The resonant antenna network. A review

Nuclear Physics B (Proc. Suppl.) 28A (1992) 48-53 North-Holland

~,~`O GM3 U~

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THE RESONANT ANTENNA NETWORK. A REVIEW Guido PIZZELLA Physics Department, University of Rome Institute for Nuclear Physics, Rome The basic features of resonant antennas for the search for gravitational waves are reviewed. These antennas detect the Fourier component of the metric tensor perturbation h(t) at the antenna resonance. By means of optimum filters it is possible to reach a sensitivity which, for short bursts of gravitational radiation, is basically limited by the noise of the electronic amplifier. Ore cryogenic antenna with mass M = 2300 kg and temperature T = 20 mK should have a sensitivity, for short bursts, of the order of hm ;n ^r 3 x 10 -21. A brief review of the activity going on all over the world by the experimental groups working with resonant antennas is given. At present three cryogenic resonant antennas are in operation: the Louisiana State University antenna and Explorer and Altair of the Rome group.

1. INTRODUCTION

The gravitational wave (g .w.) experiments started

with Joe Weber at the University of Maryland in the early sixties. VVeber worked alone for about ten years and finally he showed experimental evidence for coincidences between two g.w . antennas located at large

distance between them, one in Maryland and the other one at the Argonne Laboratory. Althought it appeared

difficult to interpretate Weber's results in terms g.w ., various other groups tried, in the period 1970-1975, to

repeat the experiment with similar techniques, which consisted in using ton heavy alluminium bars at room

temperature, equipped with piezoelectric ceramics for the detection of the bar small vibrations . They did not confirm Weber's observations ; however, in the writer's opinion, no group obtained experimental data that could clearly show Weber was wrong.

As matter of fact other groups entered in the field, developing new techniques, in spite that, if the g.w.sources were just those predicted by the General Relativity (GR), no hope to detect them existed before several tens of years. In particular, the groups of Stanford, Louisiana State and Rome Universities started in 1971 to construct cryogenic antennas, and the groups of MIT, Max-Planck in Munich and Glasgow University started, around 1975, to develop laser interferometers.

The most important final goal for all groups is to reach a sensitivity such to be able to detect gravitational collapses occurring in the Virgo Cluster. Although many

progress have been made, this goal appears to be still very far.

As well known, the reason for this difficulty is the extreme weakness of the signal due to the gravitational force as compared with the noise due to the other forces in Nature .

The milestones

that

mark

the experimental

progress in the resonant detector development are, after the initial work of Weber: -in 1982 the sensiti

vity reached by the Stanford group with their cryogenic antenna', -in 1986 and finally in 1990 the steady

operation reached by the Rome group with a similar antenna2 ~ 3,4,5 . Finally, only in may 1991 two large cryogenic antennas entered in simultaneous and continuos

operation with high sensitivity : the Explorer antenna of the Rome group and the Louisiana (LSU) antenna.

The search for coincidences between these two an-

tennas has just started, marking a new phase in this

fascinating field of fundamental physics. 2. THEORETICAL ASPECT

We recall, very briefely, how the g.w. are predicted

in GR. Starting with the Einstein non-linear equations,

in the unknown metric tensor for of the type

g ;k,

the solution is looked

+ h ;k, where gild is the minkowskian metric tensor and hck is a tensor whose g;k

=

gik )

component absolute values are much smaller than unity. This is caned the weak field solution . The Einstein

equation becames the linear d'Alembert wave equa-

0920-563Z9M .00 0 1992- Elsevier Science Publishers B.V All rights reserved.

