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6 Search for Gravitational Waves. Opportunities . LASER INTERFEROMETER DETECTOR WITH 5-KILOMETER BASELINE In the limit where random forces on the end masses dominate the antenna noise budget, the gravitational-wave amplitude sensitivity of a laser interferometer improves with arm length as h x LO (assuming that L is less than half the wavelength). Existing laser interferometric antennas (L c 40 m) are usually limited by random forces at low frequencies and, as laser power is increased, may become so at many frequencies of interest in the gravitational-wave search. The way to overcome this noise limit on the sensitivity of interferometric antennas is to increase the arm length. A current study for the National Science Foundation envisions an interferometer with arm lengths of 5 km, increasing the strain sensitivity by factors of 102 to 103 over that of current interferometer antennas. (See Figure 6.1.) A further increase in laser power by a factor of 103 or 104 (10 mW to 10 or 100 W) will be necessary to bring the gravitational-wave search using 5-km baseline interferometric antennas into the sensitivity regime required to inter- sect the present estimates of source strengths. Figures 6.2-6.4 show the sensitivity prospects for 5-km baseline interferometric antennas along with estimates of strains due to impulsive, periodic, and stochastic gravitational-wave sources. Detection of several source types is antic- ipated. 49
50 GRA VITA TION ~~- At ,., - ,r,,,%~. .... _ . , - . Vibration PI Itere \~ ..~,. Pendulum ~ \\~/ Suspenslon ~ / 5km "'a Multipase / Optical ,~,,~/ CavIty Photodetectors GO ~ ~,` ~SplitI Inertial Mase ...-~. .,^~., .~.~.,4 ~ ,..~..~` Add.,,,: Servo Controlled Inertial Assess a) Laser FIGURE 6.1 One half of a proposed long-baseline interferometric gravity-wave detec- tor. A passing gravitational wave changes the light travel times differently in the two interferometer arms, causing a tiny shift in the light intensities at the detectors. The current design calls for S-km vacuum pipes connecting the end stations. The signals from two such instruments, widely separated, are correlated to identify and remove ejects from local noise sources. Two stages of development are shown in the figures. The upper (solid) curve is the anticipated performance of current receiver designs in the large-baseline interferometric system. These receivers use modest extensions of the technology employed in the present proto- types. The lower (dashed) curve is the anticipated performance of second-generation receivers. Receivers of this sensitivity have been conceptually designed but not yet constructed and will not be effec- tively tested until a large-baseline facility is available. To emphasize the importance of increased sensitivity we note that, if extragalactic sources can be reached (e.g., decaying neutron star binary systems in the Virgo cluster), the event rate increases dramatically, scaling as h-3, which varies with arm length as L3 for interferometers limited by certain types of noise. It is expected that increases in laser power and seismic isolation will not require great technical advances or expense. The main expense of long-baseline interferometers is in the vacuum system and site con- -
SEARCH FOR GRAVITATIONAL WAVES: OPPORTUNITIES 51 PERIOD iday dhr dOOs is -14 16 48 s O -20 -22 24 1 ms p onetary IMPULSIVE ~ Spacecraft GRAVITATIONA L _ 7 . Long Baseline (5 km) ~ 10 Me: Interferometer Current ~ ·. J Intcrforomebr _ · ~ I | REV Limit \/~rs User Interferometer I ~~' In Space (106km) 1~ OOZE c,, 9` 9~/ _ ~ ,, _ SOURCES ~ 3GPC ~ _ Neutron Star Binary (distance) ~ ~, _ -- - Supernova in Galaxy (GW energy) _ Black Hole Formation (mass,distance) _ l 4 - 2 0 2 4 LOG FREQUENCY (Hz) FIGURE 6.2 Prospects for detecting impulsive gravitational waves. This figure indi- cates projected sensitivities of the various gravitational-wave detection schemes for impulsive or burst sources. The sensitivities are given in terms of the rms strain noise of the detectors in a frequency band equal to the reciprocal pulse length. In order to compare them with the strain amplitude of the hypothetical sources shown, the detector sensitivities should be degraded by a factor of [ln(TpR)]~2, where Tp is the pulse length and R the event rate, to account for pulse detection statistics. Binary-system decay events are quasi-periodic; the detection sensitivity for these events improves as the square root of the number of cycles n observed in the wave train. Two assumptions are made for the ground-based detectors. The solid curves show the sensitivities possible with modest extensions of current technology; the dashed curves assume some advanced development. For example, in the S-km interferometer it is assumed that initially the optical power will be 10 W with a light storage time of 1/2 (gravity-wave period); the dashed curve assumes that laser power is 100 W. mirror reflectivity is 0.9999, light is recycled from the output port back into the input port, and seismic noise will be eliminated forf > 10 Hz. The projected bar detector consists of an array of four resonant masses ranging in mass from 5 x 103 kg (840 Hz) to 42 x 103 kg (100 Hz). The dashed curve assumes a quantum-limited (QL) linear amplifier; the solid curve assumes an amplifier with 100 times more noise.
