Gravitational Radiation and Its Dete~t ion' ,~

G. PAPINI I)c,l)(rrlttrc,trr c!f'Plr?.sic..s otrtl Aslrotrotrr?.. Utril.rr.sily o f ' S t r . s A r r ~ c ~ l ~ c ~ ~ ~ ~ ( ~ ~ ~ . Regi~rcc Crr t~rpr~s , Rcgi~rrr. Soskr r~che~~~t r t c S4S OA2

Received November 23, 1973

A review is presented of the theoretical and experimental aspects of the field of gravi- tational radiation. This article, aimed particularly at showing that the problem of gravitational radiation can be tackled experimentally in various meaningful ways, in- cludes, for completeness, a short theoretical introduction and a discussion of possible radiation sources. Several detection schemes are discussed and the experimental situation is reviewed, with attention to the questions it raises.

On passe en revue les aspects thCoriques et exptrimentaux du champ de rayonnement gravitationnel. L'article q ~ ~ i vise particulitrement ii montrer que le problkme du rayon- nenient gravitationnel peut Ctre abordt exptrimentalement de plusieurs fasons significa- t i ve~ , inclut aussi, pour Stre complet, une courte introduction thkorique et une discussion des sources possibles rayonnement. On discute plusieurs mtthodes de dttection et on examine la situation experinlentale en attirant l'attention sur les questions qu'elle soulkve. [Traduit par le journal]

Can. J . Phys..52.880(1974)

1. Introduction

T h e physics of gravity has been characterized in the first half of this century by very important theoretical developments, but scanty experimental confirnlations. Thanks t o the refinement of old experimental t e c h n i q ~ ~ e s a n d the introduction of new ones, this situation is rapidly changing. New and old q ~ ~ e s t i o n s now are experimentally answerable, o r may be expected to become s o in the near f i~ ture .

With gravity, the problem of detecting gravi- tational radiation has recently become one of the niost pressing a n d interesting questions of modern physics. Its successful solution could, in fact, open a new window o n the universe a n d provide information a b o u t phenomena no t otherwise observable.

Regrettably, the pioneering efforts of Professor Weber of the University of Maryland have no t yet been followed by tha t intense a n d wide- - - 3 p Y e a d acti<i'tj; 'that the relevance a n d the challenges offered by this new research field should spur . Yet the problem is exquisitely experimental a n d more, it can be meaningfully tackled in a variety of ways. T h a t this is indeed the case will be shown, it is hoped, in this review.

2. Sources of Gravitational Radiation

2.1 A Brief Theoretical Introduction It became apparent almost immediately after

the discovery of the general theory of relativity tha t gravitational fields can propagate with the speed of light a n d that waves can carry energy (Einstein 1916, 191 8). This can be seen immedi- ately by comparing the wave e q ~ ~ a t i o n for electromagnetic fields with the 'weak field' form of the Einstein equat ions (Landau a n d Lifshitz 1962; Weber 196 1 ; Misner et al. 1973)3

where

a n d

[2.1.3] $,,"," = 0

In [2.1.2], kPv a r e small quantities of the first- o rder representing the deviation of the actual geometry of spacetime f rom that of tlie special theory of relativity

Alternatively, the quantities hPv may be inter-

'This work was supported in part by the National Research Council of Canada.

2The survey of the literature for the theoretical part of this review was concluded in July 1973; that for the experimental part in October 1973.

-

3Greek indices vary from 0 to 3; Latin indices from 1 to 3. Here, and in what follows, summation over repeated indices is understood. The Minkowski metric is repre- sented by q,, = (- 1, 1, 1, 1). A comma followed by an index means ordinary differentiation.

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PAPINI: GRAVITATIONAL RADIATION 881

preted as gravitational potentials. T," is the energy-momentum tensor describing the source of the gravitational field and G is the Newtonian gravitational constant.

As in electromagnetism, [2.1.1] can be immediately integrated to give

where the subscript t - (Rlc) means that T,," is to be taken at the time t - (Rlc).

The simplest of all solutions to [2.1 .I], with vanishing right hand side, is in the form of plane waves

where $," represents the amplitude and k, is the wave vector satisfying

By using [2.1.5] and determining the reference frame uniquely, it is possible t o reduce the number of independent components of h,, to two. Thus, as plane electromagnetic waves admit two polarization modes, so d o plane gravitational waves. Any given wave can, therefore, be resolved into two linearly polarized components or into two circularly polarized components.

Other correspondences can be established between electromagnetic and gravitational quan- tities. While, for instance, / I , , plays the role of the electromagnetic potential A, as previously mentioned, the role of the gauge invariant electromagnetic tensor

plete theory as well, where /I,, is replaced by g,, and [2.1.6] by the complete expression for the Riemann tensor. It should be noticed, however, that while F,, depends on the first derivatives of the potential, only the second derivatives of the potential appear in RpVup. The Riemann curvature tensor does, therefore, describe the rate of change of the gravitational force at the field point. Accordingly, gravita- tional waves can be interpreted as a propagating field of relative (or tidal) forces.

A few sources of physical interest can be handled within the framework of the linearized theory. For slowly changing sources, for in- stance, a << h, where a represents the order of magnitude of the source dimensions and h the wavelength of the radiation emitted. The ex- pression for the field at large distances can then be simplified. From [2.1.4], one obtains in fact

where r is the distance from the origin chosen anywhere inside the source. Use of the equation

TPV,, = 0

that can be derived from [2.1.1] and [2.1.3], allows the calculation of the space components of JI,'

where p is the mass density of the source. The energy loss of the system per unit time can also be calculated, and yields

F," = A,, , - A",, [2.1.7] -

is played in the weak field form of Einstein's th;or; by the linearized Riemann tensor where P.1.61 _R,vu, - +(h,,,,", + h"u,,p - - -am -.. I , - - _

- hvp,,u - h,.,"p)

Expression [2.1.6] is, in fact, invariant in form with respect to the transformations

induced by the coordinate transformation

where cP is smooth enough to keep h,, small. This correspondence is not, in general, limited to the linearized theory but exists in the com-

is the mass quadrupole moment (Landau and Lifshitz 1962, 104). Strictly speaking, the derivation of [2.1.7] from [2.1.1] is valid only for systems which are not bound by gravitation. However, as shown by Peters (1964), the final result applies also t o the case of gravitational interactions. Typical sources which can be termed slowly changing and weak (a >> 2GM/c2 - Schwarzschild radius) and to which [2.1.7] applies, are, for instance, binary star systems and the solar system.

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882 C A N . J . PHYS. VOL. 5 2 , 1974

TABLE I . Binary stars1 - - - - - -- . -

- - - -- --

Distance from - dEldt Q, at Earth Star T,,, in days ~ ~ 7 1 /Mo tll2/Mm Earth in cm in ergis in erg/cmz s

UV Leo 0.60 1.36 1.25 2.1 x 1020 1.8 x lo3' 3 .5 x 10-l2 V Pup 1.45 1.66 9 .8 1.2 x lo2' 4 x lo3' 2 .3 x lo-'' i Boo 0.268 1.35 0.68 3 .8 x l0 l9 1 .9 x 1030 1 . 1 x lo-1o YY Eri 0.321 0.76 0.50 1 .3 x 1020 2.6 x lo29 1 .3 x 10-lZ SW Lac 0.321 0.97 0.83 2.3 x 1020 I .1 x lo30 1.7 x r( Cas 480 yr 0 94 0.58 1.82 x 1019 5 .6 x lO1O 1.4 x 5 Boo 149.95 yr 0.85 0.75 2.06 x l0l9 3 .6 x 10l2 6.7 x Sir~us 49.94 yr 2.28 0 98 8.02 x 1 . 1 x l0l5 1.3 x Fu46 13.12yr 0.31 0.25 2.00 x 10l9 3 .6 x l0l4 7.1 x lo-z6 B L Y ~ 12.925 19.48 9.74 1.01 x lo2] 4.9 x 1oZ8 3.8 x lo-" UWCMa 4.393 40.0 31 .O 4.53 x lo2 ' 4.9 x lo31 1.9 x 10-l3 p Per 2.867 4.70 0.94 9.25 x 10" 1.4 x lo2& 1.3 x 10-l3 WUMa 0.33 0.76 0.57 3.39 x 1020 4.7 x lo2g 3.2 x 10-l3 WZ Sge 81 min 0 .6 0.03 3 x 1020 3 .5 x lo2' 3 x 11-l3

- - - - - - -- -- 'Br~lg~nsh~l, V. H. 1966. Sov. Phys.-Usp. 8, 513, Rufin~, R. 'ind Wheeler, J A.. 1971. ESRO SP-52.

If the source is s t rong ( a - 2GM/c2), but h >> a , [2.1.7] can still be applied, but the mass quadrupole must be calculated differently. It is, in fact, defined as the quadrupole moment of the source's Newtonian potential in the region 2GM/c2 << r << h ( lpser 1971). Its calc~l lat ion can be very involved a s it req~lires the use of the complete theory. Calculations have been per- formed for pulsars (Ipser 1971) and for non- radially pulsating relativistic stars (Thorne and Campolat taro 1967, 1968; Price a n d T h o r n e 1969; Thorne 1969a,b; Carnpolat taro and Thorne 1970).

Most other sources, rapidly changing either weak o r s t rong, require, in general, approxima- tions that start froin the complete theory. Falling in this class are the p r o b l e n ~ s o f a snlall mass passing a larger o n e in a n ~ l n b o u n d trajectory with emission of gravitational brenis- strahlung (Peters 1970) a n d of two masses nongravitationally bound and with relativistic velocities (Peters 1972). T h e gravitational col-

.- , .~ lapse -o f - slightly nonspherical objects (de la

- ..-* _ r , .

C r ~ l z ef a/ . 197b), iadiat ion emitted in the fall of small objects down a black hole (Zerilli 1970; Davis et a / . 1971 ; Ruffini 1973), and vibrating black holes (Press 1971) have also been in- vestigated. S o m e of these problems will be considered in more detail later.

A more n~a themat ica l and rigorous discussion of the problem of gravitational radiation within the framework of the general theory o f relativity can be f o ~ l n d in a recent book by Zakharov (1973).

2.2 Bitlary S t a r Systetlls A s previously mentioned, binary s tar systems

a re weak, slowly changing sources whose energy loss can be calculated from [2.1.7]. All known binary stars have, in fact, periods longer than o n e hour and have very weak internal fields. Detailed analyses of these systenis can be found in the l i terat~lre (Peters and Mathews 1963; Zeldovich a n d Novikov 1971, 3 1.13). T h e pre- dicted energy loss is given by the relation

where a is the senl i -~najor axis, e the eccentricity of the orbi t , t n l a n d ti?? the s tar masses, and

T h e filndamental f req~lency of the radiation is twice the orbital frequency and has harlnonics LIP t o order 10 depending on the value of e. It follows from [2.2.1] a n d [2.2.2] that, a m o n g binary systems, the most promising sources of gravitational radiation a re those stars o f large mass a n d short period.

Calculations o f the radiation ou tpu t o f sorne binary systems have been performed by Brag- inskii (1966) a n d by Ruffini and Wheeler (1971) a n d a re collected in Table 1.

