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black frost

space-time in general relativity with no cosmological term is the Schwarzschild space-time. Since the latter is static, this also rules out monopole gravitational waves. Further, the empty space-time inside a spherically symmetric source must be flat. Generalizations with the inclusion of a Maxwell field and cosmological constant have been given. See Schwarzschild solution.

Bjerknes See Bergen school.

Bjerknes circulation theorem The rate of circulation change is due to either the baroclinicity or the change in the enclosed area projected in the equatorial plane:

Dt

= −

ρ

− 28

Dte

DC

 

dp

 

DA

where C is the relative circulation, p is the pressure, ρ is the density, 8 is the Earth’s rotation rate and Ae is the enclosed area projection in the equatorial plane. D is the absolute derivative along the flow. In a barotropic fluid, the relative circulation for a closed chain of fluid particles will be changed if either the horizontal area enclosed by the loop changes or the latitude changes.

Bjerknes feedback An ocean-atmospheric interaction mechanism first proposed by Jacob Bjerknes in 1969 to explain the El Nino/ Southern Oscillation phenomenon. Normally the easterly trade winds maintain a tilt of equatorial thermocline, shallow in the east and deep in the west. The equatorial upwelling induced by the trades brings cold upper thermocline water to the surface in the eastern equatorial Pacific. A slight relaxation in the trades weakens equatorial upwelling and depresses the thermocline in the east, both acting to warm the eastern Pacific. The warming in the east shifts the center of active atmospheric convection eastward and relaxes the easterly trades on the equator even more. This constitutes a positive feedback among the trade winds, thermocline depth, upwelling, and sea surface temperature.

black aurora Name given to structured dark patches appearing on the background of bright aurora. Their origin is uncertain.

black-body radiation The radiation from a hypothetical thermal radiating body with perfect emissivity. Practical black body sources consist of a heated cavity with a small exit aperture. Because radiation interacts repeatedly with the walls of the cavity before emerging, the emerging radiation is closely black body.

The spectral distribution of black-body radi-

ation is given by Planck’s formula:

 

 

dω

 

2πc2h

1

 

 

 

 

=

 

 

 

 

 

 

 

dλ

λ5

 

exphc/(λkT ) −1

(Joules per second per wavelength interval and per unit area of the emitter) in which h = 6.62608×10−27 erg sec is Planck’s constant and k = 1.3807 × 10−16 erg/K is Boltzmann’s constant; this was the first understood instance of a quantum phenomenon. At long wavelengths the spectral distribution is approximately

dω

kT

 

2πc

 

,

dλ

λ4

which corresponds to earlier classical descriptions by Wien and others. The peak of the distribution obeys:

λPlanckT = .2898 cm K .

This is Wien’s law.

blackbody temperature The temperature at which the radiation distribution from an object can be characterized by Planck’s blackbody equation. The distribution of radiation from most hot, compact astronomical objects is closely approximated by a blackbody temperature, yet not exactly. The energy spectrum of the sun, for example, has an energy distribution that is closely but not exactly described by a blackbody having a temperature TB = 6300 K. The effective temperature of the sun, which takes into account the sun’s surface area and total output power, is Teff = 5800 K. See effective temperature, excitation temperature, color temperature.

black frost Temperatures falling below freezing in air dry enough that white hoar frost does not form. Or, the blackening of vegetation due to water freezing within and disrupting their cells. See hoarfrost.

© 2001 by CRC Press LLC

black hole

black hole A region of spacetime from which the escape velocity exceeds the velocity of light. In Newtonian gravity the escape velocity from the gravitational pull of a spherical star of mass M and radius R is

vesc =

 

2

R

,

 

 

 

 

GM

 

where G is Newton’s constant. Adding mass to the star (increasing M), or compressing the star (reducing R) increases vesc. When the escape velocity exceeds the speed of light c, even light cannot escape, and the star becomes a black hole. The required radius RBH follows from setting vesc equal to c:

2GM

RBH = c2 .

For a solar mass black hole M 2 × 1033 gm, and RBH 3 km. (An equivalent conclusion was first derived by P.S. Laplace in the 18th century, even though the notion of a black hole originated in relativity theory in the 1960s.) The so-called gravitational radius (or horizon radius) RBH for the Earth is equal to about 0.88 cm. Thus, the Earth and the sun, squeezed to form black holes, would be extremely dense; such densities are not met anywhere in the real world. However, if ρ¯ denotes the mean massdensity inside an object, then M = 13 πρr¯ 3, i.e.,

r M1/3 and RBH M, which means that with increasing mass RBH grows much faster than r. The radius would be one astronomical unit for a black hole of 108M ; a spherical object whose mean mass-density equals that of water (1g/cm3), would become a black hole if its radius exceeded about 4.01 · 108 km = 2.68 astronomical units. This means that if the center of such an object were placed at the center of the sun, then its surface would be between the orbits of Mars and Jupiter. Hence, black holes might form under reasonable conditions.

