progress depends on the mass of the sun and the mean radius and speed of the Earth’s motion around the sun, and, to a smaller extent, on the mean gravitational perturbations of the planets. Therefore, in 1991 the IAU established a time standard representing what an SI clock would measure in a coordinate sys-

tem, such that the barycenter of the solar system was stationary in this nearly inertial system, as was the clock, but the clock was so far removed from the sun and planets that it suffered no gravitational effect. That time is T CB = T DB +LB ·(JD2443144.5)·86400 sec, where LB = 1.550505 · 108 by definition as of mid-1999, and JD stands for the Julian Date in TDT. Presumably, the “constant”, b, is subject to revision when and if the mass content of the solar system or the properties of the Earth’s orbit are redetermined. See Barycentric Dynamical Time.

Barycentric Dynamical Time (TDB) In 1977, Dynamical Time was introduced as two forms, Terrestrial Dynamical Time (TDT) (q.v.) and TDB, on the basis of a 1976 IAU resolution. The difference between these two consists of periodic terms due to general relativity. TDB is commonly used for the determination of the orbits of the planets and their satellites, except those of the Earth. It is particularly suited to this purpose because it is adjusted from TDT in such a way as to represent what a clock on the geoid would measure if the Earth orbited the sun in a circular orbit of radius 1 astronomical unit (q.v.), while TDT contains relativistic effects of the eccentricity of the Earth’s orbit. See also Barycentric Coordinate Time (TCB). Approximately, T DB = T DT + 0.001652825 cos(g)s where g is the mean anomaly (q.v.) of the Earth in its orbit. See Ephemeris Time, dynamical time.

baryogenesis Period of the early evolution of the universe when baryons were generated from quarks. Observationally, the universe is made of normal matter, containing baryons and leptons with no observational evidence of significant amounts of antimatter anywhere. Similarly to the successful predictions of nucleosynthesis, the unfulfilled goal is to build a scenario where, starting from a baryon symmetric state, quark and lepton interactions lead to an excess of matter over antimatter as the photon temperature drops. It will suffice to produce an excess of 1 baryon every 109 antibaryons to give rise to a universe made of normal matter and a baryon- to-photon ratio η 109, as observed.

© 2001 by CRC Press LLC


In 1967 Sakharov identified the three necessary ingredients to dynamically evolve a baryon asymmetry: (i) Baryon Number Violation. If a baryon number is conserved in all interactions, the absence of antimatter indicates asymmetric initial conditions. (ii) C and CP Violation. If not, B-violating interactions will produce excesses of baryons and antibaryons at the same rate, thereby maintaining zero baryon number. (iii) Non-thermal equilibrium, otherwise the phase space density of baryons and antibaryons are identical. So far, a successful model has not been made because it requires physics beyond the standard model of particle interactions.

basalt Volcanic mafic igneous rocks containing minerals such as pyroxene and olivine. The most common volcanic rock. Produced by about a 20% melting of the mantle.

basaltic lava A form of molten rock that emerges in volcanic outflows at a temperature of 1000C to 1250C. Examples include eruptions in the Hawaiian chain.

basement In many parts of the continents the surface rocks are sediments. Sediments are products of erosion. These sediments lie on top of either metamorphic or igneous rocks. The boundary is termed basement. The depth to basement can range from a few meters to a maximum of about 20 km.

basic MUF Defined as the highest frequency by which a radiowave can propagate between given terminals on a specified occasion, by ionospheric refraction alone, and may apply to a particular mode, e.g., the E-layer basic MUF. The basic MUF depends on the critical frequency (fc) of the ionosphere at the mid-point of the path and the angle of incidence (I) of the radiowave on the ionosphere, and to a good approximation MUF = fc sec(I). The factor, sec(I), is called the obliquity factor for the circuit because it relates the vertical incidence ionospheric information to the oblique incidence path. A further correction is required to allow for a curved Earth and ionosphere. For a given radiowave takeoff angle, the obliquity factor reduces as the reflecting layer height increases; thus it is greatest for the E

and Es layers and least for the F2 layer. It is conventional to use a standard 3000 km obliquity factors, M(3000)F2, for the F region and convert this to other pathlengths. The M(3000)F2 can be measured directly from ionograms. See ionospheric radio propagation path, operational MUF.

Batchelor scale Length scale at which turbulent concentration (or temperature) gradients in a fluid are damped out by molecular viscous effects; alternately, the length scale, at which the sharpening of the concentration (or temperature) gradients by the strain rate is balanced by the smoothing effect of molecular diffusion. This length depends on the kinematic viscosity ν, the molecular diffusion coefficient κ, and the dissipation rate of turbulent kinetic energy :

LB =

νκ2 1/4

At scales smaller than LB , scalar fluctuations disappear at a fast rate and subsequently the Batchelor spectrum drops sharply off. Most commonly the Batchelor scales are used for temperature = κT) and salt = κS), respectively. In oceanic turbulence studies, LB is most commonly defined using κT, because temperature is easily measured. The Batchelor scales for temperature and salt (typical scales of mm and sub-mm in natural waters, respectively) are smaller than the Kolmogorov scale LK , since in water molecular diffusivities are much smaller than viscosity ν (DT100 and DS1000 in natural waters). See also Kolmogorov scale.

Batchelor spectrum Under isotropic and stationary conditions, the power spectrum of the one-dimensional temperature fluctuations follows










φT (kz) =

















exp xx2

π(1 erf (x))












where kz denotes the one-dimensional wavenumber [rad m1], x = kzq 2LB = kzκT1/2

© 2001 by CRC Press LLC

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