F o r a comparison, a hypothetical binary coluposed of two neutron stars o r black holes 10 knl apar t , tn , = t11, = M o , at a distance of 103 pc froni ear th, with a period of 0.39 n u ,

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PAPINI: GRAVITATIONAL RADIATION 883

radiates at the rate of 3.25 x erg/s, while as well as collisions, capture among fragments, @ - 2.7 x l o L 2 erg/cm2 s (Misner et al. 1973). and final fragment recombination to form a

Finally, Mironovskii (1965) has estimated the neutron star may contribute substantial amounts total flux at earth generated by all binary of gravitational radiation. This would be in the systems in the Galaxy with period greater or form of an initial major pulse followed by equal to one hour to amount to - lo-' erg/cm2 s, several smaller pulses intervaled by periodic the distant binaries being the major contributors. The corresponding spectrum is peaked in the neighborhood of a wave period of 4 hours.

Because of the back reaction of the waves (Burke 1971 ; Chandrasekhar and Esposito 1970; Thorne 1969b), a binary system is damped. In particular, its components tend to approach each other with a change in angular velocity (Peters 1964). Thus, one could test, in principle, the existence of gravitational radiation by

radiation. The spectrum of the major pulse would be broadband, with a critical upper frequency o - (112~) (rcGp)-'I2, where p is the density of matter in the final stages of collapse. Typical values of the critical frequency could therefore range from lo3 to lo4 Hz, while the energy emitted per unit frequency could be as high as 5 x lo5' erg/Hz below the critical frequency, with a total output of 5 x lo5' erg. The entire process would last only a few seconds.

observing changes in the period of rotation of For later use, it is also convenient to give the binary systems over long periods of time. In r.m.s. value of the dimensionless amplitude of practice, however, it woi~ld not be easy from the wave for a burst of frequency 103 Hz and earth to discriminate between changes in period energy Mc2 (Press and Thorne 1972) due to the emission of gravitational radiation and those due to other loss mechanisms. For example, mass transfer from one star to the (I7) - 0.5 lo-' other and mass loss can also affect the rotation of short period binaries strongly (Struve 1950). The combination of gravitational radiation losses and the mass transfer induced bv the ensuing - decrease in scale of the system may very well be responsible for the fast evolution of a 10 h period binary to a short period one (Faulkner 1971 ; Vila 1971 ; Paczynski 1967). Radiation reaction effects integrated over long periods of time may therefore have very significant astro- physical consequences. These effects, which can also be studied for relativistic objects like neutron stars (Thorne and Campolattaro 1967, 1968; Price and Thorne 1969; Thorne 1969a), show the inner consistency of the theory of radiation of gravitational waves.

2.3 Birtlz of Neutron Stars In the gravitational collapse of a star which is

- - rotating, and thus -possesses a quadrupole moment, gravitational radiation may be emitted. The quadrupole moment may, in fact change in time during the collapse for a variety of reasons. As pointed out by Ruffini and Wheeler (1971), a rotating star with a dense core may collapse to a pancake neutron star which may, in turn, release a fraction of its binding energy- between 0.01 and 0.3 M o (Hartle and Thorne 1968)-by fragmentation. In addition, the periodic motion of fragment around fragment,

If the end product of the collapse is a pulsating neutron star, more gravitational radiation is produced (Thorne 1969a) over a period of a few days (Zee and Wheeler 1966).

Finally, if in its first few seconds of life, a neutron star had the shape of a nonaxisym- metrical Jacobi ellipsoid (Ruffini and Wheeler 1971), then the radiation would be mono- chromatic, in the kHz range, and very powerful, about lo5 ' erg/s (Chandrasekhar 1970a,b,c). This would be the case if the star had a large enough angular momentum and if the adiabatic exponent characterizing the stiffness of the equation of state were larger than 2.2. Whether the value of 2.2 car! be exceeded at all, and, if so, in which part of the star, depends very much on the detailed knowledge of the physics of a neutron star and on the astrophysicist's ability to calculate a realistic equation of state (Cameron 1970). It is therefore unclear, as yet, whether a neutron star can really achieve an 'extreme' configuration.

Once the neutron star has been born, radiation is produced by rotation, as shown in the next section.

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884 C A N . J . PHYS. VOL. 5 2 . 1971

2.4 Pulsars It is well known that in the general theory of

relativity bodies shaped as ellipsoids of revolu- tion do not radiate gravitational waves. How- ever, in the case of a pulsar, even a very small difference between the longer and shorter semi- axes in the equatorial plane may be responsible for strong emission of gravitational radiation. The deviation from perfect rotational symnietry could be produced by very high rotational velocities, just before the star breaks LIP, or, niore probably, by the presence of very strong magnetic fields, if the rotation axis does not coincide with the direction of the magnetic moment. In tlie latter case, in fact, a dipole magnetic field would tend to flatten the star in the region of the magnetic poles, much the same as in the case of rotation, but the flattening would be asymmetric with respect to the axis of rotation. Tlie corresponding time dependence in the ql~adrupole moment results in emission of gravitational radiation.

Estimates of the rate of emission of radiation may be based on relation [2.1.7]. For a homo- geneous oblate spheroid of moment of inertia I, period T, arid ellipticity E, one finds

It is, therefore, clear that among pi~lsars the most promising emitters of grav~tational radia- tion are those stars with the shortest period of rotation, markedly NP 0532. The Crab pi~lsar has in fact a period T = 0.033 s. As a lower limit for E, one may take tlie value

calci~lated by Ferraro (1954) for a l1q111d star of nniform density with a uniform magnetic field inside and a dipole field outside. For the 1.4 Mo neutron star model of Hartle and Thorne

-. . -411Y68), tlie s'ii; h d i u s is a - 106 cm and I - 1035 g cni2, which gives E - 10- ' . Tlie cor- responding value of the flux at earth is 4) 3 2.8 x erg/cm2 s. On the other hand, the maxi~iium value of E conipatible with observa- tion is E - or the star would slow down more than necessary, with (1) 5 2.8 x lo-' erg/cni2 s.

It is also possible to express the radiation rate in ternis of tlie corresponding quantity for electroniagnetic radiation (Bertotti et 01. 1969;

Gold 1969)

where p, the component of the magnetic moment normal to the axis of rotation, is of order a 3 ( B s ) and ( B , ) is the average field a t the star surface (Melosh 1969). By combining [2.4.1], [2.4.2], and [2.4.3] one obtains

This expression contains however the structure parameters I and a, contrary to what is clainied by Melosh.

At birth, and for a period of time during which the braking mechanisni has not yet slowed down the star appreciably, the pi~lsar eniits gravitational radiation milch more strongly. This may be expected on the basis of [2.4.1]. Also, in the model of Ostriker and Gunn (1969), for an interval of time

with

where D, is the component of the niass quad- rupole normal to the rotation axis and w, is the angular velocity at some fiducial time, the gravitational quadrupole radiation always donii- nates over the niagnetic dipole radiation. If the initial value of o is -10" s - I , the loss of gravitational energy per unit tinie for a pillsar like NP0532, estimated from the prevision formulae, is -3 x 1 0 " ~ erg/s and equals the electromagnetic loss rate after about 80 years (Ostriker and Gunn 1969).

An estimate for tlie total flux at earth from all pulsars of our galaxy LIP to a distance of a few kpc has been given by Press and Tliorne (Press and Thorne 1972). The value is (P - 1 erg/cm2 s and tlie corresponding value of ( h ) is - lo-"'. For the pi~lsars in the Virgo cluster, where neutron stars shoi~ld be born about once a month. the same authors give 0 - erg/cm2 s and (11) - lo-".

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2.5 Black Holes The need of providing an explanation for

Weber's experimental results has motivated much of the recent research on black holes. A truly strong source, a black hole is not easily handled theoretically. The results reported below may thus look unspectacular in several respects. On the other hand, the existence of these objects is turning rapidly from a fascinating theoretical prediction into a dramatic reality. If they exist, many of their properties may not be observable with present experimental means because of their very nature. Hence, the great importance of detectors of gravitational radia- tion as i ~ n i q i ~ e research tools in this field.

Among the various possibilities of astro- physical relevance, massive black holes may exist at the center of many galaxies, including our own, where they may generate the strong nonthernial radiation observed to come from soliie galactic nuclei (Lynden-Bell 1969). 111 the model proposed by Lynden-Bell, a nucleus is essentially a dead quasar which disappears through its Schwarzschild radius and is sur- rounded by stars. Subsequently, activity in the nucleus is produced by the slow accretion of gas around the black hole and by the infall of gas. Mass estimates for tlie black hole at the center of our galaxy are difici~lt to make because of tlie lack of data on circi~lar velocities at distances < I pc from the center. Any mass less than - lo8 M , would seem compatible with our present knowledge (Lynden-Bell and Rees 197 1).

Tlie problem of the production of gravita- ti011i1l radiation in the radial infall of niatter down a nonrotating black hole has been first studied by Zerilli (1970). In Zerilli's work, the incoming particle of mass 111 is considered as making a sniall perturbation on the Schwarz- schild geometry. The pertubation in the geometry is then analyzed into tensorial spherical har-

,.. . - monk-s,,, ,. .- - -

Zerilli's equations have been solved ni~nleri- cally (Davis et a/. 1971) for a particle starting fro111 rest at infinity. The total energy radiated away in gravitational waves is

E,,, = 0.0104t11'c2/~

where M is the mass of the black hole,and M >> 171.

Tlie s p e c t r ~ ~ ~ i i of the outgoing radiation consists of the superposition of a number of overlapping peaks, one for each of the contributing millti-

'IONAL RADIATION 885

poles. Approximately 9 0 z of the total radiation is concentrated in the quadrupole mode, 9% in the octupole, and the rest in the higher multi- poles. The total spectrun~ is peaked at w = 0.32 c3/GM. The detailed shape of the energy pulse can also be calci~lated (Davis et 01. 19720). A sharp burst is preceded by a precursor and followed by a ringing tail. Since the tail pro- duces many zero crossings of the Riemann tensor, it does not appear possible to distingi~ish from the shape of the pi~lse among possible processes that might produce it. This disagrees with the qualitative conclusions reached by Gibbons and Hawking (1971). It is suggested, in fact, in this paper that in gravitational capture the components of the Riemann tensor change sign only once during the burst.

If instead of falling from rest, the test particle has kinetic energy (Rufini 1973), the amount of gravitational radiation emitted increases signi- ficantly and the spectrilm does not vanish any more at low frequencies. Also, the contribution of higher order multipoles becomes niore signi- ficant, while the peak frequency of the spectru~ii does not change substantially.

In the fall of matter into a rotating blackhole, the total alnount of gravitational radiation per unit mass may increase somewhat (Bardeen 1970), as the binding energy of the last stable corotating circular orbit is appreciably larger for a maximal Kerr black hole than a Schwarz- schild one. The increase, however, is not expected to be dramatic.

Numerical compi~tations have also been carried o i ~ t for the problem of a vibrating black hole (Press 1971). Altlioi~gli a test particle falling radially into a black hole can excite vibrational modes, weakly for high nii~ltipoles (Davis et crl. 1971), it is not yet clear whether high multipole vibrations can be excited pre- ferentially by turbulent influx of matter or other specific processes of infall. But, if vibrations coi~ld be excited, then gravitational radiation coi~ld be emitted at frequencies higher than c 3 / G M in long, nearly sinusoidal wave trains.

