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Dictionary of Geophysics, Astrophysic, and Astronomy.pdf

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Dessler–Parker–Sckopke (DPS) theorem

their plasma and replacing its pressure by that of the magnetic ﬁeld.

depth of compensation The depth over which the density of the Earth varies in order to “compensate” the excess mass of topography.

Derrick theorem Let φ be a scalar ﬁeld subject to the generalized Klein–Gordon equation

2 − ∂t2 φ = 1 V (φ) ,

with V (φ) the potential. The theorem states that there is no stable, time-independent and localized (i.e., with ﬁnite energy) solution of this equation in more than one dimension. The theorem seems to imply the non-existence of topological defects; however, this is not the case, as one usually assumes some gauge ﬁelds which render the energy ﬁnite. On the other hand, if no gauge ﬁeld is present, as for the global cosmic string in three space dimensions, we ﬁnd that the energy is indeed (mildly) divergent, in agreement with the theorem. Notice that gravitational ﬁelds can stabilize such structures, even on a small scale. Thus, boson stars can be stable objects. See boson star, cosmic string, cosmic texture, global topological defect.

Descartes ray The ray traveling through water droplets producing a rainbow, which yields the limiting (minimum) deﬂection. Hence, there is a concentration of light near the Descartes ray; the colors of the rainbow are due to different refraction of different colors in the droplets, giving slightly different return angles for the Descartes rays corresponding to the different colors.

Desdemona Moon of Uranus also designated UX. Discovered by Voyager 2 in 1986, it is a small, irregular body, approximately 29 km in radius. Its orbit has an eccentricity of 0, an inclination of 0.2◦, a precession of 245◦ yr−1, and a semimajor axis of 6.27×104 km. Its surface is very dark, with a geometric albedo of less than 0.1. Its mass has not been measured. It orbits Uranus once every 0.474 Earth days.

deSitter Universe A solution of Einstein’s equations that describes a spacetime devoid of

any matter and gravitational ﬁelds in the presence of the cosmological constant. When Einstein introduced the cosmological constant, he hoped that it would have a second consequence (in addition to providing a static model of the universe; see Einstein Universe): that a solution of Einstein’s equations corresponding to such a completely empty space would not exist. This expectation resulted from his belief in Mach’s principle that said, in effect, that gravitation is induced by matter and would not exist in the absence of matter. Einstein expected that his theory of relativity would automatically obey Mach’s principle. It turned out not to be so, and the deSitter Universe was the ﬁrst counterexample. The word “universe” applied to this particular solution of Einstein’s equations is justiﬁed by tradition only; according to today’s criteria, deSitter’s metric is not a model of the actual universe.

Despina Moon of Neptune also designated NV. Discovered by Voyager 2 in 1989, it is a small, roughly spherical body approximately 74 km in radius. It is very dark, with a geometric albedo of 0.059. Its orbit has an eccentricity of 0.00014, an inclination of 0.066◦, a precession of 466◦ yr−1, and a semimajor axis of 5.25 × 104 km. Its mass has not been measured. It orbits Neptune once every 0.335 Earth days.

Dessler–Parker–Sckopke (DPS) theorem

An approximate theorem in magnetospheric physics, by which the change 2B in the surface magnetic ﬁeld at the magnetic equator (in a magnetic storm) is proportional to the energy E of the additional ring current due to the storm. If Be is the ﬁeld of the Earth’s dipole at 1 RE and Ue = Be2RE3/3 is the magnetic energy of the dipole ﬁeld above 1 RE, by the DPS theorem 2B/Be = (2/3)E/Ue. The theorem was derived for a speciﬁc simple model by Dessler and Parker in 1959 and was extended by Sckopke in 1966: further work suggested that the actual dependence was nonlinear, and that for large magnetic storms it overestimated E by a factor 1.5 to 3. Still, the theorem helps estimate the energy deposited in the inner magnetosphere by magnetic storms. The magnitude of 2B may be obtained from the Dst index.

detritus

detritus The particulate decomposition or disintegration products of plankton, including dead cells, cell fragments, fecal pellets, shells, and skeletons, and sometimes mineral particles in coastal waters.

deuterium 2H ; the isotope of hydrogen whose nucleus consists of 1 proton and 1 neutron. The nucleus is called a deuteron.

deuterium burning The capture of a proton by a deuteron to produce 3H e (which then easily burns through to 4He; see proton-proton chain). Deuterium burning occurs at the lowest temperature of any important nuclear reaction, about 106K. Thus, its onset marks the end of the protostellar collapse stage of star formation (see proto-star). It is the only reaction that occurs in the lowest mass stars, near 0.08 solar masses (see brown dwarf), and it has long ago destroyed all the deuterium in the sun and other normal stars. Thus, the presence of deuterium in the Earth and other planets means they are made of material that was never inside the sun. Deuterium is produced only in the early universe (see Big Bang nucleosynthesis).

