scatter-free shock acceleration

is evaluated. Examples are the value of pressure beneath the ocean as a function of position, or the value of the temperature as a function of position and time in a room. See vector, tensor.

scale factor The function of time in the homogeneous isotropic cosmological models that determines the changes of distance between any two points of space as time passes. In the simplest such model, the one with flat Euclidean spaces of constant time, the metric is

ds2 = −dt2 + R2(t) dx2 + dy2 + dz2

where R(t) is the scale factor. The distance between points P1 = (x1 , y1 , z1) and P2 = (x2 , y2 , z2) at any time t is thus

l =R(t) (x2 − x1)2

+ (y2 − y1)2 + (z1 − z1)2 1/2 ,

a function of time. The dependence of R on time is obtained by substituting the metric, and a matter source into the Einstein equations. For many sources, R(t) vanishes at a particular time (conventionally t = 0), so the distance between any two points is zero at that time, the Big Bang. See Robertson–Walker cosmological models.

scaling solution (cosmic string and cosmic texture) In theoretical cosmology, a state of evolution of a network of topological defects in which the energy in the structure (strings or textures) is radiated away as gravitational radiation or in other massless forms of energy. In such a situation, the energy in the defects maintains a constant ratio to the energy content in the radiation of the universe. Since energy density of the radiation eventually falls below that of ordinary matter, this guarantees that the defects do not dominate the universe at late times. See cosmic string, cosmic texture, cosmic topological defect, intercommutation (cosmic string), Goldstone boson.

scarps A more or less straight or sinuous line of cliffs, seen on the Earth, the moon, or other terrestrial planets. The cliff may be the result of one or more processes including tectonic, volcanic, impact-related, or degradational processes.

scatterance The fraction of the incident power at a prescribed wavelength that is scattered within a volume.

scattered disk, scattered disk object The minor bodies in high eccentricity orbits in the ecliptic plane beyond Neptune. Objects in the scattered disk may be escapees from the Kuiper belt and/or may be scattered Uranus–Neptune planetesimals.

scatter-free shock acceleration Dominant mechanism for particle acceleration at quasiperpendicular magnetohydrodynamic shocks. The relative motion of the shock with respect to the plasma generates an electric induction field E = −uu × Bu = −ud × Bd in the shock front, with ui being the plasma flow speeds in the shock rest frame and Bi the magnetic fields in the upstream and downstream medium, respectively. The field is directed along the shock front, perpendicular to both the plasma flow and the shock normal. The shock-front is also associated with a jump in the magnetic field strength. Thus, gradient drift forces particles to move along the shock front. The drift direction depends on the charge of the particle and is always such that the particle gains energy. With increasing energy, the particle’s velocity component perpendicular to the shock increases, too, eventually becoming larger than the shock speed. Then the particle escapes from the acceleration site. The details of the particle trajectory, in particular whether it traverses the shock or is reflected back into the downstream medium, strongly depend on the particle’s initial energy and pitch-angle, leading to a characteristic angular distribution of the accelerated particles: an initially isotropic angular distribution of particles in both the upstream and downstream medium is converted to a very strong field-parallel beam in the upstream medium and to a smaller beam perpendicular to the field in the downstream medium. The energy gain depends on the time the particle can drift along the shock front. This in turn depends on the particle speed perpendicular to the shock: if this is small, the particle sticks to the shock; if it is large, the particle escapes. The energy gain can be estimated from the conservation of the magnetic moment across the shock. For an exactly

© 2001 by CRC Press LLC

scattering albedo

perpendicular shock, the momentum perpendicular to both shock and magnetic field after the interaction between particle and shock is

p2 = Bd = rB . p1 Bu

The normal component of the momentum remains unchanged. Thus, the change in momentum (and energy) is determined by the magnetic compression rB, the ratio between the downstream and upstream magnetic field strength. For oblique shocks, the gain in momentum is smaller than in the above equation. A crude approximation for the energy gain here is E ouu/θBn with uu being the upstream plasma speed and θBn as angle between magnetic field direction and shock normal. On average, the energy gain during one interaction between particle and shock is a factor between 1.5 and 5. Additional energy gain, for instance to accelerate MeV particles out of the solar wind plasma, requires repeated interactions between shock and particle and therefore sufficiently strong scattering in the upstream medium to reflect the particle back to the shock front. See diffusive shock acceleration.

scattering albedo See albedo of single scattering.

scattering angle The angle between the directions before and after scattering.

scattering coefficient The limit of the ratio of the incident power at a prescribed wavelength that is scattered within a small volume to the distance of photon travel as that distance becomes vanishingly small [m−1].

scattering cross-section When a beam of radiation or particles with a uniform flux f of energy or particles (e.g., N particles per second per square centimeter) is incident on a scatterer, the amount scattered per unit time is: f = f A, which defines the scattering cross-section A. Cross-section has units of area.

scattering efficiency factor The ratio of the scattering cross-section to the geometrical cross-section of the particle.