An attempt to explain Weber's resi~lts as due to gravitational synchrotron radiation has been niade by Misner. Tri~Iy, if instead of sirnply falling from infinity a particle did approach a black hole of nearly maximal Kerr metric from a very energetic trajectory, the particle could be accelerated to relativistic energies and would radiate substantially niore (Misner 1972; Press

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886 C A N . J . P H Y S .

and Teukolsky 1972; Bekenstein 1973). Energy could also be extracted from the black hole via the Penrose effect (Penrose 1969; Christodoulou 1970; Penrose and Floyd 1971): A particle of energy E > 0 can split in the ergosphere of a black hole into a particle with energy E' < 0, captured by the hole, and a particle of energy E" = E + I E'J which escapes to infinity. It is, however, difficult at present to see how the energetic orbits could be attained astrophysically.

Black holes may exist at the center of globular star clusters (Wyller 1970; Press and Thorne 1972) or form themselves into short lived dense clusters (Kafka 1970; Bertotti and Cavaliere 1970; Zeldovich and Novikov 1971). In all of these source models, gravitational radiation would be emitted by collision and capture of a collapsed object by another. A collision between black holes followed by capture should, in fact, produce a strong burst of gravitational radiation ofduration and period - 10-%/M, s (Gibbons and Hawking 1971). Although the occurrence of these processes may be infrequent, the efficiency of conversion of rest mass into energy c o ~ ~ l d be as high as 29.37 for two nonrotating black holes of eq~lal mass (Hawking 1971). This upper limit decreases with decreasing initial separation when the initial system can be regarded as con- sisting of two separate nonrotating black holes gravitationally bound (Gibbons and Schutz 1972).

2.6 Birtl~ of Galaxies Gravitational radiation of intergalactic wave

length - I to 10 Mpc-may have been associated w ~ t h the initial irregular~ties that gave rise to galaxies and clusters when the primordial gas expanded (Wheeler and Schwarzschild 196 1 ; Zeldovich and Novikov 1970; Rufini and Wheeler 1971). The effective flux of gravitational radiation would amount to lo-' to erg/cni2 s,,and the pert~~rbation in the metric to ' ( h ) < lo-'' (Press and Thorne 1972). The possibility that such radiation generates observ- able effects on the dynamics of galaxies has also been discussed with opposite concl~~sions by Rees and Jackson (Rees 1971 ; Jackson 1972).

2.7 Laboratory Generation of' Gracitational Radiation

Laboratory production of gravitational radia- tion with conventional techniques looks rather unpromising. A few examples should suffice.

VOL. 5 2 , 1974

For a rod of mass M spinning about an axis perpendicular to its length L the emission rate is from [2.1.7]

The maximum a n g ~ ~ l a r velocity is reached at the breaking point when the peripheral speed of the rod e q ~ ~ a l s the speed of sound in the material

where Y is the tensile strength. For a steel rod of mass M - 4.9 x IOs g, L - 2 x lo3 cni, o ,,;,, - 28 rad/s, the radiated power is -2.2 x

erg/s. The frequency of the wave is twice the orbital frequency, while the rninor boundary of the wave zone starts at a distance of 2.7 x 109 cm from the rod (Ruffini and Wheeler 1971).

A large crystal, or more in general, a solid, driven to the breaking point, can produce gravitational energy at the rate

where P,,,,, is the effective tensile strength and h the gravitational wavelength. If the excitation power is 10' W and the solid is about 102 cm on a side, -d E/dt - 10-l3 erg/s (Weber 1962).

Minute amounts of gravitational radiation could be emitted in nuclear explosions (Wheeler 1960). The process is however of no practical interest. The sanie can be said of most atomic and molecular processes.

More interesting approaches have been dis- cussed by Nagibarov and Kopvillem (1969), Braginskii and Rudenko (1970), and Ceapk (1972).

3. Detectors of Gravitational Radiation

3.1 Laser Ititetferometers Conceptually, the sinlplest possible antenna

consists of two free masses placed a distance lapart . If the masses are aligned along the I axis, their relative displacement 5 due to the gravita- tional acceleration - c21Rl,, , satisfies the simple e q ~ ~ a t i o n

The next question is how to measure 5. A laser interferometer has been used for this

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PAPINI: G R A V I T A T I (

purpose by Moss (1971) and Moss et al. (1 97 1). The laser is operated in a single mode to avoid low frequency noise generated by secondary beating between intermode frequencies. In this way the sensitivity limits are set only by acoustic and ground noise. The noise power of the system in terms of the equivalent displacement 5, in a detection bandwidth Ao is

which is close to the photon noise limit

for the particular power P and frequency w of the laser, the efficiency 11 of the photodetectors, and a bandwidth of a few Hz. The smallest distances measured correspond to approxi- mately lo- ' ' cni or 5 x 1 0 - a fringes, with I - 10' cm. Improvenients on these measure- ments c o ~ ~ l d in principle be achieved by in- creasing the laser power and decreasing the bandwidth.

Laserranging techniques, if s~~fliciently refined and applied over considerable distances, c o ~ ~ l d provide sensitive wideband antennas. They c o ~ ~ l d be particularly ~ ~ s e f u l in detecting low frequency gn~vitational radiation for which re- sonant detectors of reasonable dimensions are not easy to develop.

Despite what one might think, laser ranging to the nioon is absolutely impractical to the effect of observing gravitational radiatior?. The impressive accuracy of I0 cm that can be achieved after the installation of reflectors on tlie surface of the nioon is not suficient to detect 'reasonable' fluxes of gravitational radiation. The limits implied by the present accuracy correspond to fluxes Q, - 1.4 x 10" erg/cm2 s for wave periods o f -a few seconds (Ruflini and Wheeler

' - . 19717 : m e existe~ike of fluxes of this intensity co~lld hardly be reconciled with present niodels of the Universe!

3.2 Rocla, Railgirlg Radar tracking of spacecrafts is presently

perforliied with accuracies of several millimeters per second in velocity and - 10 m in range. Still not the attainable limit, these accuracies allow the detection of wave amplitudes ( A ) 3 10-" for frequencies o < lo-' Hz. The existence of gravitational radiation of this intensity can u

3NAL RADIATION 887

however be discounted on cosmological grounds. In particular, tlie tracking perturbations studied by Anderson (1971) w o ~ ~ l d correspond to Q, 2 6 x l o L 3 erg/cm2 per event or to the disappearance of 3 x 10' M, per event fro111 the center of the Galaxy (Gibbons 1971)!

3.3 Mecl~ai~ical Resoimtors of' Webei.'.~ T J ~ J C The typical detector developed by Weber

consists essentially of a large cylinder suspended at its central nodal plane, with piezoelectric transducers attached to its surface in tlie region of maximum strain. The ~iiotion of tlie bar is observed in its fundamental compressional mode. This is because gravitational radiation c o ~ ~ p l e s to the longitudinal modes of a cylinder according to an inverse square law in the mode number for odd modes, while, for even modes, the coupling vanishes. Even modes, in fact, give rise to no change in the quadrupole moment of tlie bar (Rutlini and Wheeler 1971). Almost all detectors so far constructed are of this type. It is therefore ~ ~ s e f u l to give a more detailed analysis following Gibbons and Hawking (1971).

For simplicity, it is convenient to replace tlie bar with an equivalent q ~ ~ a d r ~ ~ p o l e oscillator. The equation of motion of the system is well known and self-explanatory

where Q is tlie quality factor of the antenna, (I)

its resonant f req~~ency, and I the d~stance be- tween the masses of the osc~llator. Equation [3.3. I], as well as [3.1. I], is a part~cular case of the more general antenna equation

[3.3.2] \,, = - ~ ~ l l < , ~ , ~ - j(p-'t ,],]),,

- + ( ~ - ' t , j , j ) , i

where p is the density of matter, s,,, the invariant strain tensor defined by

and t , , , represents the internal stress density tensor (DeWitt 1962). Equation 3.3.2, which is completely gauge invariant, is partic~ilarly useful in the stitdy of more con~plex systems.

In the pa r t i c~~ la r problem at hand, the right hand side of [3.3.1] should be supplemented with acceleration terms pertaining to Brownian or extraneous electrical and n~echanical pertur- bations. In what follows, the Brownian niotion

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888 C A N . J . P H Y S .

is assumed to represent the main perturbation in the state of the bar. The incoming signal is at first assumed to consist of a short burst of radiation a few wave cycles long, as it may be emitted in the collapse of a star or other astro- physical events. In this case, the advantage of a high Q system does not lie in the amplification of the displacement, but rather in the lengthening of the time scale over which the thermal fluctua- tions of the bar take place. In other words, the noise power is q ~ ~ i t e small if the Q of the bar is high enough. At any time, in fact, the thermal oscillations of the bar may be considered as arising from a large number of small uncorre- lated impulses, each one decaying in a time Q/o . Since there are Q/2rc cycles in the damping time, the mean value of the energy of oscillation in one cycle is 2rrltTIQ and the noise power okT/Q. With a time resolution of n cycles, one could therefore observe gravitational bursts of energy 2rcnkTlQ rather than lt7' only (Gibbons and Hawking 1971; Maeder 1971, 1972; Faulkner and Buckingham 1972).

The motion of the bar is observed by means of piezoelectric transducers whose output is fed into an amplifier. Electrically, the transducer may be represented by an eq~~ivalent circ~tit in which the transducer acts as a charge generator in parallel with its capacitance C and a resistance R = tgS/oC that represents its electrical losses. The term tgS is called the dissipation factor. The main noise sources to be considered are the Brownian motion of the bar, and Johnson noise due to the transducer impedance. The Johnson noise produces a mean square voltage per bandwidth A o given by

- . Thus, a p!~lse of gravitational radiation can be ..- .. 7 -

detected again3 transducer and Brownian noise only if its output voltage satisfies the condition

where ( vB2) is the mean square voltage produced by the Brownian motion

Here ci is the voltage output of the transducer

VOL. 5 2 , 1974

per unit displacement. The optimum time resolution is determined by the maximum sensitivity condition

( VT') = (2nnlQ)( VB') One obtains

n2 = ~ t ~ S / 8 n ~ P

where

represents the ratio of the electric energy in the transducer to the elastic energy of the bar. Once the shape of the p ~ ~ l s e is known, 6, the integrated energy flux per n nit area at the observer can be evaluated from the solution of [3.3.1]

[3.3.4] 5 = A(t) e(-'m12a)+im)t

where

and the relationship

In [3.3.6], r is the length of the pulse. For bursts shorter than the damping time Q/o, [3.3.4] is nearly independent of Q if Q is large enough, as previo~~sly mentioned. If, for the sake of definite- ness, the p ~ ~ l s e is assumed to consist of a single cycle of a sine wave, then from [3.3.4], [3.3.5], and [3.3.6] one obtains

Since the smallest detectable energy is 2rcnltT/Q, for maximum sensitivity

while the optimum time resolution is given by

For burst radiation, a high Q resonator may be advantageous over broadband detectors as, in it, signals decay over times longer or equal to

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PAPINI: GRAVITATIONAL RADIATION 889

the time resolution of the system. This may not be the case for broadband detectors. For

c ~ ~ ~ ~ R , ~ ~ ~ I ~ Q (5') = w4

instance, if the laser interferometer of Sect. 3.1 could achieve the noise limit given by [3.1.2], rather than the value of 5 immediately after the optimum displacement per root Hz would signal arrival. Thus, at maximum sensitivity not exceed 0.8 x 10-l6 ~ m / ( H z ) ' / ~ . The shortest (1/4)n1w~('~) = kT time over which this displacement can take place is and

where hl is the displacement 5 determined by [3.1.1]. Since 1 -- lo2 cm, for signal strengths 11 5 the value of Q is greater than s and may actually exceed in length the incoming signal, particularly if this is due to collapse, capture, or collision of collapsed objects. No measurement is possible in this case.