G. Azzella / The resonant antenna network

tion in the unknown h;k. Making use of the tracelesstransverse gauge, that is similar to the Lorentz gauge in electromagnetism, and choosing the most convenient reference system, it can be shown that the metric tensor h=k has only two independent components. For a plane wave propagating in the x direction we have hyz = h ty = hx hyy = -hzz = h+ The above quantities are functions of the argument t - x/c, all other components are zero. Notice that the g.w. propagate with the speed of light c and they are transverse. It can be also shown that, because of the conservation laws, the g.w. can be associated to a particle with spin 2 (the mass is obviously zero): the graviton . Therefore the two polarization states are changed one in the other by a spacial rotation of 7x/4 . The g.w. are not a unique feature of GR. In fact, it could be shown that any metric theory of gravity, which incorporates the Lorentz invariance in its field equations, foresees the propagation. of g.w. The speed and the polarization status will depend on the particular theory. G.w . are generated by the movement of gravitational masses. The irradiated power has a null dipole term, because of the momentum conservation law . The first non-zero term is the quadrupole one . For this reason, and also because of the small value of the gravitational constant G, the irradiated power is so small that, at present, it i-3 'PA possible to detect the g.w. that could be generated in an earth laboratory. It is necessary that the source be constituted by enormous masses moving with extreme accelerations. Astrophysical sources, like supernovas for instance, are, therefore, the best candidate supply of g.w. We distinguish between continuous and impulsive sources . Example of countinuos sources are the pulsars and the binary systems . In the first case it is necessary that the rotating collapsed star be non-spherical, in order to have a time varying mass quadrupole. Possible values for the metric tensor perturbation could be of the order of h - 10-26 - 1027, time-varying with twice the pulsar frequency . In the second case there should

49

always be a generation of g.w., but with very small frequency, well ouside the presently explored range. For the impulsive sources the most interesting one is the supernova. It is very difficult to gum the degree of non-sphericity during the collapse. If we assume that a fraction M9 .c2 of all available energy M.t.,9 is entirely converted into g.w., it is found, at a distance R on the Earth

h ... = 3 .11

1

Rr79

1 kHz 10 Mpc v9 R

10-20

8GMg. ~ C r9 Mgm i "Is Mp r9

where r9 = 1 ms is the typically assumed duration of the g.w. burst and v9 is the antenna resonance frequency. If the source is located at the center of our Galaxy we obtain for M9. = 10 -2Mo : is - 3 10_r a . If the source is located in the Virgo Cluster we get h - 3 10-21. 3. THE RESONANT ANTENNA This detector is, typically, a metallic cylindrical bar, usually of high quality alluminium alloy (for the Perth experiment the material is niobium, which has higher Q). For capturing as more energy as possible from the g.w. the mass ofthe bar needs to be as large as possible. The LSU-Rome-Stanford collaboration uses bars 3 m long, weighting about 2500 kG. When the bar is hit by a g.w. burst with amplitude h(t) and duration starts to vir9 impinging perpendicularly to its axis, it resonance modes that are coupled to the brate at those g.w. The odd longitudinal modes are the most coupled ones. The first mode has frequency vo = 7rv/L, about 900 Hz for the above considered bars (v = 5400m/ s is the sound velocity in alluminium) . The vibration amplitude, at its ends, is

40

^ 2

2

e Tv h(t)

r9

wo sir (wot)

where r,, is the relaxation time related to the merit factor r,, = Q/wo. A quick calculation for a supernova in the Galaxy gives the unthinkable very small value

G. Pizzefla / Theresonant antenna network

50

~(t) s: 3 10-18m. The maximum energy associated to this vibration is E=4Mw2~0=

from which we derive

2 4 Lv h2 r9

h_ 1 _LV_E rg v2

M

For M = 2300 kg, L = 3 m, r9 = 1 ms, for a g.w. coming from the galactic Center (h = 3 10+ 1'8 ) we obtain E = 2.7 10-24joule = 0.2 kelvin. If the same g.w. comes from the Virgo Cluster we get E = 2 10-3° joule = 1.4 10-7kelvin . The values in kelvin are usually given in order to compare this small signal with the noise of the apparatus that it is more convenient to express in kelvin units. The bar vibrations are detected by means of an electromechanical transducer followed by a very low noise amplifier. In the pioneering work by Weber the transducer was a piezoelectric ceramic (PZT ). Today most of the transducers are inductive or capacitive pickups. The capacitive transducers (used by the Rome group) consists in a metallic capacitor, one plate of which has a resonance frequency equal to that of the bar, thus forming, with the bar, a two coupled oscillator system. The oscillation energy is then transferred back and forth between the bar and the transducer. In this way all the mechanical energy available in the bar is also available in the transducer. The inductive transducer7 (used by the LSU and Stanford groups) is also coupled to the bar in a similar way. One very important property of the transducer is the ratio ,Q between its electrical energy and its mechanical energy . In passive transducers clearly ,0 < 1, in active transducers 0 can be larger than unity, but an additional energy source with its own noise is needed. The signal is embedded in noise. Most of the noise can be reduced only by comparing the data taken ,-.,ith two independent antennas located very far one from each other. Some noise can be also reduced by taking proper precautions and with a suitable data analysis . The data analysis allows to red'ice considerably two of the most important noises : t:,A coming from