Schmidt camera Type of reflecting telescope invented by Bernhard Schmidt, which uses a thin correcting lens (“correcting plate”) at the front of the telescope, which corrects the spherical aberration arising from the spherical primary mirror. This design leads to a large field of view (degrees across). Detection is usually made at prime focus in a Schmidt camera. See prime focus.

Schwarzschild black hole In general relativity, a spherical, non-spinning black hole. See black hole, Schwarzschild metric.

Schwarzschild metric (Schwarzschild solution) The unique metric of empty spacetime outside an uncharged spherical source (see Birkhoff theorem), found by K. Schwarzschild in 1915.

In spherical coordinates (t, r, θ, φ), the line element takes the form (c is the speed of light and G is Newton’s constant)

ds2 = −	1 −	2 GM	dt2
		c2 r

+ 1 − 2 GM −1 dr2 c2 r

+ r2 dθ2 + sin2 θ dφ2

where M is the mass parameter of the source. The radial coordinate r ranges from r0 (corresponding to the surface of the source) to +∞. Further, for r0 = constant to be a sensible (that is time-like) trajectory, one needs r0 > RG (region I), where RG ≡ 2 GM/c2 is the so-called gravitational radius, or Schwarzschild radius.

If one assumes that the space-time is vacuum everywhere, the above form is valid for any values of r from 0 to +∞ and one encounters a singularity at r = 0, a real singularity where the curvature tensor diverges. The value RG instead is a coordinate singularity (the curvature tensor is smooth and finite at r = RG). The properties of the Schwarzschild solution led to the introduction of the notion of a black hole. The surface r = RG, t = +∞ is the future event horizon which screens the Schwarzschild black hole of mass M. The area of the horizon is

A = 16πG2M2 , c4

© 2001 by CRC Press LLC

seafloor magnetic stripes

and the surface gravity is

κ = c2 . 4GM

For r < RG (region of type II), r becomes a time coordinate. This means that inside the horizon everything evolves towards the central singularity, which occurs at time r = 0, and where tidal forces grow so strong so as to disintegrate any kind of matter.

The Schwarzschild metric can be analytically extended by transforming to Kruskal/Szekeres coordinates so as to cover a larger manifold which contains, besides the black hole with its future event horizon and future singularity, a white hole with its past event horizon and another copy of the asymptotically flat region. Early applications of the geodesics in the Schwarschild solution included the calculation of the perihelion shift of Mercury’s orbit, which was the first observational test of general relativity. The geodesics were also used to calculate the angle of light deflection and the relativistic time-delay in the sun’s vicinity. See ADM mass, asymptotic flatness, black hole, black hole horizon, future/past event horizon, Kruskal extension, real singularity, surface gravity, trapped surface, white hole.

Schwarzschild solution	See Schwarzschild
metric.
Schwarzschild spacetime	See Schwarzschild
metric.

scintillation Random fluctuations in the amplitude, phase, and direction of arrival of an electromagnetic signal. Scattering from small irregularities in electron density anywhere along the signal path causes scintillation, which tends to decrease with increasing frequency. The S4 scintillation index, where S4 = [(< I2 > − < I >2)/ < I >2]1/2 and I is the signal intensity with <> indicating time-averaging, is the most commonly used parameter for characterizing the intensity fluctuations. Scintillation occurring in the Earth’s ionosphere is usually observed on a transionospheric satellite communication link. There are two terrestrial regions of intense scintillations: at high and low latitudes. At high latitudes, scintillation frequency and intensity are

greatest in the auroral oval, although it is also strong over the polar caps. Geomagnetic storms may cause scintillation to increase at any phase of the solar cycle. At low latitudes, nighttime scintillation shows its greatest range of intensity, with both the quietest and most severe of conditions being observed. The source of the scintillation is the irregularities on the walls of spread-F bubbles and is most prevalent during solar maximum. It may cause peak-to-peak fluctuations on 1.5 GHz and can be of the order of 56 dB above the geomagnetic equator, and as high as 20 dB for hours at a time in the equatorial anomaly region. At mid-latitudes scintillation is less severe and is positively correlated with spread-F and, to a lesser degree, with sporadic E. Interstellar scintillation, arising from similar mechanisms on a much larger scale, is ubiquitous in radio observations of pulsars. See spread F.