Besides stressing the importance of the product ml2 to the effect of-achieving greater sensitivity, [3.3.7] and [3.3.8] indicate the role of p in the search for better sensitivity coupled to good time resolution.

They also suggest alternative designs for antennas of Weber's type. In particular, a larger electromechanical coupling can be achieved by using the transducers as a spring between two metal bars (Aplin 1972; Drever 1971). As the volume of the piezoelectric transducer increases, more and more energy is stored in it. In the limit, when the transducer itself becomes the antenna, the value of j3 represents the efficiency of conversion of elastic energy into electric energy and depends entirely on the properties of the material used. Greater sensitivity can also be obtained by cooling the antenna to low temperatures (Fairbank 1971 ; Hamilton 1972; Pizzella 1972; Barton et al. 1972).

It also follows from [3.3.7] and [3.3.8] that when the coupling of the electronics to the

_antenngis.weak, 27tn.x Q as the mechanical Q practically determines the overall quality factor of the detector. Then, the bandwidth of the antenna becomes the bandwidth of the detector The smallest detectable energy is, in this case, kT, with a consequent loss in sensitivity. W-ak coupling detectors can, however, be advantageous if the incoming signal is monochromatic and slowly changing. Here one can take advantage of the Q amplification factor of the antenna as the quantity of interest becomes the mean square displacement

Moreover, for a resonator with a displacenient sensitivity 10-l4 c m / ( ~ z ) ' / ~ , comparable with that of a Weber (1969) detector, the shortest time over which the displacement can take place is

For the same values of h and I, Q' compares favorably with the corresponding value Q for the interferometer of Sect. 3.1. In fact

which, at least in the time scale, renders the measurement of small signals feasible. Very high Q systemes are, therefore, advantageous also in the detection of trains of waves.

Results similar to [3.3.7] and [3.3.8] could also be obtained by a detailed st~idy of the equivalent electrical c i rc~~i t for the detector (Gibbons and Hawking 1971 ; Tyson and Miller 1972). Tyson and Miller, in particular, discuss at length the problems of matching the antenna to the electronics and of filtering and calibrating. Of considerable importance is the condition for the Brownian noise to be observable. With present new low noise field effect transistors, transducer noise and amplifier noise are com- parable in magnitude and smaller than the Brownian noise if

where Q, is the loaded Q of the antenna, Q , the transducer Q, C the transducer capacitance, R, a resistance representing the series noise of the amplifier, and all elements are at the same temperature (Weber 1973).4

'Private communication.

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TABLE 2. Detectors operating in 1973

I 0 in in Other

Location Number 111 in g cm Q a Hz T characteristics

Argonne-Maryland

Moscow-Institute for Space Science

Bell Laboratories1 Rochester

I.B.M. Watson Research Centre

Frascati

Munich

Glasgow 1

Glasgow 2

-- -

aluminum, Weber type

aluminum, Modulator

aluminum, Weber type

aluminum, Weber type

aluminum, Weber type

aluminum Weber type

aluminum, Aplin type

aluminum, Aplin type

The enormous disadvantage of ~ ~ s i ~ i g mechani- cal resonators should also be mentioned. It consists, essentially, in the drastic reduction of information about the wave to its Fourier component at a single frequency. Any informa- tion about shape and spectrum of the signal is irremediably lost.

The majority ofdetectors that have so far been operated is of the type discussed in this section. Their locations and characteristics are listed in Table 2.

3.4 Mec l rn~~ ica l Reso~intors ~ i - i t l l M o ( / ~ / / n t i ~ i g Selisors

Mechanical resonators that make use of different pickup systems have also been built. I n these systems, the detector's mechanical motion is used to control an external source of energy. Consequently, the output is not limited by the energy deposited by the gravitational wave in tlie antenna. No general discussion of

- . - ---- --.sensitivities--ca~ be given, each detector being

based on different principles. However, the ultimate sensitivities of these systems, that are sometimes referred to in tlie literat~lre as 'modu- lators', are many orders of magnitude below what can be attained at present. The possi- bilities of improvement for 'modulators' in tlie near future are therefore excellent.

4.5 x 10-l4 cm corresponding to the r.m.s. a m p l i t ~ ~ d e of the Brownian motion is transformed into a radio frequency signal of a m p l i t ~ ~ d e 4 x lo-' V. For comparison, oscillations of the same an ip l i t~~de would be transformed into signals of anlplitude 5 x 10-10 V by a piezo- electric pickup. The antennas have each a mass 171 = 1.3 x lo6 g, Q = lo5, and operate at a f r eq~~ency of 1640 Hz (Braginskii 1972).

T o the same group belong three detectors a t present i~nder construction at Stanford (Fair- bank 197 I), Baton Rouge (Hamilton 1972), and Rome (Pizzella 1972). The antennas, al~~rninilrn cylinders of mass 4.5 x 106 g and Q - lo6 will eventually operate at 3 x K . Their resonant f r eq~~ency will be 1660 Hz. In the Stanford and Baton Rouge detectors, the sensors consist essentially of an inductor that moves with respect to a ground plane (Fairbank 1971 ; Hamilton 1972). The Rome group will use inductive coils (Modena 1973).

Some of the cryogeriic antennas which are presently being constructed by the Regina group are also equipped with inductive coils. They are of various shapes with resonant frequencies in the lo3 to lo4 Hz range. The largest antenna that will be cooled to 3 x K has a mass of 4.5 x 10" g (Barton et nl. 1973).

In the two detectors of this type const r~~cted 3.5 Detectio~i Scl~e~l les of' Var io i~s T jpes by Braginskii, 'horns' attached to the ends of a This section is devoted to a short review of cylindrical antenna convert mechanical dis- detectors that have been proposed and discussed placements into displacements between the but not yet constructed. plates of a capacitor. A vibration amplitude of Among those that still make use of meclianical

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resonance are the 'class 2' detectors discussed by Douglass andTyson(1971), the 'class I ' detectors, being Weber'scylinders, rods, discs, theearth, and, in general, those for which the resonant frequency is proportional to 111. The corresponding relation for class 2 detectors is w u 111'. T o this class belong hollow squares, tuning'forks, and rings. Their usefulness arises mainly from their reduced dimensions for the same f req~~ency relative to the detectors of class 1 . Although considerably lower than for class 1 at the same frequency, their detection efficiency at low frequencies remains comparable with that of present day detectors working in the KHz band. They might therefore be used to detect low frequency radiation for which the dimensions of class 1 detectors would simply become un- manageable. Similar considerations apply to dumbbells (Rasband et al. 1972).

A system of two pendula, well isolated but suspended in vacuo from the same support by quartz ribbons, has also been discussed (Bragin- skii and Rudenko 1970; Braginskii 1968). With pendula, very low resonant frequencies can be obtained so that the system looks promising for frequencies less than 1 Hz. Thin q ~ ~ a r t z ribbons provide very weak damping. At resonance, the Q of the system is, in fact, given by

where 1 is the length of the pendula, a the ribbon thickness, o and 11 the permissible tension stress and viscosity of q ~ ~ a r t t respectively, and g the acceleration of gravity. For q - lo6 poise, o - 2 x lo9 dyne/cin2, a - 0.04 cm and 1 = w2g = 250 cm, one obtains Q >, lo9, a factor 1 O4 better than present day mechanical resonators.

Yet another proposal for a detector makes use of two independent mass quadrupoles crossed at 90" and rota t~ng .about the same center at half the frequency of the wave incident normally to the antenna plane (Braginskii et al. 1969; Cooperstock and Booth 1969). The quadrupoles are accelerated, in the field of a circularly polarized wave, in opposite directions. If the rotation frequency deviates from the wave frequency, beats are produced. For example, two dumbbells 50 cm long, whose frequency deviates Hz from that of the incoming wave, would experience beats of measurable amplitude (10-l2 cm) when exposed to a flux of - erg/cm2 s.

One obtains a high f r eq~~ency variant of the previous detector by replacing the dumbbells with a toroidal waveg~~ide in which a train of electromagnetic waves is propagated (Braginskii and Menskii 1971). The detector is, in this case, suitable to detect waves in the f r eq~~ency range lo7 to 10 l o Hz, if they exist. The gravitational waves passing through the plane of the toroid give rise to phase shifts between neighboring sections of the electromagnetic wave train. An interesting point arises: The nlaximum anipli- tude of the shift depends quadratically on time so that integration is possible over periods of time whose lengths depend on the ringing time, and, therefore, the Q of the (superconducting) microwave resonators. Any progress in the technology of superconducting cavities is there- fore likely to improve the sensitivity of this detector. The expression for Acp,,,;,, is

which gives a minimum detectable (P - erg/cm2 s for Acp,,;,, - rad, w = 6 x 10'' s - l , and t = 1 s.

Other electromagnetic schemes of detection have been considered by Lupanov (1967), who has st~idied the problem of a charged capacitor in the field of a gravitational wave, and by Boccaletti et al. (1970). This latter work is concerned with the conversion of gravitational waves into electromagnetic ones in a static electromagnetic field. Since the power of the electromagnetic radiation produced does not depend on the frequency of the incoming gravitational radiation, this system may be considered as broadband. Another potential advantage of the scheme lies in the fact that the conversion efficiency depends on the fourth power of the static field and of its linear dimen- sion. It seems however ~lnlikely that intense static electric or magnetic fields over long distances will be produced in the near future.

Mechanical ways of increasing the sensitivities of detectors have also been studied (Lavrent'ev 1969, 1970). In this work, the amplification is achieved by the increase in the initial displace- ment produced by a rod, rigid a t the detection frequency, introduced in the gap of the coupling of a quadrupole oscillator.

The possibility of using nonelastic neutron scattering to observe the density fluctuations

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892 C A N . J . P H Y S . VOL. 5 2 , 1974

induced in the target by a gravitational wave has also been disci~ssed (Kopvillem et al. 1972).

A detection scheme based on the fluctuation in the optical radiation of stars, produced by a gravitational wave, does not seem promising. Some of the pi~blished estimates (Wintenberg 1968; Bergniann 1971) proved erroneous (Zipoy and Bertotti 1968; Press and Thorne 1972).

Superconducting and normal metals in the field of a gravitational wave emit electro- magnetic radiation of the same frequency (Papini 19700). Roi~gh estimates indicate that a detector based on this effect would become advantageoils at frequencies higher than I KHz (Papini 19706). However, several attractive possibilities offered by superconductors and, to a lesser extent, by normal metals, have not yet been investigated fi~lly. It is not yet clear, for instance, whether a broadband detector of this type woi~ld be silfficiently sensitive. Superconductors may be used, in principle, to detect waves of cosmologi- cal origin as those considered in Sect. 2.6, which, for all purposes, may be considered as stationary. I n a superconducting loop, for instance, the total flux produced by stationary electromagnetic and gravitational fields is quantized (DeWitt 1966; Papini 1966, 1967). If the loop is cooled through its critical temperature when the total flux linking it is zero, the total flux remains zero at all times afterwards. At these times, a gravi- tational field threading it generates a magnetic flux which could be nieasured in a variety of ways. The elimination of competing effects, if successfi~lly accomplished, could allow the nieasurement of mean values of h well below the upper limit of - lo-' for waves of galactic or intergalactic wave length (Papini 1974).