the thermal motions of the bar constituents (brownian noise) and that due to the electronic amplifier (electronic noise). The electrical signal from *he transducer is amplified and then processed by means of optimum filters in order to make the signal to noise ratio (SNR) as large as possible. It can be shown that if one looks for signals due to short bursts of g.w. as described above, then the minimum vibration energy of the bar that can be detected with SNR = 1 is, in a simplified treatment, kTeff ;t; kTIQQ + 2 kT,,

(6)

where T,, is the noise temperature of the electronics and T is the bar temperature . It is clear that T and T,, must be as small as possible and PQ must be large. For the PZT ceramic PQ cannot be larger than a few hundred, while for the resonant transducers one should be able to obtain QQ values up to 105 . As far as Tn a FET amplifier can have, at best, Tn . 0.1 K. The SQUID amplifier could go down to the quantum limit, that is T .^: 10-' K, but it is extremely difficult to properly match this very low noise amplifier to the transducer . By lowering the bar temperature to T = 40 mK, with ,ßQ ;z:: 106 and T,, , 10 -7 K one could get Teff 2 10-7 K that should allow to observe the collapses in the Virgo Cluster . 4. A RESONANT ANTENNA REVIEW All over the world there are several groups preparing experiments for detecting gravitational waves. Resonant antennas are being prepared by the following groups ( listed by continent in the eastward direction starting from Maryland ): Maryland, Stanford, Louisiana, Rome, Legnaro, Moscow, Tokyo, Canton and Perth . 4.1 . Maryland In addition to operate two room temperature antennas, they are constructing an Al cryogenic antenna with M ---= 1400 k9, to be cooled at T = 4.2 K. They also have plans to cool down to T < 0.1 K with a dilution refrigerator. A special emphasis is put on the development of a three mode resonant transducer 8, with the purpose to further increase the Q factor.

G. Azzella / The resonant antenna network

4.2. Stanford In 1982 the Stanford group' realized a cryogenic (T = 4.2 K) Al bar of M = 4800 kg and v -841 .7 Hz connected to a resonant inductor supercon ducting transducer7 followed by a GHz SQUID. They obtained Te ff = 20 mK , corresponding to h 810 -' 9 . This detector was damaged by the earthquake in 1989. They decided to continue their research by constructing a similar antenna cooled to T < 0.1 K by means of a dilution refrigerator. The first cooling is expected early in 1992. 4.3. Louisiana This group has been successful in putting, in may 1991, in continuos operation a g.w. antenna that is, today, the most sensitive one in the world . The antenna is made of 5056 Al alloy, M = 2400 kg, L = 3 m, frequency around 912 Hz, equipped with an inductive resonant transducer followed by an acSQUID . The noise is Tef f = 3.5 mK, corresponding to h -_ 4 10-19, and has a very good distribution, in terms of the brownian ed electronic contributions . Data are now recorded in order to do a coincidence analysis with the data of the Rome antenna. 4.4. Rome In the period from December 1985 to March 1986, the Rome group 2,3,4 has operated a cryogenic (T = 4.2 K) Al 5056 bar of M = 2270 kg, n = 915 Hz, equipped with a resonant capacitive transducer followed by a dcSQUID, and has obtained an effective temperature of the order Te f f = 10 mK, corresponding to h ;:t~ 810 -' 9. This antenna, called EXPLORER, started to operate continuosly only at the end of June 1991 at a temperature T = 3 Ks. Many years of work were needed for reaching the planned sensitivity and, a much more difficult task, to achieve the required reliability for steady performances over long and continuous periods of time. The performance of the detector is well illustrated in fig . 1.