In General Relativity for spherical black holes (Schwarzschild black holes), exactly the same expression RBH holds for the surface of a black hole. The surface of a black hole at RBH is a null surface, consisting of those photon trajectories (null rays) which just do not escape to infinity. This surface is also called the black hole horizon. Further, the gravitational redshift

of radiation originating at or inside its horizon is infinite. Both mean that radiation emitted from inside the black hole can never be detected from outside. Hence, the surface at that radius is called a horizon. Material accreting from outside can get very hot, radiating copiously. Thus, black holes are associated with some of the most luminous objects known, including quasars and other active galaxies, some X-ray binaries, and gamma ray bursters. Besides collapsed astrophysical objects, primordial particles produced during the Big Bang are possible candidates as black holes.

If the black hole gains matter from outside (e.g., an accreting disc), it will increase in mass and its horizon will cover a larger portion of space. According to quantum mechanical computations pioneered by S. Hawking, a black hole can also radiate away energy via quantum effects, in which case its horizon contracts.

Black holes were first discovered as purely mathematical solutions of Einstein’s field equations. This solution, the Schwarzschild black hole, is a nonlinear solution of the Einstein equations of General Relativity. It contains no matter, and exists forever in an asymptotically flat space-time. It is thus called an eternal black hole. Later these solutions were extended to represent the final stage in models of gravitational collapse when outward pressure does not balance self-gravity.

The general theory of relativity allows one to prove that only a small number of families of different black hole types can exist (no-hair theorems). They correspond to different mathematical vacuum solutions of Einstein’s field equations which are related to the symmetry of the asymptotically flat space-time outside the horizon (domain of outer communication) and, equivalently, to the charges (conserved quantities in vacuum) of the black hole. The simplest case is given by the Schwarzschild metric, which represents a black hole fully characterized by its mass. If the black hole is electrically charged, then one has a Reissner–Nordström metric, and rotating cases are given by the (electrically neutral) Kerr metric and the (charged) Kerr–Newman metric. In these cases, the formula for the horizon location depends on the angular momentum (and charge) as well as the mass of the black hole. Further, the general

© 2001 by CRC Press LLC

BL Lacertae

properties of the above metrics have been widely investigated, leading to a set of laws very close in spirit to thermodynamics.

Rotating black holes, described by the Kerr solution, allow rotational energy to be extracted from a region just outside the horizon, especially if magnetic fields are present. See ADM mass, asymptotic flatness, black hole horizon, domain of outer communication, black hole horizon, Kerr black hole, Schwarzschild black hole.

black hole binary An observed binary system of which apparently one member is a black hole. These are identified by their X-ray emission. Cyg-X1 is the prototype, with a compact object of mass ≈ 12M (the putative black hole) accreting mass from a hot supergiant companion star through an accretion disk which thermally emits X-radiation.

black hole horizon The future causal horizon that is the surface of a black hole: the boundary between light-rays which can reach infinity and those that do not. The description of horizons has been developed in terms of classical relativity, where one can prove, for instance, that the area of a black hole cannot decrease, so the horizon converges towards a final (bigger) future event horizon. However, Hawking radiation, a quantum phenomenon, leads to the eventual evaporation of an isolated black hole. If the black hole is eternal and does not change in time, the horizon is a true future event horizon and bounds a region of space which will never be experienced from outside the black hole. If the black hole evaporates away completely, its interior will eventually be seen from outside. If there is a limit to this effect, it must occur in the fully quantum limit, black hole mass 10−5 grams (the Planck Mass, MP l = (h¯ c/G)1/2, associated length scale 1.6 × 10−33 cm). See apparent horizon, black hole, future/past causal horizon, future/past event horizon, Killing horizon.

black ice Condition of aged ice on highway surfaces, which has a polished surface and so appears dark rather than bright.

blast wave shock Shock created by a short, spatially limited energy release, such as an ex-

plosion. Therefore, the energy supply is limited, and the shock weakens and slows as it propagates outward. In models of the energetics and propagation of interplanetary traveling shocks, blast wave shocks are often used because their mathematical description is simple, and the assumptions about the shock can be stated more clearly. It is also speculated that blast wave shocks give rise to the metric type II radio bursts on the sun.

blazar A class of active galactic nuclei which includes BL Lac objects and Optically Violently Variable (OVV) quasars, whose name derives from the contraction of the terms BL Lac and quasar. BL Lac and OVV quasars share several common properties, like high continuum polarization and large luminosity changes on relatively short time scales. All known blazars — a few hundred objects — are radio loud active galactic nuclei, and several of them have been revealed as strong γ -ray sources. Blazars are thought to be active galactic nuclei whose radio jets are oriented toward us, and whose nonthermal, synchrotron continuum is strongly amplified by Doppler beaming. See active galactic nuclei, BL Lacertae object.

blizzard Winter storm characterized by winds exceeding 35 miles (56 km) per hour, temperatures below 20◦ F (−7◦ C), and driving snow, reducing visibility to less than 1/4 mile (400 m) for 3 or more hours.