de Vaucouleurs’ classiﬁcation scheme A classiﬁcation scheme that reﬁnes and extends the Hubble scheme of classiﬁcation for galaxies, introduced by G. de Vaucouleurs in 1959. de Vaucouleurs’ scheme attempts to account for the variety of morphologies observed for each Hubble type. His scheme employs three main parameters: (1) a reﬁned Hubble type, where several intermediate stages are added to the Hubble sequence, notably E+ , S0− , S0+, which account for some lenticular features in ellipticals or weak arms in S0 galaxies, and Sd, Sm, and Im, which more closely detail the transition from Sc to Magellanic irregulars; (2) a parameter describing the spiral design, as ring shaped (r) or s-shaped (s), or intermediate (rs); and (3) a parameter designating barred galaxies (SB), nonbarred (SA), and intermediate (SAB), for galaxies where the bar is less developed than in classical Hubble’s barred galaxies. In addition, the presence of an outer ring or of a ring-like feature formed by joining spiral arms is indicated with an uppercase R preceding all other labels. The de Vaucouleurs classiﬁcation scheme has been

extensively used in the three editions of the Reference Catalogue of Galaxies, where de Vaucouleurs’ types are given for several thousand galaxies. For example, Messier 31, the spiral galaxy nearest to the Galaxy, and the nearby spiral Messier 101 are classiﬁed as Sb and as Sc according to Hubble, and as SA(s)b and as SAB(rs)cd according to de Vaucouleurs.

de Vaucouleurs’ law Empirical law describing the brightness proﬁle of an elliptical galaxy. The surface brightness of typical giant elliptical galaxies, apart from constants, decreases with radius as

log (r) (r/re)−1/4 ,

where re denotes a scaling parameter, the effective radius, within which half the light of the galaxy is emitted. de Vaucouleurs’ law applies more frequently to giant elliptical galaxies; dwarf elliptical galaxies are often better ﬁtted by other laws. See elliptical galaxies.

deviative absorption Deviative absorption of a radio wave occurs near the point of reﬂection in the ionosphere. See critical frequency.

deviatoric strain A state of strain deﬁned by subtracting one-third of the volumetric strain from the total strain. If εij is the total strain tensor, the deviatoric strain tensor is ε ij = εij − θδij /3, where θ = εii = ε11 + ε22 + ε33, and δij is the Kronecker delta.

deviatoric stress A state of stress with pressure subtracted. If σij is the total stress tensor, the deviatoric stress tensor is σ ij = σij − pδij , where p = σii/3 = (σ11 + σ22 + σ33)/3, and δij is the Kronecker delta.

dew During night or early morning, due to radiational cooling, water condensed onto objects near the ground whose temperature has fallen below the dew point of adjacent air but still above freezing. Dew often appears in warm seasons with clear weather and light winds. Although the amount of water is small, in dry season and regions it amounts to a signiﬁcant contribution to plant growth requirements.

differential emission measure

dew point The temperature at which liquid water reaches saturation with respect to a plane water surface as the temperature of a gas mixture is lowered at constant pressure in the presence of nucleation centers so supercooling is excluded. In meteorology, it is the temperature at which moisture begins to condense on a surface in contact with the air.

dex Decimal exponent.

dextral fault An alternative term for a rightlateral, strike-slip fault.

diapir A body of light material, for example salt, that moves upwards in the Earth’s crust due to buoyant forces; originally meant a form of dome or anticline folding structure produced by intrusion of ﬂuid-like material such as rock salt and mudstone. A diapir is thought to be formed by the processes that low density rock relative to the ambient country rock ﬂows viscously due to its buoyancy and ascends with a mushroom shape, deforming the upper layer with higher density. Recently, the mechanism of ascent of diapir due to inversion of density has been applied to material circulation of igneous rocks and to the whole mantle.

diapycnal Motion or transport directed across surfaces of constant density (isopycnals).

diapycnal ﬂux In hydrology, ﬂux occurring in the direction perpendicular to surfaces of equal density. Every diapycnal exchange alters the density structure and thereby affects the potential energy of the water column (sink or source of energy). In lakes, vertical and diapycnal can usually be used synonymously. In polar regions of the ocean, diapycnal and vertical deviate substantially. See also buoyancy ﬂux, cabbeling.

dichotomy of Mars The surface division of Mars into a lightly cratered third of the planet in the middle to upper latitudes of the northern hemisphere, and a remaining heavily cratered two-thirds. The lightly cratered third stands approximately 3 km lower than the heavily cratered surface.

diel Pertains to occurrences on a 24-hour cycle; any periodic diurnal or nocturnal (i.e., day or night) cycle.