52 GRAVITATION -48 -20 o J -24 -26 -28 P E R I O D day ~ hr lOOs I I I I 1 1 PERIODIC GRAVI TATIONAL WAVE S Disco \,,> W UMa Stars \ ~ `~` Double White-Dwarf sSit°°" Binaries \WESge~ / -22 - Long Baseline (5 km) - Laser Interferometer Interferometer In Space (106 km) ~ PSR 1913+46 ~ \ hems I \Puls~ _ Untuned ~ Crab Tuned Bar Vel a ~ O ~ Detector ~ Neutron Star Sources `` Spinup ~- Binary Confusion Limit Tuned _ · Individual Binary Systems o Eccentric Rotators (c = 10~5 ) is ims - _4 -2 O LOG FREQU E NCY FIGURE 6.3 Prospects for detecting periodic gravitational waves. This figure is drawn for detector integration times of 106 seconds (sensitivity improves as 4. The only guaranteed sources the known fast binary star systems (e.g., ~ Boo)~ould be seen by the laser interferometer in solar orbit. In fact, the broad beams of this antenna would include many sources of measurable strength, and sensitivity may ultimately be limited by a background of weak sources. For increased sensitivity the ground-based antennas can be tuned to sources of known frequency, such as pulsars. The interferometer is tuned by synchronously exchanging the light beams between the two arms. A different resonant bar is needed for each source, but a single large cryostat could be used. The bar curve assumes Q = 107, T = 50 mK, and m = 5 x 103 kg. struction. Two antennas are envisioned to perform coincidence mea- surements, thus eliminating local-noise events. BAR DETECTOR SENSITIVITY AND BANDWIDTH There is currently a multifaceted development program in bar detectors, which promises to continue to improve the sensitivity and
SEARCH FOR GRA VITA TIONAL WA VES: OPPORTUNITIES 53 PERIOD 1 yr ~ day ~ hr ~ OO S -12 -14 -6 ' -18 -20 o -22 -24 -26 _ 6 - 4 \ lo, ms Pulsar Tim ing -r \ is ims 1 ~ I ~ I I I If Sun ~ Oscillations \ ~ \ ED rth \ ~ \ \ Planetary Spoc ecraft ( 2 or Mor; STOCHA S TIC GRAVITATIONAL WAVES 'to B i na' ' i A\ Radiate _ ~ W0~ \ ~4 s~K \\/ Laser Interferometer\ 3 ~ \ `, In Space (106 km) ~ Long Baseline (5 km ) \ Interferometer \~ I , I I \ ~ ~ -2 0 LOG FREQUENCY (Hz ) 2 4 FIGURE 6.4 Prospects for detecting stochastic gravitational waves. The detector sensitivities in the figure assume that cross correlation of two antennas is carried out for an integration time of 106 seconds and the detection bandwidths are equal to the frequency, except for the dashed long-baseline curve where the bandwidth is narrowed by a factor of 10 owing to resonant interchange of light between the interferometer arms. The sensitivity improves as the product of the bandwidth and integration time to the 1/4 power. The straight lines in the figure are the strain spectral densities of a universe filled with the indicated fraction of the closure density in gravitational waves on the assumption that all the gravitational radiation power is concentrated in a bandwidth equal to the frequency. This figure also indicates those sources of noise that are expected to limit the sensitivity of the interferometric detectors.