4. Experimental Results

4.1 The Marylnntl-Argo1117e Esl~eri~nents (1966-1969)

-.* In a nilniker- of papers pi~blished starting in 1966, Weber has given the resillts of experiments aimed at detecting gravitational radiation from space (Weber 1966, 1967, 1968, 1970c1,b). During this period, two aluminum cylinders 153 cni long with 66 cni diameters resonating in a narrow fre- quency band about 1660 Hz were used for most experinients. The cylinders, placed in evacuated chambers and approximately 1000 km apart, were located in the east-west direction at the University of Maryland and at the Argonne National Laboratory near Chicago. In some of

the earliest experiments (Weber 1966, 1967, 1968). detectors of different characteristics were , ,

also used on a baseline of only a few kilometers. Piezoelectric crystals bonded to the detector surfaces in the region of maximum strain con- verted the lowest mode longitudinal oscillations of the cylinders into electric signals. The values of p and Q were approximately 5 x and lo5 respectively. The details of the electronics used in the 1969 experiments have also been published (Weber 1970~). The radio frequency output of the Argonne detector was transmitted to Maryland via a telephone link and fed together, with the output of the other detector, into a two channel coincidence detector. In later experinients, a second coincidence detector, with a time delay of two seconds, was operated si~ni~ltaneously in order to compare the results with those without time delay. Pen and ink recorders recorded coincidences on charts. An event was defined as a pi~lse in the output voltage of a detector crossing an arbitrarily chosen threshold. Two events were considered as coincident when their leading edges were no further apart than the resolving tinie of the electronics. Pulse heights were measured and then classified according to the nuniber of tinies N each pulse amplitude was equalled o r exceeded in the average per unit time. Thus, each coincidence belonged to a class character- ized by the values N , and N , of the coincident pillses of detectors A and B, and for which the number of expected accidental coincidences coi~ld be calculated.

T o eliminate nongravitational effects, the detectors were insulated acoustically. Moreovei., a 0.03 to I H L low frequency seisniometer, a high frequency seismometer at the detector frequency, east-west and north-south tilt meters, and a gravimeter sensitive to changes in g of a part in 101° were operated at the Maryland site, and line-voltage fluctuations continuously re- corded. The room temperature was also con- trolled to a fraction of a decree. Shields to - attenuate electromagnetic signals below the coincidence threshold were employed. In addi- tion, the effect of electroniagnetic excitation was studied by means of an independent detector with cryogenically cooled electronics, whose relaxation tinie was milch longer than that of the other two detectors. Later, a radio receiver with magnetic loop antenna operating at a frequency of 1662 Hz, with a bandwidth of 3 Hz,

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was used in the study of the same problem. The effect of cosmic rays was also investigated (Ezrow et al. 1970). Finally, the detectors' response was tested experimentally by detecting dynamical gravitational fields generated by a newly developed source (Sinsky and Weber 1967; Sinsky 1968). Good agreement was found between theory and experiment. The dynamical gravitational field was produced by the time dependent strains generated in an aluminum cylinder driven electroacoustically at the resonant detector frequency.

Coincidences were observed between the Maryland and Argonne detectors. Initially, coincidences were also observed among detectors only a few km apart. The number of coincidences was observed to decrease markedly when the time delayed coincidence detector was intro- duced. No significant correlation was found between electromagnetic and seismic effects and coincidences. No significant correlation was found between coincidences and cosmic ray effects. In the first runs, one to two coincidences per week were observed, and in the last ones, one to two per day, while the resolving time improved from 0.30 s to 0.15 s.

The distribution of the 31 1 coincidences observed during the period May 12 to December 14, 1969, presented an anisotropy a t the 6 standard deviation level when plotted with respect to sidereal time. The peaks in the distri- bution were in the direction of the galactic center, and 12 hours later, in that opposite to it. Truly gravitational bursts of radiation c o ~ ~ l d not behave better, as the earth is not expected to absorb gravitational radiation appreciably. The origin of the perturbation, however, does not appear ~~niquely localizable, and depends strongly on assumptions regarding the polarization of the source (Douglass and Tyson 1972; Tyson and Douglass 1972). There was no anisotropy with

-respecT"tB'Solar timi.; ss'dne would expect, since the difference between solar and sidereal time amounts to 12 hours over a period of 6 months. The loss of gravitational energy suffered by the galactic center was estimated to be - lo3 M,/yr.

4.2 Maryland-Argonne Experiments (1970-1973) A new type of experiment was carried out in

1970. An antenna in the shape of a disc, and with a radial mode frequency of 1660 Hz, was set u p at the University of Maryland and operated in coincidence with the Argonne

'IONAL RADIATION 893

cylinder. The experiment was designed to deter- mine the presence of a scalar component in the gravitational radiation as predicted by the Jordan-Brans-Dicke theory of gravitation (Jor- dan 1955, 1959; Brans and Dicke 196 1 ; Dicke 1964). In fact, a purely tensorial gravity wave propagating in a direction parallel to the axis of circular symmetry of the disc could not excite the radial mode. This would be excited only by a tensorial wave propagating perpendicularly to the symmetry axis, or by a scalar component in the direction of the axis. The disc was suspended centrally so that its axis passed through the galactic center when this was on the meridian of the detector location. Because of the rotation of the earth, the disc should not respond to a tensor field when looking a t the galactic center, if this contains the source of the field. It should, however, be excited by the same field 12 hours later when the symmetry axis is almost normal to its original direction. This is unlike the response of a cylindrical antenna with axis in the east-west direction. Simultaneous to the disc-cylinder coincidence experiment, coinci- dences were also taken between the Argonne and Maryland cylinders. The number of coinci- dences for the disc-cylinder experiment did exhibit a minimum three standard deviations below the mean when the disc was looking at the galactic center (Weber 1971a,b). This might be interpreted as evidence against the presence of a scalar component in the source, at least for the energy fluxes observed.

The two cylinder experiments have, in the meantime, been continued to the present (1973) with improved electromechanical coupling and fully automated data handling (Weber 1972a). In these new experiments, coincidences have been determined by observing changes in the derivative of the power output of the detectors. Coincidences have been observed between two detectors resonating a t 1661 Hz and 1580 Hz, thus showing that the bandwidth of the perturba- tion exciting the antennas is a t least 80 Hz. Later, coincidences have also been observed at 1030 Hz with a rate approximately equal to the one at 1660 Hz (Trimble 1972). Another experi- ment has shown no excess of coincidences above the accidental rate between a 1661 Hz detector and the 5000 Hz bending mode of a second detector, both located at the University of Maryland (Weber 19726). This result is consis- tent with the predictions of the general theory

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894 C A N . J . PHYS.

of relativity, according to which a bending mode should not be excited by a plane wave.

The latest experiments refer to the period April 22 to June 5, 1973, and are characterized by a markedly increased coincidence rate, in the average seven coincidences per day, and by a sensitivity of ItT/IOO (Weber et al. 1973). In these runs, moreover, a few important experimental procedures have been further tested and verified. For instance, the use of a telephone link between Argonne and Maryland has been compared with the use of separate recorders with no tele- phone connection. No substantial difference has been found in the number of zero-delay excess coincidences. Data handling has been coniputer- ized. A direct method of calibration has been introdi~ced.

4.3 Tl7e Ut7ioersity of' Moscow Experin7et1t Two detectors have been operated, one at the

University of Moscow, the other at the Institute for Space Research, 20 knl away (Braginskii et 01. 1972). The antennas, two aluminum cylinders with modulated capacitive pickups, have almost the same parameters as those of Weber. The mass of each is in fact 1.3 x lo6 g, Q = lo5, and the resonant frequency is 1640 Hz. They have also been placed in vacuum tanks and aco~~stically insulated. Changes in the oscillation amplitude of the Brownian noise have been observed with an oscillograph and recorded photographically. This process allows a time resolution of approximately 0.3 s. Two inde- pendent recording apparata, one at each site, have been used, and the results synchronized later on. The pickups coi~ld measure changes in length of 2 x lo-" cm at room temperature. With a sensitivity 1.5 times below that of the Maryland-Argonne group in 1969 no events have been observed coinciding within 0.5 s.

- - 4.4 T/7e Bell Laboratories Experimet~t

-c - < *. - . A large antehna consisting of an aluminum

bar 357 cm long and of mass 3.6 x lo6 g has been set up at Bell Laboratories (Tyson 1973). The antenna has a loaded Q of 2.2 x 10' and the frequency of its first longitudinal mode is 7 10 Hz. Four piezoelectr~c transducers have been placed symmetrically around ~ t s middle. The total coupling is P = 2 x The antenna is in a vacuum tank and the whole system has been vibrationally and acoustically insulated. Moreover, the electronics and the data recording system have been isolated from

VOL. 5 2 . 1974

the power line and electron~agnetically shielded. By electrostatic calibration (Tyson and Miller 1972), it is possible to determine whether the unperturbed motion of the bar is Brownian. Seismic and magnetic detectors have been operated simultaneously.

The signal from the four transducers goes to four parallel preamplifiers whose outputs are added at the bar frequency. Two phase sensitive linear detectors detect the resulting signal and determine the amplititde of the antenna vector in the complex plane. A computer then calculates the differences between the expected and measured positions of the antenna vector. This gives the size of any sudden change in the motion of the antenna, not only in amplitude, but also in phase. The advantage of this method lies in the fact that the sensitivity of the detector is independent of the state of motion of the bar before the arrival of an impulse. This is not the case in detection schenies using threshold crossing.

The detector is approximately 10 times more sensitive than those used by Weber until 1970. Given therefore a higher sensitivity, one could, in principle, try to check Weber's resi~lts without performing a complete two detector experiment.

In two runs for the periods December 10, 1972 to February 14, 1973 and March 5, 1973 to April 4, 1973, no increases in detector energy have been seen above (114) k T (well above Weber level) in a risetime < 1 s, and followed by a long decay. If the coincidence rate observed by Weber at 1030 Hz can be extrapolated to 710 Hz, 450 events should have been seen. This nil11 result places an upper limit to the gravita- tional radiation flux at the detector of -3 x lo6 erg/cm2 for bursts of I s length and of 3 x lo9 erg!cm2 for s duration.

An entirely similar detector has been set up at the University of Rochester.

4.5 The I B M Experimetlt A null experiment, somewhat similar to the

one described above, has been performed at the IBM Thomas J . Watson Research Centre (Levine and Garwin 1973; Garwin and Levine 1973). The characteristics of the apparatus are given in Table 2. The antenna is in a vacuum tank suspended from a pneunlatic isolation frame. A small piezoelectric transducer is attached to an end of the bar and to a seismic mass of 5 kg (suspended from pins set into the

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bar), whose resonant frequency is much lower than 1695 Hz.

