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Dictionary of Geophysics, Astrophysic, and Astronomy.pdf

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grand uniﬁcation

temperature is 10 K everything except H2, He, and Ne freezes out and ice mantles form on grains. In regions where H < H2 the less abundant heavier atoms such as O, C, and N can react with one another to form oxidized species such as CO, CO2, and presumably O2 and N2. Where H > H2 the heavy atoms are reduced and the ice mantles are dominated by molecules such as H2O, CH4, and NH3. When these ices are exposed to cosmic rays and UV photons, bonds are broken and the resulting unstable species react to form more complex materials, in some cases organic molecules of the type seen in meteorites and interplanetary dust particles.

grain chemistry: diffuse interstellar In the diffuse interstellar medium (i.e., visual extinction Av ≤ 2 magnitudes, or nH ≤ 101 cm−3), where ice is not stable, the dust is essentially bare and grain surfaces are available as catalysts and reactants. Since hydrogen is the most abundant atom, H2 formation from hydrogen atoms is by far the most common surface reaction.

grains: in other galaxies Extragalactic extinction curves are comparable to those within the Milky Way galaxy, consistent with grains in other galaxies being of similar size and composition to those in our own. Most spiral galaxies seem to have similar dust-to-gas ratios as in our own, although there are some exceptions.

grains, interstellar: destruction and formation Grains presumably form in the outﬂows from cool evolved (red giant) stars, novae and supernovae ejecta and grow as they mix with interstellar molecules, accreting ice mantles and sticking to one another. Such interstellar grains may be fragmented or destroyed by shocks, collisions, sputtering, or incorporation into forming stars. A typical grain lifetime is thought to be approximately 108 years.

grains, interstellar: size and composition

A wide-spread interstellar grain size is inferred from optical, IR, and UV extinction curves throughout our galaxy. The grains are usually deduced to have sizes in the range of 0.01 to 0.2 µm, are probably of irregular (perhaps fractal) shape, and composed of (presumably amorphous) silicates, carbon, SiC, or metal ox-

ides. The position and proﬁle of the 2175 Å bump is consistent with some of the carbon grains being graphitic, or composed from amorphous or diamond-like carbon containing graphitic (π-bonded) domains. In the diffuse instersellar medium where radiation is abundant, these grains are probably bare, but in dense molecular clouds, where the radiation is attenuated and the average temperature low, ice mantles condense on the surfaces of these grains.

grain size A measure of particle size in a sediment. Often refers to the median grain size in a sample. Typically determined by sieving.

grain size analysis A process of determining sediment grain size. Most commonly done using a stack of sieves of varying size.

grand potential The thermodynamic potential H equal to

H = U − T S − µN ,

with U the internal energy, S the entropy, µ the chemical potential, and N the number of particles in the system.

grand uniﬁcation Modern particle physics describes interactions through the exchange of so-called gauge particles, whose existence is due to an underlying symmetry. For instance, the gauge particle we know as the photon exists because of the invariance of the physics under local phase variation, which is a U(1) symmetry. When the universe had a temperature corresponding to a typical photon energy of roughly 250 GeV, the symmetry of particle physics interactions is believed to have been that of the group product SU(3) × SU(2) × U(1) describing the strong and electroweak interactions.

Whenever a symmetry is exact, as is the case for electromagnetism, the corresponding gauge particle is massless (as is the photon), while if it is broken, the gauge particle is massive and the interaction is much weaker (short range). This is in particular the case for the weak interaction. It is currently expected that the product symmetry we have at the electroweak level is just part of a larger (simple and compact) symmetry group that uniﬁes forces and interaction — hence the name grand uniﬁcation. This larger group could

granulation

have been broken at extremely high energies. Thus, many gauge particles would be very massive, explaining why we have not yet observed them. See spontaneous symmetry breaking.

granulation Cellular structure of the photosphere visible at high spatial resolution. The characteristic scale of the granulation is 1000 km, ranging widely from 300 km to over 2000 km. Typical velocities present in the granules are horizontal outﬂows 1.4 km s−1 and upﬂows in the center of the granules 1.8 km s−1. Identiﬁable granules live for 5 to 10 min and at any one time 3 to 4 × 106 granules cover the surface of the sun.

grating spectrograph An instrument for the analysis of radiation at different wavelengths, in which light is dispersed by a diffraction grating. In a typical grating spectrograph design, light focused on the focal plane of the telescope is collimated (i.e., the rays of the beam are made parallel) on a blazed diffraction grating. Light of different wavelengths is thus diffracted along different directions, and it is then re-focused on a detector, for example a photographic plate or a CCD, by a lens or a mirror. Several designs exist, based on different choices of the focusing and collimating elements, or on the use of a reﬂection or a transmission grating. The spectral resolving power, i.e., the ability to separate two close spectral lines spaced by Dλ at wave-

length λ is usually λ/Dλ	<	104. See diffraction
grating.

gravitation The interaction between objects that in Newtonian theory depend only on their distances and masses:

F = Gm1m2rrˆ −2 ,

where F is the attractive force, m1 and m2 are the masses, r is their separation, rˆ is a unit vector between the masses, and G is Newton’s gravitational constant.