dielectric strength For an insulating material, the maximum electric ﬁeld strength (volts per meter) that it can withstand intrinsically without breaking down. For a given conﬁguration of dielectric material and electrodes, the minimum potential difference that produces breakdown.

differential charging One cause for spacecraft damage in space by substorms and magnetic storms. Since electrons are much lighter than positive ions, in a plasma with equal densities and comparable particle energies, the electron ﬂux is larger. This causes the spacecraft to be hit each second by many more electrons than ions, so that it becomes negatively charged. The charging of an entire spacecraft is hard to prevent and need not cause any damage (except for distorting particle observations); but when different parts charge up differently, damage-causing discharges are possible. Electrically conducting paint is one way of dealing with the problem.

differential diffusion If turbulent diffusion is almost negligible (such as in an extremely stable water column and weak turbulence), molecular diffusion becomes the dominant ﬂux. Since the molecular diffusivities of ions, which are present in natural waters, have slightly different values, the ﬂuxes will be slightly different even for equal gradients. Over a long time period, the ionic composition of the water column will change (Sanderson et al., 1986).

differential emission measure A measure of the emitting power of a volume of plasma over a given range of temperatures T → T + dT . The differential emission measure is often employed to draw conclusions from spectral observations made of a number of distinct emission lines at a variety of temperatures. The differential emission measure, Q(T ), is deﬁned asQ(T )dT = n2edV , where ne is the electron density, and V is the plasma volume being considered.

differential heating/cooling

differential heating/cooling Due to different exposure (to the atmosphere; solar radiation, wind, etc.), changing water transmissivity (algae, kelp forests, etc.), or varying depth, neighboring water bodies may experience different rates of cooling or heating. Differential heating/cooling leads subsequently to lateral density gradient and may drive lateral convection.

differential rotation Change of the rotation speed with distance from the rotation axis.

1. Change of the solar rotation speed with heliographic longitude: the sun rotates faster close to the equator and slower towards the poles. Typical values for the sidereal rotation period of the photosphere at different latitudes are given in the table.

Sidereal Rotation

Periods of the Sun

	Latitude	Period [days]
	equator	26.8
	30◦	28.2
	60◦	30.8
	75◦	31.8

In addition, there is also a differential rotation in radius in the convection zone. In particular at latitudes above about 30◦, the rotation speed of the sun increases towards the bottom of the convection zone. At lower latitudes there is a rather small decrease in rotation speed while at latitudes around 30◦ there is no differential rotation in radius. Observed in the photosphere, low latitudes rotate at a faster angular rate (approximately 14◦ per day) than do high latitudes (approximately 12◦ per day). This pronounced latitude dependence appears to be the result of convective ﬂows driven radially by the buoyancy force and deﬂected horizontally by the Coriolis force due to solar rotation. Differential rotation plays a crucial role in the understanding of solar activity and the solar dynamo.

2. Differential rotation can also be observed in systems of stars when the rotation speed varies with distance from the center of rotation.

differentiation In geophysics, the process of separation of different materials, in geological or astrophysical settings, via different physical properties. For instance, the atmosphere of the Earth is differentiated in that hydrogen is very rare, having escaped from the upper atmosphere, while oxygen and nitrogen have not. Their larger molecular weight gives them lower speeds at comparable temperatures, so they do not achieve escape velocity at the top of the atmosphere.

Similarly, internal heating (caused by accretion, radioactive decay, tidal heating, etc.) causes the interior of a solid body to become partially or completely molten. Materials making up the body’s interior separate, depending primarily on their densities — denser material (such as iron) sinks to the center while less dense materials (such as silicates) ﬂoat to the surface. This differentiation thus creates the layered structure of the crust, mantle, and core suspected in most of the larger solar system bodies (those with diameters > 1000 km).

In mathematics, the linear operation ( ) obeying Leibnitz’ law: (ab) = a b + b a which retrieves the slope of a function if it exists, in some suitable generalization, if not.

diffraction A term relating to the spread of wave energy in a direction lateral to the dominant direction of wave propagation. Used in the description of light and water waves. Results in interference patterns (constructive and destructive) and accounts for the spreading of energy into areas that would otherwise be shadowed.

diffraction grating A light analyzer, used to disperse different chromatic elements in a light beam, based on the principle of light diffraction and interference by a series of parallel slits. A typical diffraction grating consists of a large number of equally spaced, tilted grooves ( 100 to 1000 grooves per millimeter). The spectral resolving power increases with the number of grooves per millimeter for a ﬁxed incident bandpass. A diffraction grating can either reﬂect or transmit light. To avoid loss of light because of a maximum of the diffraction pattern at zero order, the grooves are tilted to shift the maximum of the diffraction pattern toward the ﬁrst or, occa-

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