The detection scheme is similar to that used by Tyson (TYSOII 1973). The position of the antenna vector is determined every 24 ms. The mean energy of the bar is determined by cali- bration.

In a run of nine days, the data collected have been consistent with pure thermal noise, with the possible exception of one single impulse larger than 1.8 kT. This null result would be invalid if the pulses observed by Weber lasted longer than 24 ms.

Of all experiments so far carried O L I ~ . this is the one closest to Weber's, not only' in the characteristics of the apparatus, but also because it is a coincidence experiment on a base line comparable with that of the Maryland-Argonne group. Hence its importance as a check.

The cylinder material and the piezoelectric ceramic transducers are those used by Weber. The dimensions of both the Frascati and Munich antennas are summarized in Table 2, and are almost identical to those of Weber in 1971. The same applies to the precautions taken to protect the apparatus from line voltage, electromagnetic, seismic, and temperature variations. It should be noticed. in particular, that the Frascati detector is so will isolated mechanicallv and electrically that no coincidence is ever observed between antenna output and disturbance sensors.

Unlike Weber, however, the data acquisition apparatus records the changes of the antenna vector in the complex plane (Bramanti and Maischberger 1972). Also, no telephone link is used between the two sites and the detectors' outputs are independently recorded on magnetic tape and synchronized with the help of standard time services. The synchronization is tested with

- -artificial-pulses of known- strength. Since the detectors are orientated in the east-

west direction, as those of Weber, the rate of coincidences between Munich and Frascati should be the same as Weber's. The coincidence rate between the Marvland and Munich- Frascati cylinders should, however, be only 0.28 times that of Maryland and Argonne, because of the large difference in longitude.

The evaluation procedure and the results of 18 days of data taken between April 9 and April 29, 1973, under optimal evaluation

IONAL RADIATION 895

conditions, have been presented at the Paris Conference (Kafka 1973). No coincidences have been found.

Two antennas of the split bar type (Aplin 1972), already discilssed (Gibbons and Hawking 1971), have been constri~cted at the University of Glasgow. Their bandpass overlaps one of Weber's experiments at 1030 Hz for which the coincidence rate was the same as at 1660 Hz. The antenna's characteristics are listed in Table 2. The large values of P have been obtained by bonding two alumini~m half bars to a number of piezoelectric transducers. Each half bar is suspended at its center of gravity from a support structure which is acoustically insulated and placed in a vacuum tank.

Large values of P allow short time resoli~tions according to [3.3.8]. For these detectors, the time resolution is of the order s. The detectors have been calibrated by producing signals of known amplitude and form electro- statically. The detectors are 50 m apart and placed in the north-south direction.

A first experiment has been performed to determine whether a small impulsive force, such as produced by a burst of gravitational radiation, might be amplified by the antenna by the release of stored energy. This process has been some- times suggested as an explanation for the intensity of the events observed by Weber (Weber 1969, 1970a,b, 19726). In the experiment, impulses of strength just below detection level have been applied to one detector at a known rate. The small pulses have then been followed by trains of larger pillses that coi~ld be easily detected. None of the small impulses has been observed over a period of two months. In another run, a train of five pi~lses of equal amplitude has been applied to the antenna with known daily frequency to check whether the hypothesized amplification process might be more effective for the first pulse than the others. The result has again been negative.

In the coincidence experiments between the two detectors, the data have been recorded in three different ways. Of these, the most precise is the electronic one that uses a 400 channel pulse height analyzer. A time delay distribution is thus automatically produced.

Seven months of data recorded electronically and photographically from September 1972 to

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896 C A N . J . P H Y S . VOL. 52 , 1974

April 1973 have been analyzed. No significant rate of coincident pulses above the chance rate has been found. Among the rare coincident events recorded photographically, only one has the characteristics of a true gravitational event (Drever et al. 1973).

10% of all events at 1660 Hz. As the source must lie outside the solar system, the flux of gravitational radiation appears enormous. It is, in fact, about lo6 times the total flux of electro- magnetic radiation from the whole universe outside the solar system, and is comparable with the flux of electromagnetic radiation from the sun. If our understanding of the physics of the detector is correct, and these are indeed the fluxes involved-about lo4 solar masses per

4.8 Co~nn~ents It is difficult at the present time to give a

definite assessment of the ex~erimental situation. Weber's results have not sd far been confirmed by independent researchers. Yet, the evidence in favor of Weber's claim cannot be disposed of

year dissipated in gravitational radiation by the galactic nucleus-the lifetime of our galaxy may be very short indeed, only about lo6 years!

On the other hand, such a large mass loss easily. It is perhaps useful at this point to restate what appear to be the strongest arguments in support of Weber's claim: (i) the decrease in the coincidence rate when a time delay is intro-

could hardly pass unnoticed to the astronomers. Field et al. (1969), Sciama et al. (1969), and Sciama (1969) have found that the maximum

duced in one of the channels; (ii) the anisotropy of the distribution of coincidences with respect to sidereal time; weaker arguments are: (iii) the tensorial nature of the source that fails to excite

loss our galaxy can tolerate, over periods of lo9 years, cannot exceed 70 M,!yr. More substantial losses would not be consistent with the motions of nearby high velocity stars.

the disc in the disc-cylinder coincidence experi- ment in an experimental setup which depends in a complex way on the relative orientation of the antennas; and (iv) the lack of coincidences between a 1661 Hz longitudinal mode of a cylinder and the 5000 Hz bending mode of a second cylinder, both at the University of Mary- land, this s~~bject to the assumption that the

It would also seem very difficult to conceive of generating processes for gravitational radia- tion that were not at the same time responsible for the production of radiation of other nature. However, no evidence has so far been f o ~ ~ n d for coincidence between reported pulses of gravi- tational radiation and radio pulses from space (Partridge 1971 ; Charman et al. 1970) or neutrino bursts(Bahcal1 and Davis 197 1 ; Reines et al. 1971).

Mechanisms that would reduce the quantity of gravitational radiation of a source necessary to trigger Weber's apparatus have been studied. Misner (1972) has pointed out that if the source at the galactic center were assumed to radiate in a synchrotron mode, the flux of gravitational radiation w o ~ ~ l d become more reasonable. In

incoming p ~ ~ l s e has sufficient band-width. If, for the sake of discussion, one accepts these

arguments as evidence in favor of the detection of gravitational radiation, then the question of the intensity of the source must be immediately considered. In fact, while Weber has estimated the sensitivity of his 1969 detectors at threshold to be 2 x lo4 erg/cni2 s at a bandwidth of 0.016 Hz, for the a c t ~ ~ a l experimental situation, with an effective bandwidth of 5 Hz, @ is lo7 erg/cm2 s (Braginskii and Rudenko 1970; G.ibbons and Hawking 1971). For pulses that

particular, radiation in a synchrotron mode could account for the high intensity and low frequency of the source. If, in fact, the radiation were beamed at a very narrow angle with respect

'could be resolved. this would corres~ond to an to the galactic plane, a largely reduced source strength could account for the energy density at the detector, provided the detector happened to be located in the privileged plane. This last

energy density at earth of lo7 erg/cni2 per polarization. Since it is not reasonable to assume that the incoming radiation is concentrated only in a very narrow bandwidth about 1660 Hz, one may think either that the radiation bandwidth extends approximately over lo4 Hz, or that there are lo4 bursts at other frequencies for each one

condition is well satisfied because of the relatively small distance of our sun from the galactic plane. In principle, a black hole of mass M - lo7 M, at the galactic center c o ~ ~ l d radiate at a funda- mental frequency of s - ' . Its high frequency harmonics, characteristic of synchrotron radia- tion, could very well reach the lo4 s- ' freq~~ency range. Unfortunately, no satisfactory mechanism

that is observed. In eithercase, the energy flux at earth would be in excess of loL0 erg/cm2 per day. This same result could have been obtained from [3.3.7] by assuming that Weber observed

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PAPINI: GRAVITATIONAL RADIATION 897

for the production of gravitational synchroton radiation exists so far, although some progress has been made in elucidating the problem (Misner et al. 1972; Davis et al. 19726; Chitre and Price 1972).

The possibility that gravitational radiation of extragalactic origin could be focussed by the galactic nucleus acting as a gravitational lens has been considered by Lawrence (1971). The difficulty is represented here by the location of the sources. Too few of them are properly located to really render this solution appealing. A more hopeful approach considers the focussing effect of the metric on the radiation emitted near the event horizon of a maximal Kerr black hole rotating in the galactic plane (Lawrence 1973).

The possibility that the present age is one of superactivity for the Galaxy cannot be ruled out a priori, but does not appear to be satisfactory on astrophysical grounds. In fact, the galactic nucleus would have to be overactive in the production of gravitational radiation only, by several orders of magnitude over other radiation phenomena.

The question whether all events observed by Weber are really gravitational has been raised by two recent works (Adamyants et al. 1972; Tyson et al. 1973). In the first one, a significant correlation is reported between the seventeen original events collected by Weber from Decem- ber 30, 1968 to March 21, 1969 (Weber 1969) and solar and geomagnetic activity and also cosmic ray intensity. Correlation with a two day delay at 99.9z confidence level has been found between the characteristics of solar activity represented by the Wolf n ~ ~ m b e r W and the number S (Solar Data 1968, 1969), and the events. Also, correlation with no time delay at the 99.9x level has been found with the index of geomagnetic activity K, (Solar-Geophysical ~ata-~9.-94&,-69) and wit.h.cosmic rays. In the second work, the correlation has been examined between various terrestrial phenomena and a more sizeable body of 262 events observed by Weber between August 22 and December 22, 1969. A correlation at the 2.7 standard deviation level has been found with the magnetospheric ring current intensity. This might suggest that Weber's antennas are not sufficiently shielded from the extremely low frequency electromagnetic oscilla- tions due to these geophysical phenomena. However, an investigation of the response of

the Maryland detector to variable magnetic fields in the frequency range 0.1 to 30 Hz has yielded a negative result for various field orientations and intensities 100 times those of the earth field at the same frequencies (Weber and Trimble 1973). No significant correlation has been found with meteorological or seismic phenomena, with daily temperature and baro- metric pressure differences near the Maryland site, the east-west strain, and with cosmic rays. The events correlate, at the 3.0 standard deviation level with sidereal time. The body of data, however, is certainly not large.

The experimental situation is further compli- cated by the null res~llts of the Bell Laboratories and IBM groups, and by the so far negative results of the Munich-Frascati coincidence experiment. To be cautious, while the IBM detector is smaller and less sensitive than those operated at Maryland and Argonne, Tyson's passband did not overlap any of those of Weber's experiments. Moreover, Ruffini has noted that a number of models of the radiation process predict a rapid falloff in intensity below lo3 Hz (Ruffini 1972). On theoretical grounds, it appears therefore ~~nsa fe to extrapolate Weber's coinci- dence rate at 1030 Hz to Tyson's freq~~ency of 710 Hz. Differences in data evaluation pro- cedures, debated at the Paris Conference (Kafka 1973), may somewhat obscure the issue in the comparison between the Argonne- Maryland and Munich-Frascati experiments. The correlation of Weber's (1969) res~llts with geophysical phenomena may indicate, at least, that the Argonne-Maryland detectors record physical events. The same events should also be seen by similar apparata.

The University of Glasgow results indicate that Weber's (1969) events were unlikely due to pulses of gravitational radiation a few ms long. They do not exclude the possibility that the Argonne-Maryland detectors did record much longer bursts of gravitational radiation.

