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Dictionary of Geophysics, Astrophysic, and Astronomy.pdf

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F star

where E and B are the electric and magnetic ﬁelds, V is the ﬂuid velocity, c is the (vacuum) speed of light, and the integral is taken about the contour C. In ﬂuids of inﬁnite electrical conductivity (and for that matter, to an excellent approximation in most situations involving collisionless plasmas)

E + 1 V×B = 0 , c

so that

dG = 0 . dt

When this condition is satisﬁed, the magnetic ﬂux through any closed contour C that co-moves with a ﬂuid is constant; it is in this sense that magnetic ﬂux tubes may be considered to “move with a ﬂuid”. This result is sometimes called Alfvén’s theorem.

F star Star of spectral type F. Canopus and Procyon are F stars.

Fukushima’s theorem In two articles in 1969 and 1976, Naoshi Fukushima showed that the main contributions to the magnetic ﬁeld, observed on the ground from ﬁeld aligned currents which ﬂow in and out of the Earth’s ionosphere, tended to cancel (the mathematical principle might have been known before, but was not applied to the ionosphere). He showed that with a uniformly conducting spherical ionosphere, linked to inﬁnity by straight conducting ﬁlaments (an idealization of the actual geometry), there is no magnetic effect below the ionosphere. It explained why the main magnetic effect seen on the ground comes from secondary currents, the Hall currents which form the auroral electrojets.

fully arisen sea A sea condition whereby continued energy input by wind will not increase wave energy.

fully rough ﬂow Hydrodynamic ﬂow near a boundary in which the Reynolds number computed using the typical surface irregularity scaleas the length exceeds approximately 100:

u /ν ≥ 100

where u is the velocity and ν is the kinematical viscosity. See kinematic viscosity, Reynolds number.

fulvic substance In oceanography, high molecular weight organic compounds resulting from plant decay, especially phytoplankton. See colored dissolved organic matter.

fundamental tensors of a worldsheet A cosmic string is a type of cosmic topological defect which may play a role in producing the structures and features we see in our present universe. It can be conveniently described as long and inﬁnitely thin, but a line evolving in space and time and describing a two-dimensional “surface” called a worldsheet, whose evolution is known provided one knows its dynamics and its geometry. Fundamental tensors provide the knowledge of the worldsheet geometry, while the equation of state allows one to compute its dynamics.

The position of the worldsheet in spacetime requires knowledge of its coordinates xµ(I, τ) depending on two variables internal to the worldsheet: a curvilinear space coordinate I and a time τ, denoted collectively as ξa. One can deﬁne a 2 × 2 induced metric γab on the string worldsheet, using the spacetime metric gµν, through

∂xµ ∂xν γab = gµν ∂ξa ∂ξb ,

with inverse γ ab. Then the ﬁrst fundamental tensor of the worldsheet is

ηµν = γ ab ∂xµ ∂xν . ∂ξa ∂ξb

The surface spanned by the string in spacetime is curved in general. This is quantiﬁed by the second fundamental tensor Kµνρ which describes how the 2-dimensional sheet is embedded in spacetime, and is calculable by means of the covariant derivative in spacetime µ

Kµνρ = ηµσ ηνα αησρ ,

with symmetry

Kµνρ = Kνµρ , and trace

Kµ = Kαα µ .

future/past event horizon

One interesting particular case is the Goto– Nambu string, for which we simply have Kµ = 0 as the sole equation. See covariant derivative, equation of state (cosmic string), Goto–Nambu string, metric, summation convention, Witten conducting string.

future/past causal horizon The boundary that separates two disconnected regions I and O of space-time such that: 1. no physical signal originating from I can ever reach (at least) a particular class of observers in O (future horizon) or 2. (at least) a particular class of observers in O cannot send signals into I (past horizon). By causal horizon (with no further speciﬁcations) case 1. is usually meant.

future/past event horizon A future event horizon is the future causal horizon which separates an eternal black hole B from the disconnected external region O such that no physical signal originating from inside B can ever reach

any observer located in O. On the other hand, it is possible to send signals from O into B (a mechanical analog would be a one-way permeable membrane).

