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Dictionary of Geophysics, Astrophysic, and Astronomy.pdf

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spectropolarimetry

ening, and natural broadening. If we consider only quantum mechanical effects, a spectral line proﬁle must have a minimum width based on Heisenberg’s uncertainty principle; this is the natural line proﬁle and is Lorentzian, rather than Gaussian, in shape. Convolved with the natural proﬁle are the effects of the gas rotating as a whole, the velocity distribution of the gas particles, and the ambient pressure.

spectral type One of several ways of classifying stars in terms of the lines (absorption usually, but sometimes emission) that are most conspicuous in their optical (more recently sometimes infrared or ultraviolet) spectra. The classical Morgan and Keenan (MK) system is a twodimensional system: spectral type and luminosity class. In the MK system, classiﬁcation was deﬁned at moderate (3 Å) resolution in the blue region (4000 to 5000 Å). The most important physical parameter is the surface temperature of the star, and most stars can be put into a linear sequence covering the range 100,000 K down to 3,000 K or less with the types called OBAFGKML and dominant lines as shown below:

O - ionized helium B - neutral helium A - hydrogen

F - hydrogen, ionized metals G - ionized and neutral metals

K - neutron metals and molecules M - molecules

L - molecules and clouds

The OB (blue) types are referred to as “early” type stars, and the KM (red) types referred to as “late” type stars. The spectral sequence, originally based on the progression of line patterns, was a function of ionization stages of chemical elements identiﬁed in the spectra, and has proven to be ordered from the hottest and most massive stars (O and B types) to the coolest and least massive stars (K and M types). A second dimension makes use of ratios of lines that are sensitive to ambient electron pressure and so provides an indicator of stellar luminosity (via surface gravity) from type I (supergiants) on down to V (main sequence stars) and VI (subdwarfs). Yet additional reﬁnements indicate variations in the surface composition of the stars and intermediate temperatures and spectral

appearances between the primary types. Another signiﬁcant type of star is the Wolf–Rayet (W-R) star, which has unusually strong emission lines and peculiar chemical abundances. Our sun is a G2 V star. See HR (Hertzsprung– Russell) Diagram.

spectrograph An instrument to record the spectrum of some source, usually consisting of a slit through which light or other electromagnetic radiation passes, a grating to disperse the radiation, and a recording medium (photographic emulsion or electronic detector).

spectrometer An instrument for measuring the intensity of radiation as a function of wavelength.

spectrophotometry The measurements of spectral line and spectral continuum ﬂuxes, and their comparison, made over a wide range of frequency or, equivalently, of wavelength. Instrument sensitivity strongly depends on the frequency of the incoming light. To recover the radiation ﬂux and the intrinsic spectral energy distribution due to an astronomical source reaching the telescope, a wavelength-dependent correction must be applied to the recorded spectrum. A spectrophotometric calibration is customarily achieved in optical and UV spectroscopy by the repeated observations of standard stars for which the intrinsic spectral energy distribution is already known. Accurate spectrophotometry, even if restricted to the visible spectral range (≈ 400 to 800 nm) is difﬁcult to achieve from ground-based observations, and has been made possible only recently by the employment of linear detectors such as the CCDs.

spectropolarimetry The measurement of the degree of polarization of radiation, and of the polarized radiation ﬂux, as a function of frequency or wavelength. Optical spectropolarimetric measurements are achieved by inserting a half-wave or quarter-wave plate and a polarizer in the optical path of the light allowed into the spectrograph. Astronomical spectropolarimetry can in principle achieve high precision ( 0.01%). However, partly oblique reﬂections due to telescope and spectrograph design may polarize intrinsically unpolarized ra-

= K2

spectroradiometer

diation and limit observations. Some emission mechanisms like synchrotron processes can produce a high degree of polarization, but real sources typically show optical spectra with a small degree of polarization, reducing the collected ﬂux. As a consequence, spectropolarimetric measurements have been, until recently, rather sparse and limited to relatively bright objects.

spectroradiometer A radiometer that measures radiant energy as a function of wavelength.

spectroscopic binary A binary star system that reveals itself because the stars have a component of their orbit velocities along the line of sight to us, so that Doppler shifts move the absorption (or emission) lines in their spectra back and forth in wavelength. The period over which the pattern repeats is the orbit period; the amount of the shift is the orbit velocity projected along the line of sight. When the system is also an eclipsing binary, then the projection angle is known and the orbit velocities can be used to compute the semi-major axes of the orbit leading to a measurement of the masses of the stars, using Kepler’s third law of planetary orbits in

modiﬁed form: (M1 + M2)P 2 = a3 M1

where the M’s are the masses of the stars in solar masses, P is the orbit period in years (most spectroscopic eclipsing binaries have periods less than about a year), and a is the semi-major axis of the relative orbit, found from the two stellar

velocities, K	1	and K	2	by a	=	2π	(K1+K2)	. a
	1		2		=		P

must be converted to astronomical units for use in the formula as given. Additional complications arise, but systems can still often be analyzed usefully when (a) the orbit is not circular,