Several objections have been frequently moved to the electronics or other aspects of the experi- mental setup of Weber's experiments. However, Weber's analysis of the noise performance of his electronics (Weber 19706) has been inde- pendently confirmed (Garwin and Levine 1973), while questions regarding calibration scheme, data analysis, and the Argonne-Maryland tele- phone link have been recently reinvestigated and answered negatively (Weber et al. 1973): The

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'? , ,

i TABLE 3. Sources . ... .. .

Frequency' Flux at a : earth Q, Observable Detection Other

Type Hz ; erg/cm2 s (11) Existence (1 973) scheme characteristics

Binary stars 2 .5 x 1 0 s 3 I . I x 10-'O 1 . 4 x Real Not yet Wide band detectors, Continuous (Wz Sge) (i Boo) (i Boo) free masses in space,

laser interferometry Birth of neutron lo3 to 104 lo7 to 10'0 2 x l o - ' t o Real At the present Mechanical reson- Pulses s to a stars from super- 1 0 - l 7 limit ators of Weber type, few seconds long, novae-in our almost free masses infrequent (perhaps galaxy once every lo2 yrs) -in galaxies to 10 to 10" 2 x to Real Not yet Mechanical reson- More frequent distance -10 Mpc ators Weber type (perhaps once every

and type 11, almost month) free masses

Pulsars o G 60 3 x < 0.7 x G Real Not yet Mechanical sonators Continuous ( N P 0532) 4, < 3 x lo-7 (IT) 2 0 . 7 x of I1 type, wideband

lo-24 antennas Pulsars a few days 1 o3 I lo-" Real Not yet Mechanical reson- Infrequent after birth ators, wide band -in our galaxy antennas. almost

free masses -in the Virgo l o - c lo -z5 Real Not yet As above One neutron star cluster should be born

every month Asymmetric (1.5 x lo6 (8.6 x x Predicted Observable for Mechanical Pulses s to a .gravitational collapse

Black hole I O - ~ G o G M - 105 to lo8 M g at the center of Galaxy Condensation of 10- l 5

galaxies Explosions in to lo -5 distant quasars and galactic cores

every time it swallows a star of mass -1 M g Q, 5 10-2

sufficiently resonators few s long large M

Conjectured Not yet Wide band, detectors, Of great astro- superconductors physical interest

(11) G l o - 7 Predicted Not yet Free masses in space, superconductors

(11) 5 lo-2' Real Not yet Free masses in space, Broad band superconductors

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PAPINI: GRAVITATI ON.4L RADIATION 899

significant excess of coincidences over accidentals remains.

T h e situation clearly calls for more experi- mental and theoretical work.

also, flux quantization in superconductors may prove useful in this connection in the no t t o o distant future.

T h e development of wideband detectors should deserve particular attention. As previ- ously mentioned, information about the wave is lost in the detection with mechanical resonators. It would be, o n the contrary, very useful t o acquire information about the spectruni of the radiation a n d the shape of the burst. All this can be d o n e only with wide band detectors, a l though mechanical resonators of the type

5. Conclusions T h e existence of gravitational radiation has

been predicted by almost every theory of gravitation, a n d niany astrophysical objects may emit it, a t least in theory. T h e problem is a t the moment almost exclusively experimental, a n d guidelines for experimental strategies should perhaps be developed. F o r some time yet increases in detector sensitivity a re desirable, a n d should be expected ~ ~ n t i l the facts a re firmly established. M u c h can still be d o n e t o improve

proposed by Aplin can have large bandwidth a n d a re capable of resolving the structure of very short pi~lses of radiation. Then, entirely new experimental approaches may be developed over

the sensitivity of mechanical resonators (Bonaz- zola a n d Chevreton 1973). Cryogenic resonators, when fully developed, will probably enable the rneasurenient of strains of to

the next few years. This new experimental field is wide open, a n d perhaps the interested experi- mentalist may like t o choose from Table 3 the f r e q ~ ~ e n c y range in which t o work a n d develop

Most resonators, either in operation o r under construction, a re limited for several reasons t o the lo3 H z f r e q ~ ~ e n c y band. Sources of extreme

his own detector. H e might, however, end LIP observing entirely different sources, even as- sunling the correctness of Weber's conclusions.

astrophysical interest, like pulsars shortly after birth a n d stars tlndergoing gravitational collapse, emit presumably in this frequency range.

Other interesting sources may radiate a t lower

There I S , in fact, n o field of human endeavor yet in which man's creativity equals nature's variety.

Finally, if, by increasingly improved experi- nients and the determination of ever decreasing

frequencies. Pulsars in o u r galaxy o r in others, for instance, could emit gravitational radiation in the 0. I t o 100 H z frequency range. Mechanical resonators of Weber type operating a t about 100 H z could, in principle, be constructed but would be unmanageable because of the large dimensions. Mechanical resonators of the second type, proposed by Douglass a n d Tyson, could be

upper limits fo r the flux a t the detector o n e could rule o u t the existence of gravitational radiation, then this a lso would constitute a contribution of great importance. According t o information theory the lesser the probability of a n event, the greater the inforniation attached to it.

Acknowledgments very useful for this purpose together with the almost free mass device proposed by Braginskii and Rudenko.

It is a pleasure t o thank Drs. K . Maischberger a n d W . Winkler of the Munich-Frascati g r o u p a n d Prof. G . Pizzella of the R o m e group for interesting conversations a n d exchange of infor- mation.

A t lower frequencies still, binary stars, ex- plosions in distant quasars , and galaxies, a n d matter falling in to large black holes a t the center -

- of gaTaTi'es may bi ' r t?$~nsible for the emission Part of this work has been written while the au thor was visiting the Space Astrophysics Laboratories in Frascati. It is a pleasure t o thank Professors L. Gra t ton a n d V. Castellani for their kind hospitality.

A National Research Council of C a n a d a Travel Fellowship is gladly acknowledged.

of considerable arnoun-ts of rrravitational radia- " tion. Primordial gravitational radiation of ap- proximately I M p c wavelength may have been emitted when the galaxies condensed o u t of the expanding primordial gas. The phenomena associated with many of these sources a re of extreme cosn~ological importance a n d (nay not be observable by other means. Free masses in

ADAMYANTS. R. A , , ALEKSEEV, A. D., and KOSOSNITSYN, N. 1. 1972. JETP Lett. 15, 194.

ANDERSON, A. J . 1971. Nature, 229,547. APLIN. P. S. 1972. J . Gen. Rel. Grav. 3, I l l . B A H C A L L , J. N. and DAVIS R. 1971. Phys. Rev. Lett. 26,

662.

space, and laser interferometry over large distances, may have t o be developed in order t o observe these sources. In the author 's opinion,

Can

. J. P

hys.

Dow

nloa

ded

from

ww

w.n

rcre

sear

chpr

ess.

com

by

99.2

34.1

12.9

9 on

03/

31/1

4Fo

r pe

rson

al u

se o

nly.

900 C A N . J . P H Y S .

BARDEEN. J. M. 1970. Nature. 226, 64. BARTON. R.. KOS, J. , P A P I N I . G., PACHNER, J . . RAMA-

D A N . B.. TWARD, E..and WOLFSON, J. L . 1972. Paper presented at the 4th Cambridge Conference on Ex- pel-imental Relativity. M.I.T., Boston (and Physics in Canada. 28.43).

BARTON. R.. KOS. J., P A P I N I ~ G . , RAMADAN. B., TWARD. E., and WOLFSON. J. L. 1973. Physics in Canada, 29, 23.

BEKENSTEIN. J. D. 1973. Phys. Rev. D. 7.949. BERGMANN. P. G. 1971. Phys. Rev. Lett.26, 1398. BER.~OTTI. B. and CAVALIERE. A. 1970. Nuovo Cimento

B. 2,223. BERTOTTI, B., CAVALIERE. A,, and PACINI , F . 1969. Na-

ture. 221.624. BOCCALETTI, D., DE SABBATA, V., FORTINI. P.. and

GUALDI . C. 1970. Nuovo Cimento B, 70, 129. BONAZZOLA. S. and CHEVRETON. M. 1973. Phys. Rev. D,

8,359. BRAGINSKII , V. B. 1966. Sov. Phys.-Usp. 8, 513. - 1968. Sov. Phys.-JETP. 26,83 I. - 1972. JETP Lett. 16, 102. BR.AGINSKII. V. B. and MENSKII . M. B. 1971. JETP Lett.

13.417. B R A G I N S K I I . V. B. and RUDENKO, V. N. 1970. Sov.

Phys.-Usp. 13. 165. B R A G I N S K I I . V . B.. M A N U K I N , A. B.. POPOV, E. I . ,

RUI>ENKO. V. N.. and KHOREV. A. A. 1972. JETP Lett. 16. 108.

B R A G I N S K I I . V. B.. ZEI.DOVICH. YA. B.. and RUDENKO. V. N. 1969. JETP Lett. 10.280.

BRAMANTI. D. and MAISCHBERGER. K. 1972. NLIOVO Cimento Lett. 4. 1007.

BR..\NS. C. and DICKE. R. H. 1961. Phys. Rev. 124. 925. BURKE. W. L. 1971. J . Math. Phys. 12.402. CAMERON. A. G. W. 1970. Ann. Rev. Astron. Astl-ophys.

8. 179. CAMPOLATT,\RO. A. i~nd THORNE, K. S . 1970. Astrophys.

J. 159. 847. CEAPA. A. 1972. Nature (Phys. Sc.), 240. 102. CHANDRASEKHAR. S. 1970tr. Phys Rev. Lett. 24,611. - 1970h.(.. Astrophys. J. 161. 561, 57'1. CHANDRASEKHAR. S . and E s w s l ~ o . F. P. 1970. As-

trophys. J . 160. 153. C H A R M A N . W. N. ,JELLEY, J . V.. F R U I N . J. H.. HODGSON,

E. R.. SCOTT. P. F. . SHAKESHAFT, J . R., BAIRD, G. A.. DELANEY, T . , LAWLESS. B. G., DREVER, R. W. P., MEIKLE, W. P. S.. PORTER. R. A.. and SPENCER. R. E. 1970. Nat~lre, 228.346.

CHITRE, D. M. and PRICE. R. H. 1972. Phys. Rev. Lett.29.

-. - - . . - *z%- .ev . ---185.- , , . - . - CHRISTODOULOU. D. 1970. Phys. Rev. Lett. 25, 1596. COOPERSTOCK, F. 1. and BOOTH. D. J. 1969. Phys. Rev.

187, 1796. DAVIS, M., RUFFINI , R., PRESS. W. H., and PRICE, R. H.

1971. Phys. Rev. Lett. 27, 1466. DAVIS. M., RUFFINI. R. and TIOMNO. J . 1972rr. Phys. Rev.

D. 5.. 2932. DAVIS. M. RUFFINI , R., TIOMNO. J. , and ZERILLI , F..

19726. Phys. Rev. Lett. 28, 1352. DE LA CRUZ, V. . CHASE, J. E., and ISRAEL, W. 1970. Phys.

Rev. Lett. 24,423. DEWITT; B. S. 1962. 111 Gravitation: an introduction to

current research,etl.Oy L. Witten.(J. Wiley and Sons, New York).

