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Big Bang

ues. It would be possible then, with this biased potential, to have walls decaying sufficiently rapidly so that the cosmological problem they generate is cured. In fact, invoking quantum effects between the fields that form the walls and other particles in some models, one finds that the potential is slightly tilted (see figure) in such a way that the vacuum, defined as the minimum energy state, instead of being degenerate, becomes single-valued. This effect takes place after the phase transition has been completed so that domain walls actually form and subsequently decay. See cosmic topological defect, domain wall.

v(φ)

v(φ)

φ

φ

a

b

Possible self-interaction potentials: (a) the original potential, (b) the biased potential once the radiative cor-

rections have been accounted for.

bias frame, bias overscan CCD detectors contain a pedestal or “bias” level of counts. This is a DC offset that is added to the output signal of the CCD. Sometimes the CCD is “preflashed” to establish a bias before an observation is made. The function of this bias is to raise the number of counts for the data above some level where the detection of data is more accurate. The value of the bias can vary from pixel to pixel on a CCD, as well as vary over time or temperature. When processing observing data, one of the first steps is to remove the bias. This is a two-step process. The first step is to account for any bias changes that may vary on a frame-to-frame basis. This is usually accomplished by measuring the bias on a part of the CCD that is not exposed during the observation (this is called the “overscan re-

gion”), and subtracting this bias as a single value from the frame or fitting a function to the bias and subtracting it along columns and/or rows. The second step is to account for the pixel-to- pixel variations in the bias. This is often done by obtaining a number of bias frames or images that are essentially images with zero integration times with the shutter closed. Such frames contain only the bias, which is assumed to be representative of the bias on each data image. The average bias image is directly subtracted from each data image (including flat fields and other calibration images).

biasing parameter Ratio between the amplitude of galaxy-galaxy and cluster-cluster correlation function. By extension, ratio between the amplitude in the matter power spectrum and those of galaxies and clusters. At each scale: b2(k) = Pgal(k)/Pmatter . If galaxies and clusters of galaxies form in high density environments, then galaxies are more correlated than the underline matter distribution (and clusters even more strongly than galaxies). It is usually assumed that the bias parameter is independent of scale. The current estimated value is: b = 1.3 ± 0.13.

bidirectional reflection distribution function (BRDF) The ratio of the radiance reflected by a surface into a specific localized direction to the collimated irradiance incident from a particular direction onto the surface [sr−1].

Big Bang The initial explosion that gave birth to the universe, and a standard model of the universe in which all matter, space, and time expands from an initial state of enormous density and pressure. All models of the universe constructed in the classical relativity theory (General Relativity) must take into account the fact that at present the universe is expanding (see expansion), i.e., that any two clusters of galaxies recede from one another. If the matter in the universe is either a dust or a perfect fluid, then Einstein’s equations imply that at a certain moment in the past any given small portion of matter must have been squeezed to zero volume. This moment of infinite compression is called the Big Bang. It is a formal mathematical conclusion that only implies that every region of the

© 2001 by CRC Press LLC

Big Bang cosmology

universe must have been much denser and hotter in the past than it is now (and observations confirm this implication). The infinite compression implied by the models shows that classical General Relativity does not apply to such states of matter and must be replaced by a suitable generalization (nonexistent so far). Quantum gravity is a likely candidate to produce this generalization. The Robertson–Walker models imply that the Big Bang occurred simultaneously for all matter in the universe, but more general models exist in which there is a nonsimultaneous Big Bang. See inhomogeneous models, singulari- ties.

Big Bang cosmology Cosmological model that assumes that the whole observable universe has expanded from an earlier state of much higher density. It was originally proposed by George Gamow, Ralph Alpher, and Robert Hermann in the late 1940s long before the observations of cosmic microwave background radiation and abundances of light elements suggested the existence of very high densities and temperatures in the past.

The model is based on the cosmological principle. The dynamics are described by Einstein’s general relativity theory. Contrary to the steady state model that requires new physics, the Big Bang model assumes the current laws of physics are locally valid everywhere. The dynamics are described by Friedmann models and only three parameters are necessary to specify the evolution of the universe: mean density, Hubble constant, and cosmological constant. The extrapolation of the atomic, nuclear, and particle physics to explain the behavior of the universe at early times has proven to be very successful: the present abundances of light elements and the existence of a cosmic microwave background radiation with a degree of anisotropy close to 10−5 have been confirmed by observations. The model has its own shortcomings. The existence of a particle horizon poses a difficulty as to how to explain the high degree of homogeneity of the observed universe. A solution to this problem has been proposed appealing to a period of rapid expansion. See inflation, Big Bang nucle- osynthesis, Friedmann–Lemaître cosmological models, cosmic microwave background.

