DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

exact solution
The path of a star in the Teff , L plane (the
Hertzsprung–Russell, HR, diagram) as those
physical parameters change is called the star’s
evolutionary track. This track is primarily a
function of the star’s initial mass. Collections
of these tracks derived from theoretical stellar
evolution models are often plotted on an HR diagram
along with data from a collection of stars
to estimate initial masses and ages.
exact solution (of Einstein’s equations) A
solution of Einstein’s equations, i.e., a metric.
The term exact solution is used only when it is
necessary to stress that the metric was derived
from Einstein’s equations by strict mathematical
procedures. The opposites of exact are an
approximate (i.e., a perturbative solution) and a
numerical solution. This opposition is irrelevant
for several purposes; for example, all observational
tests of the relativity theory necessarily
involve approximations, and numerical calculations
are often performed on top of exact solutions
to obtain quantitative results. However,
some theoretical problems (among them cosmic
censorship and the existence of singularities)
have been extensively studied within the
framework of exact solutions.
excitationtemperature Inagivenobject, the
constituent atoms and molecules are in quantum
mechanicallyexcitedstates, andtheratiooftheir
numbers in the ground state to the excited state
is characterized by an excitation temperature,
such that
Nu
Nl
= gl
e
gu
−hν/kTex
where Nu and Nl are the number per volume
in the upper and lower states, respectively, and
gl and gu are the statistical weights. The excitation
temperature Tex characterizes this distribution
for a given upper and lower state. If
the atoms and molecules are in thermodynamic
equilibrium (collision dominated), then the kinetictemperature,
whichdescribesadistribution
in speed of the atoms and molecules, is equal to
the excitation temperature.
exosphere The outermost part of the Earth’s
atmosphere, beginning at about 500 to 1000 km
above the surface. It is characterized by den-
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164
sities so low that air molecules can escape into
outer space.
exotic terrane Continental deformation is
partly achieved through folding, which preserves
the juxtaposition of stratigraphic layers,
but also through faulting. A terrane is a block of
continent bounded by faults with a stratigraphy
that is internally coherent but distinct from that
of surrounding blocks. Mountain chains may be
composed of several such blocks. A “suspect
terrane” is a terrane whose geology appears to
be unrelated to the surrounding rock. If it can
be shown (through paleomagnetic methods, for
example) that the rock in the terrane originated
far away from the surrounding rock, then the
terrane is known as an exotic terrane. This may
happen if part of a continent is sliced away by
a long strike-slip fault (such as the San Andreas
fault) and is later attached to the continent or
another continent elsewhere, or if an island arc
or other oceanic landform collides with and is
engulfed by a continent.
expansion The mathematical quantity (a
scalar) that determines the rate of change of
volume of a given small portion of a continuous
medium (see also acceleration, kinematical
invariants, rotation, shear). An observer
placed in a medium in which acceleration, rotation,
and shear all vanish while expansion is
nonzero would see every point of the medium
recede from (or collapse toward) him/her with
the velocity v proportional to its distance from
him/her, l, so that v = 1 3θl. The factor θ is the
expansion (θ >0for receding motion, θ