Any external observer (in O) not falling in the gravitational ﬁeld of the black hole sees a signal sent towards the black hole approach the horizon but never cross it. An observer co-moving with the signal, as any locally inertial observer, would instead cross the horizon at a ﬁnite (proper) time without noticing any local effect (without experiencing any particular discomfort).

It can be proven that an event horizon is a light-like surface which necessarily shares the symmetry of O. This leads to a classiﬁcation of all possible families of black holes in terms of the ADM mass and a few other parameters see No-hair theorems.

A past event horizon is the past causal horizon circumventing a white hole. See ADM mass, black hole, black hole horizon, future/past causal horizon, Rindler observer, white hole.

galactic noise

gabbro A coarse-grained igneous rock with the composition of basalt, composed of calcic plagioclase, a ferromagnesium silicate, and other minerals. Classiﬁed as plutonic because the large crystal size indicates formation by slow crystallization, typical of crystallization at great depth in the Earth.

galactic bulge Many spiral galaxies have a central core region which is roughly spherical with radius greater than the disk thickness. This is the galactic bulge.

galactic cluster See open cluster.

galactic coordinates Coordinates measuring angular positions on the sky, taking the location of Sagittarius (RA 12h49m, dec 27◦24 ) as the origin of galatic latitude (measured north or south of the galactic plane), and longitude, measured increasing eastward. The north galactic pole is taken in the same hemisphere as the pole north of the celestial equator. The tilt of the galactic plane to the celestial equator is 62◦36 . Transformations between galactic and celestial coordinates are:

cos bII cos(lII − 33◦)

=cos δ cos(α − 282.25◦) , cos bII sin(lII − 33◦)

=cos δ sin(α − 282.25◦) cos 62.6◦

+sin δ sin 62.6◦ ,

sin bII = sin δ cos 62.6◦

− cos δ sin(α − 282.25◦) sin 62.6◦ , cos δ sin(α − 282.25◦)

=cos bII sin(lII − 33◦) cos 62.6◦

−sin bII sin 62.6◦ ,

sin δ = cos bII sin(lII − 33◦) sin 62.6◦ + sin bII cos 62.6◦ ,

lII = new galactic longitude , bII = new galactic latitude ,

α = right descension (1950.0) , δ = declination (1950.0) ,

For, lII = bII = 0 :

α = 17h42m4 , δ = −28◦55 (1950.0) ; bII = +90.0, galactic north pole:

α = 12h49m , δ = +27◦. 4(1950.0) .

galactic disk A relatively thin (400 to 1000 pc) component of disk galaxies extending out to 15 to 25 kpc, usually exhibiting a spiral structure of bright stars. Stellar population is mostly Population I (young) stars. In the Milky Way Galaxy, the oldest Population I stars have 0.1 times the metal abundance of the sun and have slightly elliptical orbits rising up to 1000 pc from the disk plane. Stars like the sun (0.5 to 1 times solar metal abundance) can be found up to 300 pc from the plane. Stars with metals 1 to 2 solar extend to 200 pc above the disk. Star forming regions in the spiral arms (containing O and B stars) have circular orbits and are within 100 pc of the disk. Metal abundances there are 1 to 2.5 solar. See metalicity, galactic bulge, spiral arm.

galactic globular cluster Associations of 100,000 to a million stars which have extremely high stellar densities. These clusters are composed of stars that all have the same chemical composition and age. The stars all formed from the same proto-Galactic fragment of gas, which accounts for the fact that the stars have the same composition. Moreover, all of the stars in a globular cluster are the same age because 20 to 30 million years after the ﬁrst stars formed, the ﬁrst supernovae would have detonated. These supernovae drove all of the remaining gas out of the cluster, thereby ending star formation. As the oldest stellar populations in the Milky Way Galaxy, globular clusters provide a ﬁrm lower limit to the age of the galaxy, and therefore the universe.

