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OCR for page 36
4
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Gravitational Waves:
General relativity theory can be tested on Earth and in the solar
system only through its weak-field, slow-motion effects. When gravita-
tional fields become strong, and when matter velocities approach the
speed of light, new phenomena occur. A black hole, formed by grav-
itational collapse of a stellar core, is one example. Another is a wave
in the space-time metric, traveling at the speed of light the gravita-
tional wave. Gravitational waves interact only weakly with matter and
thus are hard to detect. The detection of gravitational waves is the most
important unsolved problem in experimental gravitation today. Their
detection would provide an important test, in a new regime, of Ein-
stein's general theory of relativity and might also open a new astro-
nomical window and give new kinds of information about the sources
of gravitational waves. Intriguing possible sources are collapsing stellar
cores, colliding neutron stars or black holes, decaying binary systems,
rotating or vibrating neutron stars, and new sources of unknown nature.
Development of several kinds of gravitational-wave detector has
continued for two decades, with great advances in technology, but with
no discovery as yet. Current trends in technology of the detectors,
together with the best theoretical guesses of strength and event rate of
astronomical sources, lead one to anticipate that gravitational waves
may be detected within the next decade or two.
Meanwhile, the discovery and long-term observation of a radio
36
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SEARCH FOR GRA VI TA TIONAL WA VES: INTROD UCTI ON 37
pulsar in a binary stellar system has provided impressive evidence that
gravitational waves do exist. The orbit of this system is decaying at just
the rate expected owing to gravitational-wave damping.
THEORY
In any theory of long-range forces that is consistent with special
relativity, the force must act at the speed of light rather than instanta-
neously. Consequently there is a strong expectation that, along with
the static long-range gravitational force, there must exist in nature
some kind of gravitational-field excitation that travels at the speed of
light and that can remove energy from an isolated system gravita-
tional radiation or gravitational waves.
Einstein himself showed the existence of gravitational waves in the
general theory of relativity, soon after the theory was complete.
However, he used the linear approximation to general relativity in
deriving this result, and the fact that general relativity is intrinsically a
nonlinear field theory led many to doubt the existence of waves. For
about 40 years confusion reigned on the issue of whether gravitational
waves were or were not a prediction of general relativity, and the
theoretical issue was settled only in the early 1960s. The theoretical
properties of gravitational waves, presuming the correctness of general
relativity theory, are now thought to be well understood.
Alternative theories of gravity usually also predict gravitational
waves, although with significant differences from the predictions of
general relativity. In some such theories (either those with prior
geometry or with more than one metric tensor) the speed of gravita-
tional waves may differ from the speed of light and from the speed of
all other massless particles. The difference typically depends on the
ratio of the gravitational potential to c2 and amounts to about 1 part in
106 for gravitational waves traveling in the gravitational field of our
galaxy. But this already amounts to a difference of arrival time of
several days between the gravitational-wave pulse and the neutrino or
photon pulse from, say, a supernova in our galaxy, and a greater
difference for extragalactic sources. Alternative theories also generally
predict different polarization properties for gravitational waves. This is
because general relativity contains only a spin 2 (tensor) field, while
other theories typically also incorporate scalar fields of spin 0 or vector
fields of spin 1. Therefore general relativity theory predicts only
quadrupole deformations of a gravitational-wave antenna, while other
theories predict monopole or dipole deformations as well.
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38 GRA VITA TION
SOURCES
Because of the weakness of the gravitational interaction, it seems
impossible to create on Earth a source of gravitational waves strong
enough to be sensed by any conceivable detector; this means that it is
impossible to carry out the gravitational analog of Hertz's experiment,
and we must depend on cosmic sources to excite detectors.
Astrophysical phenomena involving the coherent motions of large,
compact masses at relativistic speeds are the sources most likely to
emit measureable gravitational radiation. It is, however, just these
extreme phenomena that, if they can be observed, will allow us to test
relativistic gravitation in the strong-field, high-velocity regime. A view
held by many is that this is the most important reason to engage in the
search for gravitational radiation. The signatures of gravitational waves
may well be the most definitive means to establish the existence of
black holes and to study the interactions of compact objects of all kinds
with their surroundings. Thus, the detection of gravitational radiation
has become an important problem in relativistic astrophysics.