Scorpius X-1 The brightest X-ray source

in the sky, identified with the spectroscopic binary V818 Scorpii at 16h19m55s, −15◦38 2 .

V818 Scorpii has a magnitude range of 11.80 to 13.20 with period 0.787313 days. The X-ray source has variations with the same period, and quasiperiodic oscillations of approximately 165 sec.

scour The process by which flowing water removes sediment from a seafloor, lake, or river bed. Typically most pronounced where engineering structures such as piles or jetties meet the seafloor.

scri (I , Script I) Null infinity in an asymptotically simple or weakly asymptotically simple space-time. See asymptotically simple space-time, weakly asymptotically simple space-time.

sea The ocean, or a smaller body of salt water. Also used to describe the locally generated wind waves.

seafloor magnetic stripes Alternating bands of magnetic polarization found in the seabed floor. The Earth’s magnetic field reverses with a period of hundreds of thousands of years. Seafloor spreading from the central seafloors oc-

© 2001 by CRC Press LLC

seafloor spreading

curs at a rate of centimeters per year, consistent with seafloor magnetic field alternations on the scale of 5 to 50 km. A similar banding was found on Mars via the magnetometer/electron reflectometer instrument on board NASA’s Mars Global Surveyor spacecraft. An area in the southern highlands near the Terra Cimmeria and Terra Sirenum regions, centered around 180◦ longitude from the equator to the pole was surveyed. The bands are oriented approximately east-west and are about 150 km wide and 1000 to 2000 km long, suggesting past active tectonics on Mars as well.

seafloor spreading The process by which new seafloor crust is created by the volcanism at divergent boundaries. As buoyant basaltic magma moves up from the interior and erupts at the rift zone of divergent boundary, new crust is attached to the plates on either side of the rift zone (mid-ocean ridge). The continual upwelling of new magma pushes the plates apart to make room for the new crust, causing the seafloor to spread at a half rate of up to several centimeters per year to either side. The new oceanic crust will retain the orientation of the terrestrial magnetic field polarity which existed at the time of its solidification, hence study of the polarity reversals (which are mirror images on either side of the rift zone) which results in alternating directions of magnetization of the oceanic crust and can provide information about the rate at which the plates are diverging. The discovery of seafloor spreading (which says the ocean floors are moving) in the 1960s, combined with the earlier theory of continental drift (which says that the continents are moving), led to the development of the theory of plate tectonics to explain the geologic activity of the Earth.

sea level There have been major variations of sea level on geological time scales. Low stands in sea level (50 m or more) are associated with glaciations (on time scales of 10,000 years). Major high stands of sea level, for example in the Cretateous some 80 million years ago, are associated with periods of rapid plate tectonics when the large number of ocean ridges displaced ocean water causing high sea levels of 200 m or more. Many variations in sea level are not understood. Increase in sea level of or-

der 10 cm/century is attributed to recent anthropogenic increases.

seamount A cone-shaped isolated swell with height difference of more than 1000 m from its ambient ocean bottom. A swell with height difference of less than 1000 m is referred to as a knoll, and the one with relatively large, flat top is called a guyot. Most seamounts originate from submarine volcanoes. There are many seamounts from the mid to western Pacific ocean. Recently, many cobalt-rich crusts were discovered on slopes of seamounts, worthy of notice as valuable submarine resources in the future.

seasonal thermocline

See thermocline.

sea stack Remnant small islands within or near the surf zone, composed of weather rock that has not yet been eroded away.

seawall A man-made wall, typically vertical, built to resist wave impact and erosion of the sediments that are situated landward.

SeaWiFS The Sea-viewing Wide Field-of- view Sensor satellite launched in 1998 that measures radiance in wavelengths centered at 412, 443, 490, 510, 555, and 670 nm (all with 20 nm bandwidth) and 765 and 865 nm (both with 40 nm bandwidth).

Secchi depth The depth at which a Secchi disk disappears from view as it is lowered in water [m].

Secchi disk A disk of diameter 20 to 30 cm, used to assess water clarity. The disk is painted with a high-contrast painting scheme and lowered into the water, and the depth at which it is no longer visible is noted. Repeated measurements are often used to assess changes in water clarity.

second Unit of time equal to 1/86400 of a day whose length was based on the rotation of the Earth (see mean solar time), and now, because of the nonuniformities in the former, is based on atomic time. The second is the unit of International Atomic Time and is included in

© 2001 by CRC Press LLC