DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

where r is the distance from the center of the
Earth,v is the local appropriate wave speed, and
θi is the angle that the direction of phase propagation
makes with a radial vector from the center
of the Earth. It can be shown that
p= dT
d
whereT is the travel time of the ray from source
to receiver, and is the angle between lines
from the two to the center of the Earth. In a horizontally
stratified situation (which is approximately
true near the Earth’s surface, where variations
inr can be neglected to first order) the ray
parameter simplifies top=R⊕ sinθi/v. Ifv is
known as a function of radius or depth, then it
is easy to use p to calculate the path taken by a
ray emitted from a seismic source at a particular
angle θi.
ray tracing Determining the path of a wave
propogation by the use of the laws of reflection
and refraction, ignoring diffraction.
ray tracing: wave packet approximation
The method by which the dominant wave behavior
of light or other waves is taken into account,
inwhichthecentralmotionofapproximatelydescribed
wave packets determines the ray paths.
R Coronae Borealis stars Highly evolved,
asymptotic giant branch stars that have shed (or
burned) all of their hydrogen, leaving an atmosphere
made mostly of helium and carbon. The
carbon sporadically condenses into dust, veiling
the visible light from the stars, so that they fade
by many magnitudes in a few weeks. The dust
is gradually blown away, and the stars brighten
back to normal, only to fade again in a few
years. Most are also pulsationally unstable (see
instability strip) and show rather subtle periodic
changes in size and brightness with periods of
one to a few months.
RE
See Earth radius.
real singularity In general relativity a region
in space-time where some invariant geometrical
quantities diverge, or where extension of finite
acceleration curves is impossible.
Examples are the centers of black holes and
white holes (e.g., see Schwarzschild metric).
© 2001 by CRC Press LLC
red giant
Singularities can be space-like (occurring everywhere“simultaneously”)ortime-like(occurring
over a period of time). See black hole, white
hole.
recombination (in atomic and molecular
physics) Any of a number of processes in
which an atom or molecule with positive charge
reacts with another species or particle of negative
charge. The different types of recombination
can be represented:
X + +e − →X+hν (radiative)
X + +e − →X ∗ →X+hν (dielectronic)
XY + +e − →X+Y ∗ (dissociative)
X + +Y − +M→Z+M (three–body)
X + +Y − →X+Y ∗ (mutual neutralization)
where hν represents a photon released in the
process,e − an electron,Y ∗ represents an excited
state of species Y,M is a third particle that can
absorb the energy released, and Z can be X, Y,
or a new resulting species.
recombination line An emission line produced
by the quantum transition between two
states of an atom or molecule, in which the energetically
higher state was produced by the recombination
of an atom or molecule with an
electron either directly or by other transitions
following the recombination event. See emission
line, recombination.
reconnection A process in a magnetized
plasma, such as the solar magnetosphere,
wherby diffusion of the ions allows adjacent oppositely
directed flux lines to merge and cancel,
lowering the total energy of the field. See also
intercommutation (cosmic string).
recurrent novae Ordinary novae of the sort
involving a nuclear explosion on the surface of
a white dwarf, but where the hydrogen to be
burned collects fast enough again that more than
one event has been seen in historic times. Only
about six examples are known, and particular
systems are often added to or subtracted from
the inventory as we learn more about them.
red giant The evolutionary phase of a star
of 0.8 to about 5 solar masses during which the
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