Estimates of the gravitational-wave spectrum incident on the Earth
suffer from our limited knowledge about massive compact objects in
the universe. If the precedent set by the development of radio, in-
frared, and x-ray astronomy serves as a guide, chances are excellent
that the first sources of gravitational waves to be detected will not have
been included in the present inventory of hypothesized sources.
Several classes of known astrophysical objects have been proposed as
emitters of gravitational radiation. A few of these are described below,
and estimates of their strength at the Earth are shown in Figures 6.2-6.4
in Chapter 6.
The collapse of stellar cores in Type II supernovae may produce
millisecond bursts of gravitational radiation provided there is sufficient
departure from spherical symmetry in the collapse. A supernova at the
center of our galaxy, if it released I part in a thousand of its total mass
into gravitational waves, would produce strains* of the order of 10-~8
at the Earth. Such a strain measurement is just barely within the
capabilities of currently operating detectors. The supernova rate in our
* A passing gravitational wave causes two freely falling masses to undergo relative
acceleration and a displacement proportional to their separation. Similarly, a strain is
induced in a solid body. Thus, the strength of a gravitational wave is customarily
measured by the displacement per unit separation, or strain h. This quality is also equal
to the perturbation in the space-time metric accompanying the wave.
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SEARCH FOR GRA VITA TIONAL WA VES: INTRODUCTION 39
galaxy is however only about 1 per 10 years. To gain event rates of a
few per year one must reach out to the Virgo cluster of galaxies with
strain sensitivities of 10-2~. Detectors having such a sensitivity would
be able to detect supernovae in our own galaxy in which only 10-9 of
the mass is converted to gravitational radiation.
Neutron stars in binary systems gradually spiral together owing to
the emission of gravitational radiation. The binary pulsar PSR 1913 + 16
is an example of such a system. In the final hours of its existence the
binary system will emit a strong chirp of gravitational radiation
sweeping from 10 Hz to 1 kHz, terminated by the tidal disruption of
one or both of the stars themselves. The event in PSR 1913 + 16 would
produce strain amplitudes of 10-~8 at the Earth, but we will have to
wait about 108 years for this to occur. By inferring a death rate for such
binary systems from pulsar observations, one can anticipate that
detectors having a strain sensitivity of 10-22, by reaching deeper into
the universe, would detect several events of this type per year.
The above examples illustrate impulsive or burst sources; some
periodic sources have also been posited. For these the anticipated
gravitational-wave strains are much smaller; and correspondingly any
practical search for them will most likely be restricted to our galaxy. A
compensation, however, is that the observations can be extended over
long integration times to improve strain sensitivity. Pulsars (rotating
neutron stars) would emit gravitational radiation as a result of any
deviations from axial symmetry; the radiation frequency can be at the
pulsar rotation frequency and at twice that frequency. The gravitational
wave's strain amplitude is proportional to the ellipticity of the source. If
the Crab or Vela pulsars had ellipticities as large as 10-s, they would
produce periodic strains at the Earth of 10-26 at 60 and 22 Hz, respec-
tively. These strain amplitudes could be within reach of some proposed
detectors after a month of integration (see Figure 6.3 in Chapter 61.
A final category of cosmic gravitational radiation is the stochastic
background- a gravitational-wave background noise detectable as a
correlated noise component in the output of a pair (or more) of
detectors. The sources of such a background would most likely reside
in the early universe, probably at epochs not accessible by electromag-
netic radiation. Since a gravitational-wave background has energy
density, experimental limits are usually quoted in terms of the
universe's closure density Pc.*
* Closure (or critical) density p<. is that density that results in sufficient gravitational
force eventually to stop the universal expansion. Currently, p<. ~ 10-29 g cm-3.