54 GRAVITATION bandwidth of searches for kilohertz gravitational waves. The next few years should see coincidence experiments carried out at a strain sensitivity better than 10-~8, at frequencies near 1 kHz, with band- widths in the range 10-100 Hz. Within a decade, further improvement of strain sensitivity by 2 to 3 orders of magnitude should be achievable, through further cryogenic cooling and use of advanced transducers and amplifiers. Techniques are also under study to increase the bandwidth of bar detectors; the use of cascaded, strongly coupled mechanical resonators can in principle give both high sensitivity and wide bandwidth in a single bar. It is estimated that bandwidths of several hundred hertz or more can be achieved. Development of low-noise amplifiers that can be well coupled to transducers is important, notably superconducting quantum interfer- ence devices (SQUIDs). In the past, the gravitational-wave community has mostly depended on outsiders to develop improved SQUIDs; continued support for SQUID development is an important element in the bar detector program. Within the next decade, operational bars could approach the naive quantum limit. Techniques for passing beyond the limit will be neces- sary then, and current ideas merit study. Arrays of bars also provide a path to greater sensitivity and wide bandwidth. The strain sensitivity of an array increases as the square root of the number of bars; bandwidth can be increased by tuning different bars to different frequenciesa "xylophone" for gravitational waves. OBSERVATIONS WITH BAR DETECTORS At current sensitivity levels, the event rate for burst sources of gravitational waves is thought to be only about 1 per 10 years or worse. Therefore, detector development and construction should take prece- dence over major observing programs at present. However, some significant observing runs are desirable for two reasons: to keep development attuned to the actual problems that occur in observing, and especially to understand any noise or interference that appears; and not to miss a chance to see sources should the theoretical best estimates be quite wrong. We again emphasize that nature has pro- vided stronger sources than theorists predicted in the electromagnetic radiation bands. Coincidence observations should be planned for every order-of-magnitude enhancement in strain sensitivity.
SEARCH FOR GRA VITATIONAL WAVES: OPPORTUNITIES 55 PULSAR SEARCHES The discovery of a binary pulsar in a clean system, and also the later discovery of several pulsars with periods in the millisecond range, have been of great importance for the study of gravitational radiation. Further progress could come with more such discoveries; for example, the availability of several pulsars with the short period and excellent frequency stability of PSR 1937+214 would in principle allow, by cross-correlation, a sensitive search for gravitational waves of micro- hertz frequency passing through the solar system. A deep radio search for fast pulsars should have high priority. Such a search will require a substantial investment in data processing, both on-line and offline. Further searches for millisecond periods among x-ray pulsars should also be carried out, because accreting neutron stars with rotational periods in the millisecond range could be significant periodic sources of gravitational waves. SPACECRAFT TRACKING Accurate tracking of interplanetary spacecraft offers, at present, our only opportunity to search for gravitational radiation in the frequency range 10-' to 10-4 Hz. The long travel time of interplanetary signals and the inherent precision of time measurement account for the good sensitivity of this technique to low-frequency waves. With a single spacecraft the method is most sensitive to impulsive gravitational waves, but the use of two spacecraft makes possible a search for a stochastic background as well. Sensitivity estimates are shown in Figures 6.2 and 6.4. Preparations are currently being made to search for gravitational waves using the Galileo mission to Jupiter and the Ulysses (formerly International Solar Polar) spacecraft. About 40 days of observations are planned to start in October 1987 when both spacecraft are near Jupiter. For Galileo, the National Aeronautics and Space Administra- tion has arranged for X-band tracking on the uplink and S- and X-band frequencies on the downlink. The expected system sensitivity to impulsive radiation with frequency components in the lo-4- to 10-~- Hz range is h = 3 X 10-'5 a factor of 10 improvement over past spacecraft. To.improve substantially the sensitivity for gravitational- wave detection beyond the level expected for Galileo, two main types of noise source must be addressed. Fluctuations in the interplanetary and ionospheric electron densities can be measured and removed by
