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OCR for page 42
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Gravitational Waves:
Highlights
BINARY PULSAR
General relativity predicts that a binary stellar system will lose
energy in the form of gravitational waves, so that the orbital period will
decrease as the two stars spiral together. Although many binary
systems are known, only for the binary pulsar system PSR 1913 + 16
can the motion of the system be measured accurately enough to test
this prediction. Moreover, most stellar systems do not provide clean
tests of gravitational physics for point masses, because tidal interac-
tions, changes of stellar mass distribution, and mass exchange or mass
loss cause unpredictable and often large changes in the orbit. Fortu-
nately the binary pulsar does seem to be clean according to available
observational evidence (see section on Systems of Compact Stars in
Chapter 3~.
Observations of the orbit of the binary pulsar over the 10 years since
its discovery have shown that the orbital period is decreasing at a
fractional rate of (2.71 + 0.10) x 10-9 per year (see Figure 5.11.
General relativity predicts an orbital decay rate due to gravitational-
wave emission of (2.715 + 0.002) x 10-9 per year. This agreement is a
most impressive and beautiful confirmation of the theory and provides
strong evidence for the existence of gravitational waves. Still, one
cannot completely rule out the unlikely possibility that tidal and/or
mass exchange effects conspire to just compensate for an error in the
42
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SEARCH FOR GRA VI TA TIONAL WA VES: HIGHLIGHTS 43
DECAY OF Bl NARY PULSAR ORBIT
- 0.2
J
0.'
0.0
~ —~
~ —2
A)
3
~ _4
m
1 ~
t
_ PSR 1943~16
_`
-
-
1976 1978 4980 4982 19"
DATE
FIGURE 5.1 Evidence that gravitational radiation is correctly predicted by general
relativity. The predicted change in orbit phase due to gravitational radiation by the
binary system is shown by the solid line; dots are the observations' including errors.
Residuals are shown with the expanded scale on the upper graph. The orbital motion
(period ~8 hours) modulates the phase and frequency of the pulsar. By following the
pulsar phase for many years, the orbit is measured with exquisite accuracy.
rate predicted by general relativity. Independent evidence that the
pulsar's companion star is also a collapsed star would settle this issue.
In any case, these results already place stringent restrictions on
alternative theories of gravity; in many theories, the decay rate of
binary systems containing neutron stars or black holes is much greater
than in general relativity theory owing to dipole gravitational radiation.
In general relativity, monopole and dipole radiation are absolutely
forbidden, and the lowest allowed mode is quadrupole radiation. The
orbital decay observed in the binary pulsar is completely consistent
with the quadrupole formula of general relativity.
BAR DETECTORS
Bar detectors have undergone 20 years of development, resulting in
improvement of strain sensitivity by more than 4 orders of magnitude
(8 orders of magnitude in energy-flux sensitivity). Major improvements
achieved in the past decade include the following: cryogenic cooling;
increase of the Q of bar materials to values approaching 108 in
aluminum and exceeding 109 in sapphire and silicon monocrystals;
improvements in several transducer types including inductive, capac-
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44 GRAVITATION
itive, and resonant cavities; and improvements in coupling schemes
and amplifiers. Vigorous work is continuing on all these critical and
generally useful technologies.
Recently a bar antenna (see Figure 5.2) has been operated for several
months at pulse-strain sensitivities of about 10-~8 in a narrow-band
mode near 1 kHz. No gravitational-wave signals were identified, but
the thermal noise limit for the 4-K bar was achieved. Operation in
coincidence of two or more bar detectors, distant from one another,
permits much better detection capability by eliminating noise and inter-
ference events generated locally. Such coincidence observations have
only been carried out over short time periods with recent detectors,
although they were made over long intervals with early bar detectors.
No fundamental barriers are apparent to further improvements in the
sensitivity of bar detectors by several orders of magnitude. Moreover,
several current instrumentation developments could significantly ex-
tend the bandwidth of bar detectors. When bar detectors reach a strain
sensitivity of about 10-2°, they will approach the so-called naive
quantum limit. This means that gravitational-wave excitations of the
fundamental mode of an initially unexcited bar will amount to about
one quantum of acoustic oscillation, and issues of quantum measure-
ment of the bar's state will become crucial. Techniques are now known
which in principle allow one to measure an arbitrarily small fraction of
a quantum of excitation. These are known as quantum-nondemolition
or backaction-evasion techniques, and work is now under way to
develop them in practice. When other sources of noise are reduced so
much that bars are at the naive quantum limit, these techniques will be
needed.
INTERFEROMETRIC DETECTORS
Laboratory-scale interferometric antennas with arm lengths extend-
ing from 1.5 to 40 m are now in operation at several laboratories around
the world. Two of these instruments have achieved displacement noise
spectral densities of 10- cm HZ-/2 in the 1- to 10-kHz frequency
range. The corresponding root-mean-square strain sensitivity over the
30- and 40-m baselines is 10-~7 for a 1-kHz bandwidth.* One of these
* Strain spectral density in(f) [Hz-"2] is used to characterize broadband radiation and
detectors with wideband frequency response. For signals of finite bandwidth B. the strain
is h = h(f)Bi/2. For example, a bar detector with h = 10-~8 has sensitivity in(f) = 3 x
10-20 HZ-/2 to a 1o-3-s impulsive signal.