BL Lacertae Prototype of extremely compact active galaxies [BL Lacertae objects, or Lacertids (also Blazar)] that closely resemble Seyfert and N galaxies, radiating in the radio, infrared, optical, and X-ray. BL Lacertae, of magnitude 14.5, is located at RA22h00m40s, dec 42◦02 and was observed in 1929 and incorrectly identified as a variable star but observed to be a radio source in 1969. About 40 Lacertids are presently known. They are characterized by a sharply defined and brilliant (starlight) nucleus that emits strong nonthermal radiation and whose continuous visible spectrum has no emission or absorption lines. Surrounding the bright nucleus is a faint halo resembling a typical elliptical galaxy from which redshifts can be measured. BL Lacertae is thus found to have a red-

© 2001 by CRC Press LLC

BL Lacertae object

shift z = 0.07, comparable to those of the nearer quasars; PKS 0215+015 is a BL Lac object with z = 0.55. BL Lacertae objects radiate most of their energy in the optical and infrared wavelengths and undergo rapid changes in brightness in visible light, the infrared, and X-rays brightening to the brightness of the brightest quasars. The central radio source is very small, consistent with the rapid fluctuations in brightness. X-ray brightness may vary in periods of several hours, suggesting that the emitting region is only a few light-hours across. It has been conjectured that the Lacertids, quasars, and radio galaxies are actually the same types of objects viewed from earth at different angles that either obscure or reveal the galaxy’s central powerhouse of radiation, presumably powered by accretion onto a central black hole.

BL Lacertae object An active galaxy very similar to quasars in appearance but with no emission lines, with a strong continuum stretching from rf through X-ray frequencies. There are no known radio quiet BL Lac objects. They can exhibit dramatic variability.

blocking A persistent weather pattern where the mid-latitude westerly jet is blocked and diverted into a northern and a southern branch. The blocking is associated with a pair of anticyclonic (blocking high) circulation to the north and cyclonic circulation to the south. When a blocking occurs, extreme weather conditions can persist for a week or longer. Blockings often occur in winter over northwestern North Pacific off Alaska and northwestern North Atlantic off Europe.

blocking patterns High-amplitude quasistationary wave disturbances in the extratropical atmosphere.

blue clearing (Mars) The difference in albedo between Mars surface features is small in blue, except for the polar caps. Therefore, albedo features visible in green and red are not usually identified in blue. However, they are sometimes identified even in blue; this phenomenon is called blue clearing. In the first half of the twentieth century, it was thought that the Martian atmosphere was thick enough to hold

a haze layer which absorbs light in blue, and that the albedo features are visible in blue only when the haze disappears and the sky clears up in blue, but the haze layer is now not believed to exist. The blue clearing has been observed most frequently around the opposition of Mars. The opposition effect may be one of the causes of the blue clearing. The degree of the opposition effect is larger in bright areas than in dark areas in all visible wavelengths, not only in red but also in blue. Therefore, albedo features are identified even in blue around the opposition. However, the degree of the opposition effect may depend on the Martian season, for the surface is covered with a thin dust layer and uncovered in a cycle of a Martian year.

blue ice Old sea ice that has expelled impurities and appears a deep translucent blue in sunlight.

blue jet A long-duration luminous structure observed directly above an active thundercloud, extending upwards from the cloud top for many tens of kilometers. The name is derived from their highly collimated blue beam of luminosity, which persists for several tenths of a second. Unlike sprites and elves, blue jets are relatively rare and consequently are poorly understood.

blue straggler A star whose position on the HR diagram is hotter (bluer) and brighter than that allowed for stars of the age represented in the particular star cluster or other population under consideration. Such stars are sometimes interlopers from younger populations, but more often they are the products of evolution of binary stars, where material has been transferred from one star to another or two stars have merged, giving the recipient a larger mass (hence, higher luminosity and surface temperature) than single stars of the same age.

body waves Earthquakes generate seismic waves that are responsible for the associated destruction. Seismic waves are either surface waves or body waves. The body waves are compressional p-waves and shear s-waves. These waves propagate through the interior of the Earth and are the first arrivals at a distant site.

© 2001 by CRC Press LLC

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