56 GRA VI TA TION using two tracking frequencies on the uplink and the downlink. The effects of variable tropospheric delay can be reduced by atmospheric monitors or, better yet, effectively eliminated by using signals from a high-stability clock on board the spacecraft. Clearly, it is important to consider these needs early in the planning stage of a spacecraft mission if sensitivity to gravitational waves is to be optimized. The impacts on mission configuration and cost are relatively small. SPACE INTERFEROMETERS Any earthbound gravitational-wave detector is subject to seismic noise, which in practice imposes a lower cutoff on the detectable gravitational-wave frequency, in the neighborhood of 1 Hz. For high sensitivity at lower frequencies (10-6 to 1 Hz) a laser interferometer in space is an attractive possibility. Separate spacecraft would carry the three interferometer end stations, as shown in Figure 6.5. Preliminary studies envision the three spacecraft orbiting in formation around the Sun, with 1-year periods and with separations of about 106 km. Lasers of 1-mW power in each station would communicate using 50-cm- diameter mirrors, with the end station lasers phase locked to the signals received from the central station. The end mirrors and central beam splitter for the interferometer are mounted on masses that are pro- tected from spurious forces due to the solar wind and solar radiation pressure. For this system the anticipated sensitivity is h ~ 10-22 for narrow-band periodic signals and 10-~9 to 10-2° for pulses at frequen- cies of 10-4 to 10-i Hz. The sensitivity degrades outside this range but is still useful from about 10-6 to 1 Hz, as seen in Figure 6.3. This sensitivity would allow detection of the known nearby binary system ~ Boo, if it is radiating as predicted by general relativity. This is also the frequency range for detecting broad spectral features due to the superimposed radiation from many white-dwarf binary systems and from classical binary systems. The expected energy density in gravi- tational waves from such sources is about 10-8 Pc (see Figure 6.41. The conjectured massive black holes would also radiate in the millihertz band. Detectable pulses of gravitational radiation are possible from pregalactic or early galactic formation of massive black holes, from coalescence of such objects, or from their falling into other massive black holes that may exist at the centers of galaxies. Observation of such events would have far-reaching consequences for gravitation, astrophysics, and cosmology. More advanced studies of a Sun-orbiting laser interferometer system
SEARCH FOR GRAVITATIONAL WAVES: OPPORTUNITIES 57 \ ~ _ EN EARTH ANTENNA A END SPACECRAFT (2) :> toe km Protective Shield \<\.J Beam As, ~\ Splitter _ ~~ / ' CENTRAL SPACECR AFT Detector Optical Inertiol Cavity Moss ~ meter FIGURE 6.5 A concept for a gravity-wave detector in space. The basic principles are the same as for the 5-km ground-based detector (Figure 6.1). However, the longer baseline and freedom from seismic noise permit operation at low frequencies 1 Hz to 10-6 Hz. Passive optical cavities would be used for precise frequency control, and the mirror-carrying masses would be shielded from solar-wind buffeting. are needed to evaluate the technical and cost aspects of a possible . . space mission. EVENT RATES AND SOURCE CALCULATIONS Theoretical activity in modeling possible sources, and in attempting to determine their frequency of occurrence in the universe, is key to an effective search for gravitational waves. The main uncertainties in theoretical estimates of gravitational-wave source properties are not due to physical understanding, which we think is good, or computa- tional ability, which is already considerable and steadily improving, but to our uncertainties about the astrophysical boundary conditions. Easy answers are not to be expected, and the best support for the experi- mental program comes with the investigation of all plausible sources and the best possible estimates of their observable properties.
58 GRAVITATION COMPUTATION The computation requirements for operating gravitational-wave de- tectors have not been studied in detail. In one mode of operation, namely in searches for narrow-band periodic sources of unknown frequency and celestial position, the computational needs are likely to be large but not impossible. The difficulty of the data-reduction problem in this mode of operation arises because it is necessary to search simultaneously in three parameters (frequency, right ascension, and declinations. Therefore, as multidetector observations get under way, appropriate computing facilities will be needed. Deep radio pulsar searches at millisecond periods, and searches for millisecond periodicities in known x-ray sources, also require substan- tial computational power. Computational needs for gravitational-wave source calculations are discussed in Chapter 9 in the section on Computation.