In the more accurate description in general relativity, the gravitational ﬁeld is a symmetric rank two tensor in four dimensions, which obeys Einstein’s equations, which have as a source the stress-energy tensor of the matter. General relativity reduces to the Newtonian description in weak-ﬁeld, quasi stationary situations. See

Newtonian gravity, general relativity, Newtonian gravitational constant.

gravitational collapse One of several possible ﬁnal episodes of stellar evolution. Stars are supported against collapse under their own weight by gas pressure resulting from high temperature. The equilibrium of cold matter can be supported by the pressure of degenerate electron gas. The equilibrium of white dwarf stars is thought to be due to this. Chandrasekhar showed in 1939 that the maximal mass of a white dwarf is 1.4 solar mass and that stars more massive than this will collapse (to a neutron star or to a black hole).

gravitational constant G In Newtonian physics, the acceleration of a particle towards the Earth is Gm/r2 where m and r are the mass and radius of the Earth, respectively and

G = 6.670 × 10−8 cm3/g · sec2

is the gravitational constant.
gravitational deﬂection of light	The pres-

ence of a central mass (e.g., the sun) causes local curvature of spacetime, and trajectories of photons (the quanta of light) are deﬂected (attracted to the mass). In the case of a spherical central body, for small angle deﬂection, the angle de-

ﬂected is

θ = 4GM/dc2 ,

where M is the central mass, G is Newton’s constant, c is the speed of light, and d is the impact parameter of the light past the mass. If the deﬂection were as if the photon were a particle in Newtonian gravity traveling at the speed of light, the deﬂection would be half the relativistic result. Deﬂection of light has been veriﬁed to parts in 1000 by observations of the direction to extragalactic radio sources, as the sun passes near their position in the sky. In the case of distant sources, deﬂection by intervening galaxies or clusters of galaxies causes lensing, leading to the appearance of multiple images, and of rings or arcs of distorted images. See gravitational lens, light deﬂection.

gravitational equations The ﬁeld equations of the gravitational interaction. The basic tenet

gravitational perturbations

of Einstein’s general relativity theory is that the stress-energy tensor Tαβ of a matter distribution is proportional to the Einstein tensor Gαβ :

8πG

Gαβ = c2 Tαβ

Here G is Einstein’s gravitational constant and c is the speed of light. If a nonzero cosmological constant is considered, +<gαβ is added to the left side of the equation (< is the cosmological constant). See Einstein tensor, stress energy tensor.

gravitational instability In meteorology, an instability caused by Earth’s gravity, under the unstable stratiﬁcation lapse rate condition ∂θ/∂z < 0, in which θ is potential temperature, and z is height. It can be seen that with such lapse rate, any inﬁnitesimal displacement not along θ surfaces is unstable. If instability is only caused by such conditions, it is pure gravitational instability, and Earth’s rotation has no effect. From the vertical motion equation,

Dw = g (θ − θ) Dt θ

where θ is the potential temperature of the moving air parcel, θ is the potential temperature of the environment, w is vertical velocity, t is time, and g is the gravitational acceleration. If ∂θ/∂z < 0, the value of an air parcel’s vertical speed will always be accelerated, whether it is moving upward or downward.

gravitational lens A gravitating object (in observational practice usually a quasar, galaxy, or cluster of galaxies) whose gravitational ﬁeld deﬂects the light rays emitted by another object (usually a galaxy or a quasar) so strongly that some of the rays intersect behind the deﬂector (see also light deﬂection). An observer placed in the region where the rays intersect sees either multiple images of the source or a magniﬁed single image. Unlike optical lenses that have welldeﬁned focal points, gravitational lenses do not produce easily recognizable images of the light sources. For a spherically symmetric lens, the angle of deﬂection is approximately given by the Einstein formula Dφ = 4GM/(c2r), where G is the gravitational constant, M is the mass of the light-deﬂector, c is the velocity of light, and

r is the smallest distance between the path of the ray and the deﬂector’s center. The formula applies only when the ray passes outside the deﬂector and r rg, where rg = 2GM/c2 is the gravitational radius of the deﬂector. Hence, rays passing closer to the lens are deﬂected by a larger angle, and so an image of a point-source is smeared out throughout a 3-dimensional region in which the rays intersect. Qualitatively, gravitational lenses are just a manifestation of the gravitational light deﬂection, conﬁrmed in 1919 by A.S. Eddington. For nonspherical or transparent lenses, more complicated formulae apply. In spite of the distortion of the image, given the mass-distribution in the deﬂector and the light- intensity-distribution in the light-source, it is possible to calculate the patterns of light intensity seen at the observer’s position. Comparing the patterns calculated for various typical situations with the patterns observed, it is possible to extract information about the massand light- intensity-distribution in the actual source and the actual deﬂector. See gravitational radius.

