DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

twistor
object that is carried away at speed v (from an
identical object that remains at rest) to a different
location and is returned to its original location
accumulates less total time interval than does its
nonmoving “twin”. In principle, if the motions
are at a substantial fraction of the speed of light
and the distances are substantial (light years),
one could demonstrate this effect with human
twins. For instance, if one newborn twin travels
5 light years at a speed of 0.99c(c = speed of
light) and then returns at the same speed, the
stay-at-home twin would see the return at age
10, while the elapsed time for (the age of) the
traveling twin would be
Age = t
1 − v2
c 2
= 10 yr. × 0.14
= 1.4 yr .
The paradox is with everyday experience, where
these effects are so small as to be unnoticeable.
The effect has been verified in atomic
clocks flown around the Earth, in the operation
of atomic accelerators, and in the correct operation
of the global positioning satellite system.
See Lorentz transformation, special relativity.
twistor An element of the four-dimensional
spinor representation space of the group
SU(2,2). Following work in 1962–1963 with
R.P. Kerr, the notion of a twistor was put forward
by R. Penrose as a possible mathematical
tool for formulating the quantum theory of
gravitation. In the theory of relativity, a twistor
represents the state of a massless particle.
two-flow equations The two coupled differential
equations for irradiances obtained by
integrating the radiative transfer equation over
the hemispheres of downward and upward directions.
2-form A rank-2 antisymmetric covariant
tensor. A basis for 2-forms is the antisymmetric
tensor product of pairs of 1-form basis forms.
For instance, if {dxβ } is a basis for 1-forms, then
{dxβ ∧ dxα } is a basis for 2-forms. Here ∧ is
the antisymmetric tensor product, i.e.,
dx β ∧ dx γ = 1 β γ γ β
dx ⊗ dx − dx ⊗ dx
2
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490
with ⊗ the tensor product. See tensor.
two-ribbon flare A large flare that has developed
as a pair of bright strands (ribbons) on
both sides of the main inversion (“neutral”) line
of the magnetic field of the active region, usually
most prominent in Hα. Two-ribbon flares result
in a substantial reconfiguration of the coronal
magnetic field.
two-stream approximation The two-flow
approximation. See two-flow equations.
two-stream instability A broad term referring
to any of a number of resonant and nonresonant
instabilities driven by the streaming of
charged particles relative to the main body of a
collisionless plasma.
type I radio burst The metric type I burst
is continuous radio emission from the sun, basically
the normal solar radio noise. It can be
enhanced during the late phase of a flare. The
radio noise is unstructured, no frequency drift
can be identified.
type II radio burst In the metric type II
burst, a relatively slow frequency drift can be observed,
indicating a propagation of the electron
source at a speed of about 1000 km/s. It is interpreted
as evidence for a shock wave propagating
through the solar corona, but it should be noted
that the shock itself is not generating the radio
emission but rather the electrons accelerated at
the shock. As these electrons stream away from
the shock, they generate small type III like structures,
giving the burst the appearance of a herringbone
in the frequency time diagram with the
type II burst as the backbone and the type III
structures as fish-bones. The type II burst is
often split into two parallel frequency bands, interpreted
as forward and reverse shocks.
Type II radio bursts can also be observed with
frequencies in the kilometer range (kilometric
type II radio burst). The drift characteristic is
similar to that of the metric counterpart, the frequency
indicates that these bursts are excited in
interplanetary space. Consequently, the kilometric
type II burst is interpreted as the signature
of a shock propagating through interplanetary
space. It should be noted, however, that