Big Bang flatness problem Problem related to the need to fine-tune the initial value of the density parameter to allow the universe to survive 1017s being close to flat. The present observational data indicate that the mean energy density ρ is, within one order of magnitude, close to the critical density ρc, so that the universe will (approximately) expand forever, and so that the time =constant hypersurfaces (the 3-spaces) are almost Euclidean. The success in predicting the abundances of light elements (see nucleosynthesis) strongly suggests that our understanding of the physical processes occurring at t 1s is adequate. At that moment

ρ(1sec) − ρc(1sec) 10−16 ,

and at earlier times the differences are even smaller. A larger difference would imply that our universe would either have recollapsed or would have become freely expanding, with negligible gravitational deceleration by now (see Friedmann models). The fact that it is in neither of these states indicates that either the universe is exactly flat or initial conditions tuned its initial value such that at 1s it differed from unity in the 16th decimal place.

Big Bang horizon problem Problem related to the existence of particle horizons arising since fact that we can see, or affect, objects only as far away as light has traveled since the Big Bang. Causality poses a severe difficulty when explaining the large scale homogeneity and isotropy of the universe. In the standard Big-Bang model, homogeneity and isotropy are built-in (see cos- mological principle). In this context, it is not surprising that, for example, the cosmic microwave background radiation from two opposite directions in the sky shows the same black body spectra. However, since those regions came within our horizon and have been visible only very recently, there has not been time since the Big Bang for light to travel from one to the other, so they have never been in casual contact with each other. Then how could they have acquired the same physical properties? If those regions had slightly different initial densities, the evolution of the universe will amplify those differences making the initial irregularities more evident. The horizon problem is therefore

© 2001 by CRC Press LLC

binary star

a statement about why the universe is so homogeneous. As a solution, a period of rapid expansion (see inflation) has been advocated that would have stretched the observed universe out of a horizon volume at early times.

Big Bang nucleosynthesis The production of deuterium, 3He and 4He (the latter to about 25% mass fraction) in the first 500 to 1000 sec of the early universe. These light isotopes, plus measurable amounts of 7Li and trace amounts of elements B, Be, are the result of non-equilibrium nuclear reactions as the universe cooled to about 108K. Heavier isotopes were produced in stellar nucleosynthesis.

big blue bump A feature in the spectral energy distribution of active galactic nuclei, dominating the emission shortwards of 4000 Å and in the UV. The shape, luminosity, and spectral extension of the big blue bump are as yet uncertain since the big blue bump lies mostly in the unobserved far UV, with maximum emission probably right below the Lyman limit. Only the low and high energy tails of the big blue bump have actually been observed. The high energy end of the big blue bump appears to be for several objects in the soft X-ray domain, where a sharp rise toward lower energies, the so-called “soft X-ray excess” is observed. The current interpretation of the active galactic nuclei spectral energy distribution, still highly debated, ascribes this feature to thermal emission from a hot accretion disk surrounding a supermassive black hole. See active galactic nuclei, Lyman limit.

binaries, X-ray X-ray binaries are close binaries in which one of the objects is either a black hole or neutron star, and the companion is either a star with a strong wind or a star overfilling its Roche-lobe. The material transfers from the companion to the compact object and forms an accretion disk. The gravitational energy released as the material accretes onto the disk powers the X-ray flux. Two classes of X-ray binaries exist: low-mass (neutron star) and high-mass (black hole) X-ray binaries. Low-mass X-ray binaries have companion star masses less than 5M , whereas high-mass X-ray binaries have more massive companions.

binary black holes Two black holes orbiting each other, like stars in a binary system. A binary system of two black holes may radiate away significant orbital energy by emission of gravitational radiation, with efficiency that increases with the eccentricity of the orbit; orbital energy loss may lead to orbital decay, with the two black holes spiraling down toward each other and ultimately coalescing to form a single black hole. There is as yet no definitive evidence from observations of the actual occurrence of binary black holes. Binary black holes have been invoked to explain peculiar features of kpc-sized radio jets, of the photometric light curve of the blazar OJ 287, and of rarely observed peculiarities in the spectral line profiles of active galactic nuclei. Gravitational wave detectors may provide the first incontrovertible evidence of merging binary black holes. See black hole, black hole binary.