52 1991

h

10` 8

t

j anuary

w

~+V1,.~"~ r Lr~i

10 le

fetruary

10 8

~ Ta-en 3

10 18

-: r

10-18

.

10 `e

1

0

-

A04.M_Q;i -

vs . 5

W

10

15 20 day of the month

25

30

FIGURE 1 Hourly averages of the antenna sensitivity expressed by

35

h

(see

text) .

Here we report the hourly averages, versus time, of quantity the h calculated, during a period ofsix months, with the following formula obtained from eq. (5) h = 2.52 10-19

Tef f

with Te ff (hourly average) :a mK . This value of h ( called "conventional" because it is based on the assumption of a g.w. burst lasting 1 ms ) indicates the intensity of a g.w. which would produce a signal with energy Te ff . These data extend over a period of more than one year, but the detector was recording data for 2/3 of the total time. The rest of the time, which appears in the figure as gaps between periods of data taking, was devoted to refillings with liquid nitrogen and liquid helium, and to several tests of the vacum and electronic apparatus . In future this dead period should be reduced to about 25%, hopefully less. Thus, in Fig 1 we have reported all the recorded data, including periods during which the detector was operating very satisfactory as well as those when some disturbance occurred . With respect to the past the sensitivity appears to be definitively better, well below the 10-'8 threshold. Usually the SQUID working conditions are very stable ; in fact the stability of the system

52

G. Auella / The resonant antenna network

is the real improvement in the antenna operation . From the entire period of measurement we have taken one typical period that lasts 16 hours on 3-4 September 1990. We have plotted in Fig. 2 the integral spectrum of the h values obtained with sampling time of 0.3 seconds. We notice a few "events" outside the expected noise distribution . EXPLORER

16 hours of Cata

3-4 sept. 199o

n E 0

0 L O

a E

FIGURE 2

Integral distribution versus h (see text) for a given period of time.

It is very much likely that these events are due to unknown noise. Since the seismometer mounted on the Explorer cryostat does not indicate any mechanical disturbances we believe that these events are due to electromagnetic noise probably coming from the large accelerators of CERN. However it is very interesting to calculate how a g.w. signal would appear in Fig . 2 if it happened that a certain amount of matter Mg, located in the Galactic Center was converted into g.w. Using formulas (2) and (5), where in place of Te ff we have put the energy E of the events, we obtain lvlgw/ltilo = cR2 7r2k/8Gv 2rg M Mo = 3.93 10-5E with E is expressed in mli . Thus we see that an event with E = 300 mK could be due to a g.w. produced in the Galactic Center by the conversion of about 1% of

a solar mass. This simple calculation just shows that Explorer is indeed sensitive to possible g.w.s produced in the Galaxy. The Rome group is realizing another antenna, called NAUTILUS . This antenna is similar to Explorer, but it will be cooled to less than 0.1 K by means of a dilution refrigerator . Nautilus, fully constructed, has undergone already several test. In february 1991 has been cooled to 95 mK, the smallest temperature ever reached for a body of such large dimensions' . Nautilus will be soon installed at the Frascati National Laboratory of I.N.F.N. Another antenna of the Rome group is the antenna ALTAIR located at tire Institute for Space Physics of CNR, in Frascati. ALTAIR has recently entered in operation, althought some problems related to the long term stability still need to be solved . Altair has M = 389 kg, frequency near 1.800 Hz, T = 4.2 K and is equipped with a capacitive resonant transducer followed by a do SQUID amplifier. At present has a sensitivity Teff = 30 mK, corresponding to h 2 10-18 . 4.5. Legnaro At the Legnaro Laboratory of I.N.F.N. (near Padua) an antenna, called AURIGA, very similar to Nautilus is in construction and will be ready in twothree years. 4.6. Moscow At the University of Moscow they follow two lines: one is the development of very high Q antennas, using crystals like sapphire, the other one is, firstly, to con struct a Weber type room temperature antenna and then to procede with the construction of cryogenic antennas similar to those of the LSU-Rome-Stanford collaboration . 4.7. Tokyo. At the University of Tokyo an antenna has been realized for investigating the continuos g.w . possibly emitted by the Crab pulsar" . The antenna, M = 1200 kg, has shape such to resonate at the right frequency of about 60 Hz and is cooled with liquid helium at T = 4.2 K. They have already reached a sensitivity of about h ;t~ 10-21 and plan to reach h ;t 10-22 with an integration time of about 1000 hours .