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40 GRAVITATION
This partial listing of hypothesized sources has focused primarily on
phenomena that might produce radiation at high frequencies, say 1 Hz
to 10 kHz the spectral band accessible to detectors on the ground. At
lower frequencies from 1 Hz to 1 Hz, space techniques and astro-
physical observations must be used to search for gravitational waves.
Probable sources include classical binary star systems and white-dwarf
binary systems in the 10-i to 10-s Hz region with strain amplitudes of
roughly 10-22 to 10-2° and bursts associated with the formation and
dynamics of massive black holes. This band contains the only astro-
physical sources of gravitational radiation whose properties are well
known the nearby binary stellar systems. One particularly favorable
source is ~ Boo, a nearby binary system that produces a strain
amplitude of around 10-2° at a period of 193 minutes. PSR 1913 + 16 is
a disappointing source for direct detection because of its large distance
from the Sun. The expected strain amplitude at multiples of the orbital
frequency (lo-4 Hz) is of the order of 10-23.
DETECTORS
The first gravitational-wave detectors intended to sense waves of
cosmic origin were demonstrated in the late 1960s. These detectors
were aluminum cylinders instrumented to detect excitations of the
bar's fundamental quadrupole mode by passing gravitational waves.
The bars, typically of 1-ton mass, were suspended in vacuum chambers
on shock mounts to reduce acoustic and seismic noise. They were
operated at room temperature and achieved sensitivities limited only
by thermal excitation of the quadrupole mode, a remarkably small
noise amplitude. Coincidence detection with two separated bars was
used to reduce accidental events. Experiments with such Weber bars
have continued in several research groups throughout the world.
Instrumentation improvements and cooling of the bars have helped to
achieve a recent major improvement in sensitivity.
The second main class of detectors, the laser interferometers, began
development later and is less mature. In these detectors the change in
propagation time of light traversing a gravitational wave is measured.
The polarization of quadrupole (Einstein tensor) waves causes changes
in the propagation time of light with opposite sign in orthogonal
directions transverse to the direction of gravitational-wave propaga-
tion. Laser-interferometer detectors exploit this polarization property
by measuring the time difference of light propagating along the orthog-
onal legs of an L-shaped interferometer whose mirrors are attached to
three freely suspended masses. The time differences are measured
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SEARCH FOR GRA VITA TIONAL WA VES: INTRODUCTION 41
interferometrically with high precision. The effect grows with the time
of interaction between the light and the gravitational wave, so
multipass cavities are used.
The laser detectors are currently less sensitive than bars, but a large
increase in sensitivity is expected if long baselines can be achieved. A
ground-based system with 5-km baselines is currently being proposed,
and a Sun-orbiting interferometer with 1 06-km baselines has been
. .
envlslonec ..
Bar and interferometric detectors have been built and operated only
on Earth, not in space. Earth-based operation carries with it the heavy
penalty of seismic noise and noise due to the gravitational effects of
nearby moving masses. isolation from seismic noise at kilohertz
frequencies is practical, but isolation becomes increasingly difficult at
lower frequencies, with the eventual barrier lying probably in the range
of 1-10 Hz. Therefore it is necessary to consider space-based detectors
in order to search at lower frequencies.
One kind of space-based gravitational-wave detector has been
achieved by tracking of interplanetary spacecraft. Here the gravitation-
al-wave experiment is only one of several scientific experiments
sharing the mission. Passing gravitational waves cause deviations in
both the spacecraft trajectory and the trajectory of the Earth; the
characteristic time signature of a gravitational wave in the two-way
tracking system helps to discriminate it from other effects in the
tracking data. Light travel time to interplanetary spacecraft is minutes
or hours, so the experiment is most sensitive to gravitational waves
with frequencies in the millihertz band.
Still another kind of detector is achieved by substituting a radio
pulsar for the spacecraft. Here one has only one-way rather than
two-way signals and is at the mercy of the stability of the pulsar pulse
period and pulse shape. Nevertheless pulsar timing is currently pro-
viding the best way of searching for possible gravitational waves in the
microhertz frequency range.
Representative terms from entire chapter:
gravitational radiation