VOL. 5 2 , 1974

1966. Phys. Rev. Lett. 16, 1092. DICKE, R. H. 1964. I11 Relativity, groups and topology, etl.

by C. DeWitt and B. S. DeWitt (Gordon and Breach, New York).

DOUGLASS, D. H. and TYSON, J. A. 1971. Nature, 229,34. 1972. Astrophys. J . 178,341.

DREVER, R. W. P. 1971. Paper presentedat the 6th Interna- tional Conference on Gravitation and Relativity, Copenhagen.

DREVER. R. W. P.. HOUGH, J. , BLAND, R., and LESSNOFF, G. W. 1973. Nature, 246,340.

EINSTEIN, A. 1916. Sitz. Pre~lss. Akad. Wiss. 688. - 1918. Sitz. Preuss. Akad. Wiss. 154. E z ~ o w . D. H., WALL, N. S., WEBER. J. and YoDH.G. B.

1970. Phys. Rev. Lett. 24,945. F A I R B A N K , N. M. 1971. Paper presented at the 6th Interna-

tional Conference on General Relativity and Gravita- tion, Copenhagen.

F A U L K N E R , J. 1971. Astrophys. J . 170, L99. FAULKNER. E. A. ilnd BUCKINGHAM. M. J . 1972. Elec-

tronics Lett. 8. 152. FERRARO, V. C. A. 1954. Astrophys. J . 119.407. F IELD, G. B.. REES.. M. J.. and SCIAMA. D. W. 1969.

Comm. Astrophys. Space Phys. 1, 187. G A R W I N , R. L. and LEVINE, J. L. 1973. Phys. Rev. Lett.

31. 176. GIBBONS,G. W. 1971. Nature(Phys. Sc.),230, 113. GIBBONS.G. W. and HAW KING.^. W. 1971. Phys. Rev. D,

4.2191. G 1 8 e o ~ s . G . W. and SCHUTZ, B. F. 1972. Mon. Not. Roy.

Astron. Soc. 159,41P. GOLD. T. 1969. Nature, 221, 25. HAMILTON, W. 0 . 1972. Paper presented at the 4th Cam-

bridge Conference on Experimental Relativity M.I.T.. Boston.

HARTLE, J. B. and THORNE, K. S. 1968. Astrophys. J. 153. 807.

H A W K I N G . S . W. 1971. Phys. Rev. Lett. 26. 1344. IPSER. J. R. 1971. Astrophys. J . 166. 175. JACKSON. J. C. 1972. Mon. Not. Roy. Astron. Soc. 156, IP. JORDAN. P. 1955. Schwerkraft und Weltall (Vieweg und

Sohn, Braunschweig). '1959. Z. Phys. 157, 112.

KAFKA, P. 1970. Nature 226,436. - 1973. Paper presented at the Colloque International

C.N.R.S. No. 220 "Ondes et Radiation Gravitation- nelles." Paris.

KOPVILLEM. V. KH., NAGIBAROV, V. R., SAMARTSEV, V . V., and ZELDOVICH, S. A. 1972. Spectrosc. Lett. 5 , 53.

LANDAU, L. D. and LIFSHITZ, E. M. 1962. The classical theory of fields ( Addison-Wesley Publishing Co., Inc., Reading).

LAVRENT'EV,G. YA. 1969. JETP Lett. 10,318. 1970. Sov. Phys.-Techn. Phys. 14,989.

LAWRENCE, J . K. 1971. Phys Rev. D, 3,3239. 1973. Phys. Rev. D, 7,2275.

LEVINE, J . L. and G A R W I N , R. L. 1973. Phys. Rev. Lett. 31, 173.

LUPANOV, G. A. 1967. Sov. Phys.-JETP, 25,76. LYNDEN-BELL, D. 1969. Nature, 223,690. LYNDEN-BELL, D. and REES. M. J. 1971. Mon. Not. Roy

Astron. Soc. 152,461. MAEDER, D. G. 1971. Electronics Lett.7, 767.

1972. Electronics Lett. 9, 198.

Can

. J. P

hys.

Dow

nloa

ded

from

ww

w.n

rcre

sear

chpr

ess.

com

by

99.2

34.1

12.9

9 on

03/

31/1

4Fo

r pe

rson

al u

se o

nly.

PAPINI: GRAVITAI

MELOSH, H. J . 1969. Nature, 224, 781. MIRONOVSKII, V. N. 1965. Sov. Phys.-JETP, 21,236. MISNER, C. W. 1972. Phys. Rev. Lett. 28, 994. MISNER, C. W., BREUER, R. A,, BRILL, D. R.

CHRZANOWSKI, P. L., HUGHES, H. G., 111, and PEREIRA, C. M. 1972. Phys. Rev. Lett. 28,998.

MISNER, C. W., THORNE, K. S . , and WHEELER, J. A. 1973. Gravitation(W. H. Freeman and Co., San Francisco).

MODENA, 1. 1973. Paper presented at the Colloq~le Interna- tional C.N.R.S. No. 220 "Ondes et Radiation Gravitationnelles." Paris.

Moss, G. E. 1971. Appl. Optics, 10,2565. Moss, G. E., MILLER, L. R., and FORWARD, R. L. 1971.

Appl. Optics, 10, 2495. NAGIBAROV, V. R. and KOPVILLEM, V. KH. 1969. Sov.

Phys.-JETP, 29, 112. OSTRIKER. J. P. and G U N N , J. E. 1969. Astrophys. J. 157.

1395. PACZYNSKI, B. 1967. Actn Astr. 17,287. P A P I N I , G. 1966. Nuovo Cimento,45,66.

1967. Nuovo Cimento Lett. B. 52, 136. 1970tr.h. Nuovo Cimento Lett. 4,633, 1027.

- 1974. To be published. PARTRIDGE, R. B. 1971. Phys Rev. Lett.26,912. PENROSE, R. 1969. Riv. Nuovo Cimento, 1.252. PENROSE, R. and FLOYD, R. M. 1971. Nature (Phys. Sc.),

229. 177. PETERS. P. C. 1964. Phys. Rev. B, 136. 1224.

1970. Phys. Rev. D, 1. 1559. 1972. Phys. Rev. D, 5,2476.

PETERS, P. C. and MATHEWS-J. 1963. Phys. Rev. 131,435. PIZZELLA, G. 1972. Paper presented at the 4th Cambridge

Conference on Experimental Relativity, M.I.T., Bos- ton.

PRESS, W. H. 1971. Astrophys. J. 170, L105. PRESS, W. H. and TEUKOLSKY, S. A. 1972. Nature, 238,

211. PRESS. W. H. and THORNE. K. S . 1972. Ann. Rev. Astron.

Astrophys. 10.335. PRICE, R. H. and THORNE, K. S. 1969. Astrophys. J . 155.

163. RASBAND. S . N., PIPES, P. B., HAMILTON. W. 0 . . and

BOUGH,^. P. 1972. Phys. Rev. Lett. 28.253. REES, M. J. 1971. Mon. Not. Roy. Astron. Soc. 154, 187. REINES, F., KROPP, N. R., LANDDECKER. P., SANDIE.

W. G., LATHROP, J. . SOBEL, H. W., CROUCH, M. F., BOURNE, D., COXELL, H., KRAMER, D.. and SELLSHOP, J. P. F. 1971. Phys. Rev. Lett. 26, 1451.

RUFFINI. R. 1972. Les Houches lectures. To be published. 1973. Phys. Rev. D, 7,972.

RUFFINI, R:-andWHEELER,J. A. 1971.I11 The significance - . - -.-'b'f-Fpace resear& foi f~ndamenta l physics, Proceed- ings of an ESRO Colloquium, ESRO SP-52, European Space Research Organization, Paris.

SCIAMA, D. W. 1969. Nature, 224, 1263. S C I A M A , D. W., REES, M. J. , and F IELD,G. B. 1967. Phys.

Rev. Lett. 23. 1514. S INSKY, J. 1968. Phys. Rev. 167, 1145. SINSKY, J. and WEBER, J. 1967. Phys. Rev. Lett. 18,795.

U O N A L RADIATION 901

Solar Data, 1968. No. 12. Solar Data, 1969. Nos. 1-3. Solar-Geophysical Data, 1968, 69. Data Center A, Upper

Atmosphere Geophysics (ESSA, Boulder). STRUVE. 0 . 1950. Stellar evolution (Princeton University

Press. Princeton). THORNE, K. S. 1969ti.h. Astrophys. J . 158, 1 , 158. THORNE, K. S . and CAMPOLATTARO, A. 1967. Astrophys.

J. 149,591. 1968. Astrophys. J . 152,673.

TRIMBLE, V. A. 1972. Proceedings of the 6th Texas Sym- posium on Relativistic Astrophysics, New York. To be published.

TYSON, J. A. 1973. Phys. Rev. Lett.31.326. TYSON. J. A. and DOUGLASS, D. H. 1972. Phys Rev. Lett.

28. 99 1. TYSON, J . A. and MILLER, G. L. 1972. Preprint. TYSON, J. A,. MACLENNAN. C. G.. and LANZEROTTI, L. J .

1973. Phys. Rev. Lett. 30, 1006. VILA, S . C. 1971. Nature(Phys. Sc.),230,39. WEBER, J. 1961. General relativity and gravitational waves

(Interscience Publishers, New York). - 1962.111 Proceedings of the International School of

Physics Enrico Fermi. Co~lrse XX (Academic Press, New York). - 1966. Phys. Rev. Lett. 17. 1228.

1967. Phys. Rev. Lett. 18,498. 1968. Phys. Rev. Lett. 20, 1307. 1969. Phys. Rev. Lett. 22. 1320. 1970ti. Phys. Rev. Lett. 24, 276. 1970h. Phys. Rev. Lett. 25, 180. 1970~. Nuovo Cimento Lett. 4,653. 1971ti. Phys. Lett. A, 34,271. 1971h. Nuovo Cimento B,4, 197. 19720. J . Gen. Rel. Grav. 3, 59. 197211. Nature. 240.28.

WEBER,J . and TRIMBLE. V. 1973. Phys. Lett. A,45,353. WEBER, J., LEE, M., GRETZ, S. J., RYDBECK, G., TRIM-

BLE, V. L..and STEPPEL, S. 1973. Phys. Rev. Lett.31, 779.

WHEELER, J. A. 1960.111 Proceedings of the International School of Physics Enrico Fermi, Course XI (Zanichelli, Bologna).

WHEELER. J. A. and SCHWARZSCHILD, M. Private com- munication quoted in Weber 1961. p. 137.

WINTERBERG, F. 1968. Nuovo Cimento B. 53.264. WYLLER, A. A. 1970. Astrophys. J . 160,443. ZAKHAROV, V. D. 1973. Gravitational waves in Einstein's

theory (Halsted Press, New York). ZEE. A. and WHEELER, J. A. 1966. Annual Rev. Astron.

Astroph. 4,423. ZELDOVICH, YA. B. and NOVIKOV, I. D. 1970. Sov.

Astron.-AJ, 13,754. 1971. Relativistic astrophysics, Vol. 1 (University

of Chicago Press, Chicago). ZERILLI . F. J . 1970. Phys. Rev. D, 2,2141. ZIPOY, D. M. and BERTOTTI, B. 1968. Nuovo Cimento, B,

56, 195.

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