(b) the system does not eclipse, or (c) only one set of spectral lines can be seen (normally attributable to the brighter of the two stars); these are called single line spectroscopic binaries, as opposed to double line spectroscopic binaries where both sets of spectral lines are seen. See Doppler shift.

spectroscopy The study of a source by dispersing light into a spectrum of different wavelengths. This is usually accomplished by focusing light from the source on a narrow slit, then passing the light from the slit through a diffrac-

tion grating. The resulting dispersion shifts different wavelengths of light transversely to the slit, so the relative intensities of energies at different wavelengths can be determined.

spectrum The separation of electromagnetic radiation into its component colors or wavelengths. Spectra of visible light from the sun are often punctuated with emission or absorption lines, which can be examined to reveal the composition and motion of the radiating source. Particle spectra give information on the distribution of a given particle population with energy.

spectrum binary An orbiting pair of stars that appears as a single point of light in the sky, but whose spectrum shows absorption and/or emission lines of both stars, recognizable as such generally because they are of very different spectral type. See spectral type.

speed of light The speed of electromagnetic radiation propagation in vacuum: 299792458 m/sec.

spherical harmonic analysis A harmonic analysis method applied on a sphere. In meteorology, it is often used on harmonic analysis of geopotential height ﬁelds. For any grid point of the geopotential height ﬁeld, the height can be expressed as

Z(λ, µ)

∞∞

=anm cos mλ + bnm sin mλ Pnm(µ)

m=0 n=0

where λ is longitude, µ is cos(90◦ − φ), φ is latitude, m is zonal wave number, n is meridional wave number, Pnm(µ) is a normalized associated Legendre function, cos mλPnm(µ) and sin mλPnm(µ) are spherical harmonics, and anm and bnm are coefﬁcients of spherical harmonic analysis, as

anm =	1	s	Z(λ, µ) cos mλPnm(µ)dµdλ
	π
bnm =	1	s	Z(λ, µ) sin mλPnm(µ) dµdλ .

	π

spherical pendulum Physically the same as a simple pendulum, but with motion allowed

spiral arm

anywhere on the surface of a sphere of radius equal to the length of the suspension string. As with a simple pendulum, for small oscillations the motion is simple harmonic with angular fre-

quency

ω = (g/L) .

See simple harmonic motion.

Spica 0.98 magnitude star of spectral type B1 at RA 13h25m11.5s, dec −18◦18 21 .

spicule Chromospheric jet of plasma seen at the solar limb. Spicules are ejected from the high chromospheric part of supergranule boundaries and reach speeds of 20 to30 kms−1 and heights of about 11,000 km before fading. Spicules have typical lifetimes of 5 to 10 min, diameters of 50 to 1200 km, maximum lengths of 10,000 to 20,000 km, temperatures of 10,000

to 20,000 K and electron densities of 3×1010 to 3×1011 cm−3.

spin coefﬁcients			The connection compo-
		=		d
nents J	abcd	(	A	Cζ D	in the SL
	abcd	(	CD ζaA)ζb	ζc ¯	in the SL

(2,C) spinor dyadic basis ζaA introduced by Newman and Penrose. They are equal to the complex Ricci rotation coefﬁcients in the null basis deﬁned by the spinor dyad, and are individually denoted

		Jabcd =
\	ab
\		00	01	11
cd \
00		κ	M	π
10		ρ	α	λ
01		σ	β	µ
11		τ	γ	ν

See afﬁne connection.

spinel Olivine, (Fe,Mg)2SiO4, is one of the major constituents of the Earth’s mantle, and is expected to be an important component of the mantles of the other terrestrial planets as well.

Under high pressures ( 1010 Pa) the olivine crystal structure undergoes a phase change to a more compact phase with a resulting density increase of several percent. This more compact polymorph of olivine is called spinel. In the Earth, the olivine-spinel phase change is believed to be responsible for the density discontinuity at a depth of 400 km (pressure of 13.4 GPa).

spinor A complex 2-dimensional vector. Spinor representations are typically used in quantum mechanics, e.g., to represent the spin of an electron, and in some formulations in general relativity.