galactic noise Galactic radio noise originates in the galactic center. However, it is common to include in this any contributions from noise sources outside the Earth’s atmosphere. Because the source is above the Earth’s ionosphere,

galactic wind

some galactic noise will be reﬂected back into space and only contributions from above the local peak F region electron density will be observed at the ground. Consequently, this source of noise is only important for radio circuits operating above the local foF2. See atmospheric noise.

galactic wind Large-scale outﬂow of gaseous matter from a galaxy. Evidence of galactic winds is provided by the morphology of X-ray emitting regions, elongated along an axis perpendicular to the major axis of a highly inclined disk galaxy. More rarely, it is possible to observe, as in the case of the spiral galaxy NGC 1808 or of the prototype Starburst galaxy M82, the presence of optical ﬁlaments suggesting outﬂow from the inner disk. A galactic wind is currently explained as due to an intense, concentrated burst of star formation, possibly induced by gravitational interaction with a second galaxy. As the frequency of supernova blasts increases following the production of massive stars, supernova ejecta provide mechanical energy for the outﬂow and produce tenuous hot gas, which is seen in the X-ray images. Most extreme galactic winds, denoted super-winds, could create a bubble of very hot gas able to escape from the potential well of the galaxy and diffuse into the intergalactic medium. Superwinds are thought to be rare in present-day universe, but may have played an important role in the formation and evolution of elliptical galaxies, and in the structure of the medium within clusters of galaxies. See starburst galaxy.

Galatea Moon of Neptune also designated NVI. Discovered by Voyager 2 in 1989, it is a small, roughly spherical body approximately 79 km in radius. It is very dark, with a geometric albedo of 0.063. Its orbit has an eccentricity of 0.00012, an inclination of 0.054◦, a precession of 261◦ yr−1, and a semimajor axis of 6.20 × 104 km. Its mass has not been measured. It orbits Neptune once every 0.429 Earth days.

galaxies, classiﬁcation of A scheme, the most prominent of which is due to Hubble, to classify galaxies according to their morphology. In the Hubble scheme, elliptical galaxies are classiﬁed E0 (spherical) to E7 (highly

ﬂattened). The number indicator is computed as 10(a − b)/a where a is the semimajor axis and b is the semiminor axis of the galaxy. Spiral galaxies are divided into two subclasses: ordinary, denoted S, and barred, denoted SB. S0 galaxies are disk galaxies without spiral structure, and overlap E7 galaxies. Spirals are further classiﬁed as a, b, or c, progressing from tight, almost circular, to more open spirals. An additional class is Irregular, which are typically small galaxies, with no symmetrical (elliptical or spiral) structure.

Other classiﬁcation systems are those of deVaucouleurs, of Morgan, and the DDO system.

galaxy (1.) The Milky Way galaxy. A spiral galaxy with a central bulge, of about 1000 pc in extent, a disk component of order 1000 pc in thickness and extending about 15 to 20 kpc from the center, and a roughly spherical halo extending 50000 kpc. The total mass is about 1.5 × 1011M and the number of stars in the galaxy is of order 2 × 1011; the total luminosity is of order 1011L . The sun is located in a spiral arm about 10 kpc from the center.

(2.) A large gravitationally aggregation of stars, dust, and gas. Galaxies are classiﬁed into spirals, ellipticals, irregular, and peculiar. Sizes can range from only a few thousand stars (dwarf irregulars) to 1013M stars in giant ellipticals. Elliptical galaxies are spherical or elliptical in appearance. Spiral galaxies range from S0, the lenticular galaxies, to Sb, which have a bar across the nucleus, to Sc galaxies which have strong spiral arms. Spirals always have a central nucleus that resembles an elliptical galaxy. In total count, ellipticals amount to 13%, S0 to 22%, Sa, b, c galaxies to 61%, irregulars to 3.5% and peculiars to 0.9%. There is a morphological separation: Ellipticals are most common in clusters of galaxies, and typically the center of a cluster is occupied by a giant elliptical. Spirals are most common in the “ﬁeld”, i.e., not in clusters.

Galilean invariance The invariance of physical expressions under the Galilean transformation from one coordinate system to another coordinate system which is moving uniformly with respect to the ﬁrst. Newton’s Laws of Mechanics are Galilean Invariant. Named after Galileo

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