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SEARCH FOR GRA VI TA TIONA ~ WA VES: HIGHLIGHTS 45
FIGURE 5.2 A bar-type gravity-wave detector. The S000-kg aluminum bar is shown
end-on with its transducer mount and lead vibration filters attached. Also shown are the
suspending wires, the cryostats and the towers containing seismic isolation filters. This
bar has been successfully operated at 4 K.
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46 GRA VITA TION
detectors uses about 200 mW of laser power and 100 beam passes in
each arm, corresponding to a light storage time of 10 As. The other
detector uses several milliwatts of laser power and high-Q Fabry-Perot
cavities to achieve a storage time of about 1 ms. At high signal
frequencies the sensitivity of interferometric detectors is limited by the
available laser power.
The principal technical efforts to improve detector performance are
in two areas. The first is to enhance the displacement sensitivity by
increasing the laser power in the interferometer while controlling the
effects of scattered light. The power can be increased by using more
powerful lasers and/or by recycling the light from the output port of the
interferometer back to the input. The second major effort is to reduce
the influence of random forces on the interferometer masses. The
development of improved suspensions to reduce thermal noise and
coupling to external acoustic and seismic noise is actively being
pursued and is required in order to achieve adequate detector perform-
ance at low frequencies.
An important feature of interferometer antennas is that they are
inherently broadband and can detect and measure the wave forms of all
classes of sources: impulsive, periodic (even if the period is not known
in advance), and the stochastic background. However, an interesting
new concept would enable the antenna to be tuned to a possible source
of known period and phase, for example a fast pulsar. The light beams
in the two arms would be exchanged in synchronism with the source,
thus accumulating signal while averaging out noise.
PULSAR TIMING AND MILLISECOND PULSARS
The observed slowing-down rates of a number of radio pulsars are
stable enough to afford useful upper limits on the amplitudes of
low-freque~cy gravitational waves. Gravitational waves would shake
the Earth or the pulsar and cause deviations in the observed uniformity
of the period drift rate.
Until 1982 the fastest known pulsar was the Crab nebula pulsar with
a period of 33 ms. Then a radio pulsar, known as PSR 1937 + 214, with
a period of only 1.6 ms (a rotational frequency of 642 Hz) was
discovered during investigation of a known peculiar radio source. The
slowing-down rate for this object has unprecedented stability for a
pulsar; indeed, over time intervals longer than a few months it seems
to have as stable a drift rate as any known clock, natural or man-made.
The best-known limits on gravitational waves in the microhertz fre-
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SEARCH FOR GRA VI TA TIONA ~ WA VES: HIGHLIGHTS 47
quency range come from observations of this pulsar; already it has
been shown that waves in this band cannot contribute more than 5 x
10-4 of the critical mass density of the universe (see Figure 6.4 in
Chapter 61.
SOURCES OF GRAVITATIONAL WAVE~RECENT
DEVELOPMENTS
Earlier we used nonspherical collapse of a stellar core as one
example of an impulsive source of gravitational waves. However,
current theoretical models of Type II supernovae manage to agree
roughly with the observations by assuming that the core is spherically
symmetric during collapse. Thus there is no good reason to believe that
Type II supernovae are strong sources of gravitational waves. Type I
supernovae are less well understood, and a consensus model does not
exist, although many believe that short-period binary systems are
involved. Some models of Type I events predict strong gravity-wave
emission; others do not. For instance, one model posits a close pair of
white-dwarf stars as the presupernova object; mass accretion causes
one star to spin up and eventually collapse, perhaps to a neutron star.
Such a binary system would be a strong source of gravitational
radiation at frequencies below 1 Hz; and the stellar collapse would be
highly nonspherical, producing a strong burst of gravitational waves
with frequencies around 1 kHz. The properties of collapsing, rotating
stellar cores are now the subject of active investigation, often involving
large-scale numerical work.
Discovery of the binary pulsar, which probably consists of two
neutron stars, emphasized the possibility that decaying compact/
compact binary systems are strong sources. Discovery of millisecond
pulsars showed that rapidly rotating neutron stars do exist. If born
rapidly rotating, these cores could have been moderately strong
sources of gravitational-wave bursts. If, on the other hand, they owe
their fast rotation to subsequent spinup by mass exchange with a close
companion, they could have been sources of periodic gravitational
radiation. (This model assumes that they have been spun up above the
threshold for secular instability for gravitational-wave emission.) It
should be noted that only a few years ago, before these discoveries,
most theorists saw little hope that neutron stars could be sources of
detectable gravitational waves. Again nature has outrun our imagina-
tions, emphasizing the need for sensitive measurements.
More conjectural sources might exist at millihertz and microhertz
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48 GRAVITATION
frequencies. These include collisions of massive or supermassive black
holes, which may exist in galactic nuclei, and even primordial gravi-
tational waves from an early inflationary era of the universe's expan-
sion, or waves emitted by decaying cosmic strings, which, according to
certain grand unified theories, would have been created by phase
transitions in the early universe. Perhaps detection of their gravita-
tional waves will be our best handle on these intriguing processes.
Representative terms from entire chapter:
bar detectors