S–P interval Time difference between P- and S-waves√ arriving at a point. P-wave velocity is about 3 times as fast as S-wave velocity. When underground velocity structure can be regarded as homogeneous, S–P interval (τ sec) is proportional to hypocentral distance (R km). Thus, for shallow earthquakes

R =kτ (Omori’s formula for

hypocentral distance)

with

k =	VpV s

	Vp	−	V s

where Vp and Vs are P- and S-wave velocities, respectively. The value of k is dependent on locations and depths of earthquakes, taking values of about 6 to 9 km/s.

spin up The transient initial stage of certain numerical ocean simulations when the various modeled ﬁelds are not yet in equilibrium with the boundary and forcing functions.

spiral arm The part of the spiral pattern of a galaxy which is more or less continuously traceable. Spiral arms are very evident in the blue and visual bands (and hence were revealed since the early days of extragalactic astronomy) or, with a more “knotty” appearance, in narrow band images centered on the hydrogen Balmer line Hα. This indicates that spiral arms are sites of recent star formation. Spiral arms accordingly become less and less prominent at longer wavelengths, and almost undetectable in the near infrared, where most of the light is produced by

spiral galaxy

more evolved stars. (Although all masses of stars are formed in the star forming region, the massive blue stars are brighter, and they live a substantially short time, so they remain near the spiral wave that triggered their formation; they expire before they have a chance to move far from their birthplace.) Dust lanes, ﬁlamentary absorption features that appear dark on the emission background of the galaxy’s disk, are often associated with spiral arms. The physical origin of the spiral pattern of galaxies is a subject of current debate; it is presumably a density wave in the rotating galactic disk, moving through the disk at approximately 20 km/sec; the regions of compression become regions of star formation. “Grand design” spirals have been linked to the gravitational perturbation by a nearby companion galaxy, as in the case of M51. See also M51.

spiral galaxy A galaxy showing a bright spiral pattern, superimposed to smooth disk emission. Spiral galaxies are composed of a spheroidal bulge and a ﬂattened system of gas and stars (the disk), over which the spiral pattern is seen. While the bulge of a spiral galaxy loosely resembles an elliptical galaxy, the disk shows an exponential decrease in surface brightness with increasing distance from the nucleus. Both the prominence of the bulge and the shape of the spiral pattern vary along the Hubble sequence from S0, the lenticular galaxies, to Sa (which show large nuclii and faint spiral structure), to Sb, to Sc galaxies which have small nuclei and strong spiral arms. Many galaxies show a bar across the nucleus, in which case a B is added to the classiﬁcation, as in SBc. In total count, S0 amount to 22%, and Sa, b, c galaxies to 61% of all galaxies observed. Spiral galaxies are most common in the “ﬁeld”, i.e., not in clusters (“morphology-density relation”). See also Hubble sequence, spiral arm.

split-hull barge A barge that is constructed so that its hull can be opened to drop the contents of its hold. The hinge runs along the long axis of the barge.

Spoerer’s law Describes the spatial distribution of sunspots during the solar cycle: sunspots always start at relatively high latitudes (about 30◦) and move towards the equator. In addition,

during the solar cycle the latitude of emergence of sunspots moves also toward the equator.

spontaneous symmetry breaking In condensed matter physics, the zero magnetization of an (initially) isotropic ferromagnetic system takes on a nonvanishing value (and thus, the magnetization points in a particular direction) as the temperature decreases below the critical temperature Tc. Thus, the initial symmery (the isotropy) is spontaneously broken. The case for particle physics is described by a scalar ﬁeld φ called the Higgs ﬁeld, and now the order parameter characterizing the transition is the vacuum expectation value |φ| of this ﬁeld. The vacuum expectation value is the expected value of a ﬁeld in its lowest possible energy conﬁguration.

Research done in the 1970s in ﬁnite-tempera- ture ﬁeld theory led to the result that the temperature-dependent effective potential for the Higgs ﬁeld can be written roughly as

VT (\|φ\|) = −	1	m2(T )\|φ\|2 +		λ	\|φ\|4
	2		4!

with Tc2 = 24m20/λ, m2(T ) = m20(1 − T 2/Tc2), this potential has one minimum energy (the

“false vacuum”) at |φ| = 0 when T is large, but a different value given by !|φ|"2 = 6m2(T )/λ where m0 and λ are two positive constants when T is small. Because this minimum depends only on the magnitude of |φ|, not on its sign or phase, there are possibly more than one low temperature minima, a situation called degenerate true vacuua.

For energies much larger than the critical temperature (in appropriate units), the ﬁelds are in the highly symmetric state characterized by|φ| = 0. But, when energies decrease the symmetry of the system is spontaneously broken: the scalar ﬁeld rolls down the potential and sits in one of the nonvanishing degenerate new minima. See cosmic phase transition.

sporadic E Sporadic E (Es) layers are transient localized thin patches of relatively high electron density occurring at (95 to 140 km) E layer altitudes. While the peak sporadic E electron density can be several times larger than the normal E region, it is independent of the regular solar produced E layer. Although the layers

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VT (\|φ\|) = −	1	m2(T )\|φ\|2 +		λ	\|φ\|4
	2		4!