binary fraction The fraction of stars in a stellar association which are binary stars. For many years it was believed that there were no binary stars among Population II stars. However, it now seems that there may be no difference in the relative number of binary stars between groups of stars of the same age, regardless of whether they are Population I or Population II.

binary pulsar The pulsar PSR 1913+16, which is in orbit with another neutron star; both stars have a mass of approximately 1.4 solar masses. Orbital parameters are extracted from the almost periodic Doppler shifts of the pulses from the pulsar. The pulse repetition period is 59 milliseconds, and the orbital period is 2.79 × 104 sec. General relativistic effects, including periastron advance, are verified, and they, along with a general relativistic model of gravitational radiation from the orbiting neutron stars (period decrease of −2.4×10−12), give excellent agreement with observations.

binary star Two stars gravitationally bound together. There are numerous types of binaries including, among others, the following classes: Algol, RS Canus Venaticorum, W Ursa Majoris (see contact binary), β Lyrae, cataclysmic variables. Some binaries show eclipses as one star passes in front of the other. In such systems, the amount of light received as a function of

© 2001 by CRC Press LLC

binary star system

time (see light-curve) varies. The binary appears brightest when neither star is eclipsed and is fainter when one star is eclipsed by the other.

binary star system A pair of stars in a gravitationally bound orbit around each other. Half or more of all stars in the sky are binaries, with the fraction varying from one cluster to another and one stellar population to another. The statistical properties of a binary population include the distribution of periods, total masses, mass ratios, and orbital eccentricities, and these also vary from one place to another (for reasons that must have to do with the conditions of star formation but which we cannot currently model). The range of orbit periods is less than an hour to millions of years; the range of separations from the sizes of the stars themselves is to at least 0.1 parsec; the range of masses is essentially the same as for single stars (see initial mass function); and the range of eccentricities is from 0 (circle) to at least 0.9, with short period systems generally in circular orbits.

Binary stars can be subdivided in several ways. Wide binaries are ones whose separation is larger than the maximum size either star will reach (as a red giant, super giant, or asymptotic giant branch star), so the stars evolve independently. Close binaries interact at some point in their lives, generally via gas flowing from the more rapidly evolving star (the more massive one) to its companion. They can also be subdivided by the method of detection, including visual binary, astrometric binary, eclipsing binary, spectroscopic binary, photometric binary, and spectrum binary systems.

Habitable planets are unlikely to be found in most binary systems because only orbits very close to one star or very far away from both will be stable. Most of our knowledge of the masses of stars comes from the analysis of binary systems. See initial mass function, parsec, star formation.

biogenic stratification In low saline water, biogeochemical processes, such as photosynthesis and subsequent settling of biogenic particles and mineralization by bacteria, may significantly change (generally enhance) vertical salinity gradients and thereby increase the stability N2 of the water column. This phenome-

non, common in many deep and eutrophic lakes (especially close to the sediment) is usually the cause of permanent density stratification (socalled meromixis). Ca2+ and HCO3- are often the dominant ions for biogenic stratification.

bioluminescence Light produced by organisms as a result of conversion of chemical energy to radiant energy.

biomass The amount of living matter per unit of water surface or water volume (i.e., in the water column) [kg m−2 or kg m−3].

biosphere That part of the earth and its atmosphere that can support life. This extends from the upper atmosphere to underground into rock where living bacteria have been found. In more colloquial terms, it refers to the first hundred meters of the Earth’s atmosphere, the oceans, and the soil down to bedrock, where easily recognizable organisms are found.

Biot–Savart law If the electromagnetic fields are time independent within a given region, then within the region it holds that the magnetic field for a given point in space is proportional to volume integral of the vectorial product of the current density times the unit vector in the direction of the relative position divided by the square of the relative position. In CGS units the constant of proportionality is the inverse of the speed of light. Named after Biot and Savart who in 1820 presented experimental evidence that established the law.

BIPM See Bureau International des Poids et Mesures.

bipolar flow The flow of material from a star in two streams in opposite directions. It is thought to be caused by the effects of stellar rotation on the mass outflow.

Birkeland current Field aligned electric current linking the Earth’s ionosphere with more distant regions, often associated with the polar aurora and with substorms.

Birkhoff theorem (1923) The only spherically symmetric asymptotically flat vacuum

© 2001 by CRC Press LLC

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