gravitational multipole moments Coefﬁcients of the asymptotic expansion of gravitational ﬁelds, introduced by Thorne, Epstein, and Wagoner. There exist two inﬁnite series of gravitational multipole moments. The 0th mass moment or monopole moment characterizes the total mass of the source distribution. The odd mass moments are absent — a manifestation of the attractive nature of the interaction. The current moments are odd, beginning with the current dipole moment generated by the rotation of matter. A theory of exact gravitational multipole moments has been developed by Geroch and Hansen for axially symmetric and stationary ﬁelds.

gravitational perturbations Small deviations from a given space-time with metric gab0 . The metric of the perturbed space-time has the form gab = gab0 + hab where the quantities hab and their derivatives are inﬁnitesimal. These techniques are used in the theory of cosmological perturbations, gravitational radiation theory, and in quantization schemes. See linearized gravitation.

gravitational potential

gravitational potential The gravitational potential energy per unit mass. The gravity ﬁeld of the Earth is the gradient of the gravitational potential (usually with a minus sign).

gravitational radius The radius, also called Schwarzschild radius, at which gravitational attraction of a body becomes so strong that not even photons can escape. In classical Newtonian mechanics, if we set equal the potential energy of a body of unit mass at a distance r in the gravitational ﬁeld of a mass M, GM/r, to its kinetic energy if moving at the speed of light, c2/2, we ﬁnd r = Rg with the gravitational radius Rg = 2GM/c2, where G is the gravitational constant, and M is the mass of the attracting body. An identical expression is found solving Einstein’s equation for the gravitational ﬁeld due to a non-rotating, massive body. The gravitational radius is ≈ 3 km for the sun. (The relation is not so simple for rotation in nonstationary black holes.) The gravitational radius deﬁnes the “size” of a black hole, and a region that cannot be causally connected with our universe, since no signal emitted within the gravitational radius of a black hole can reach a distant observer. See black hole.

gravitational redshift Frequency or wavelength shift of photons due to the energy loss needed to escape from a gravitational ﬁeld, for example from the ﬁeld at the surface of a star, to reach a distant observer. Since the energy of a photon is proportional to its frequency and to the inverse of its wavelength, a lower energy photon has lower frequency and longer wavelength. The gravitational redshift is a consequence of Einstein’s law of equivalence of mass and energy: even a massless particle like the photon, but with energy associated to it, is subject to the gravitational ﬁeld. The shift increases with the mass of a body generating a gravitational ﬁeld, and with the inverse of the distance from the body. A photon will be subject to a tiny frequency shift at the surface of a star like the sun, but to a shift that can be of the order of the unshifted frequency if it is emitted on the surface of a compact body like a neutron star.

gravitational wave In general relativity, the propagating, varying parts of the curvature ten-

sor. The notion is in general approximate, since the nonlinearity of the gravitational equations prevents a unique decomposition of the curvature to a background and to a wave part.

General relativity allows for a description of gravitational waves which travel through space with the velocity of light. Exact solutions of the ﬁeld equations representing plane-fronted gravitational waves are known. The detection of typical astrophysical gravitational waves is extremely difﬁcult because laboratory or terrestrial sources are very weak. Calculations show that even violent phenomena occurring at the surface of the Earth produce undetectably weak gravitational waves. For example, a meteorite of mass 2 · 107 kg hitting the Earth with the velocity of 11 km/sec and penetrating Earth’s surface to the depth of 200 m emits 2 · 10−19 ergs of energy in the form of gravitational waves. This would be sufﬁcient to raise one hydrogen atom from the surface of the Earth to the height of 120 cm (or to raise one ﬂu virus to the height of 0.29·10−9cm, which is somewhat less than 13 of the diameter of a hydrogen atom). Hope for detection is offered by astronomical objects, such as binary systems or exploding supernovae that radiate strongly gravitational waves. The strength of gravitational waves is measured by the expected relative change of distance l between two test masses induced by a gravitational wave passing through the system, A = Dl/l, where l is the initial distance and Dl is the change in distance. For known astronomical objects that are supposed to be sources of gravitational waves, this parameter is contained between 10−23 and 10−19. Measuring such tiny changes is an extreme challenge for technology. Several detectors are under construction at present. If the gravitational waves are detected, then they will become very important tools for observational astronomy, giving the observers access to previously unexplored ranges of phenomena, such as collisions of black holes or the evolution of binary systems of black holes or neutron stars. See GEO, LIGO, LISA, pp-waves, Virgo.

graviton The putative quantum of the gravitational interaction. There exists no precise description of this term and there is no experimental evidence or consensus about the nature of the graviton. General relativity theory provides a

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