G. Pvzella / The resonant antenna network

4.8. Canton. In China they have constructed two Weber type room temperature antennas, and they plan to move towards constructing cryogenic antennas . 4.9. Perth In Australia they are constructing a cylindrical antenna, M = 1400 kg, made of Niobium" . At T = 4.2 K this antenna has very high merit factor, Q -- 2.3 108, and is equipped with a 10 GHz parametric transducer. This antenna should enter in operation early in 1992. REFERENCES 1. S.P.Boughn, W.M.Fa,irbank, R.P.Gifard, J.N.Hollenhorst, E.R.Mapoles, M.S.McAshan, P.F.Michelson, H.J .Paik, R.C .Taber, The Astrophys, J. 261 (1982) 1,19-1,22 . 2. E.Amaldi, P.Bonifazi, P.Carelli, M.G .Castellano, G.Cavallari, E.Coccia, C.Cosmelli, S.Fkasca, V.Foglietti, R.Habel, I.Modena, G.V .Pallottino, G.Pizzella, P.Rapagnani, F.Ricci, Nuovo Cimento, vol. 9C, pp. 829-845, luglio 1986. 3. E.Amaldi, O.Aguiar, M.Bassan, P.Bonifazi, P.Carelli, M.G .Castellano, G .Cavallari, E.Coccia, C .Cosmelli, W.M.Fairbank, S.Frasca, V.Foglietti, R.Habel, W.O.Hamilton, J.Henderson, W.Johnson, A .G .Mann, M.S.McAshan, P.F.Michelson, I.Modena, B.E .Moskowitz, G .V.Pallottino, G .Pizzella, J.C.Price, P.Rapagnani, F.Ricci, N.Solomonson, T.Stevenson, R.C.Taber, B.X.Xu, Astronomy and Astrophysics, vol. 216, pp. 325-332, giugno 1989 . 4. E.Amaldi, P.Bonifazi, P.Carelli, M.G .Castellano, G .Cavallari, E .Coccia, C .Cosmelli, V.Foglietti, S.Frasca, R.Habel, I.Modena, R.Onofrio, G.V.Pallottino, G .Pizzella, P.Rapagnani, F.Ricci, Proc. of 13th Texas Symposium on Relativistic Astrophysics, Ed. M.P.Ulmer, World Scientific, 1819(1987) . 5. E.Amaldi, P.Astone, M.Bassan, P.Bonifazi, M.G.Castellano, G.Cavallari, E.Coccia, C.Cosmelli, S.Frasca, E.Majorana, I.Modena, G.V.Pallottino, G.Pizzella, P.Rapagnani, F.Ricci, M.Visco, Zhu Ning, Europhysics Letters, 12, pp. 5-11 (1990). 6. P.Rapagnani, Nuovo Cimento 5C (1982) 385 .

53

7. H.J .Paik, J.Appl .Phys . 47 (1976) 1168-1178. 8. J.P.Richard, J.Appl.Phys . 60, 3807 (1986). 9. P Astone, M.Bassan, P.Bonifazi, E.Coccia, C.Cosmelli, V.Fafone, S.Frasca, E.Majorana, I .Modena, G.V.Pallottino, G.Pizzella, P.Rapagnani, F.Ricci, M.Visco, Europhysics Letters 16 (1991) 231-235 . 10. Y.Nagashima, S.Owa, K.Tsubono, H.HiraKawa, Rev. Sci . Instrum . 59, 112 (1988) . 11. P.J.Veitch, D.G.Blair, N.P.Linthorne, L .D.Mann, D.K.Rasnm, Rev. Sci. Instrum. 58, 1910 (1987).