Background of gravitational-wave antennas of possible terrestrial origin.-II

IL NUOVO CI~IENTO VOL. 4 C, N. 3 Maggio-Giugno 1981

Background of Gravitational-Wave Antennas of Possible Terrestrial Origin. - II (*).

E. AMALDI a n d S. FRASCA

Is t i tu to di .Fisica dell' Universi td - t~oma, I ta l ia

I s t i tu to Naz iona le di .Fisiea Nuc lea te - Sezione d i l~oma, I t a l ia

G. V. I~ and G. PIZZELLA

I s t i tu to di .Fisiea dell' Universitdt - Roma , I ta l ia

I z t i tu to .Yazionale d i F i s i ca .Yucleare - Sezione di t~oma, I ta l ia I s t i tu to P l a s m a hello Spaz io del C . N . R . - ~'rascati, I t a l i a

13. BOI~IFAZI

Is t i tu to P l a s m a hello Spaz io del C . N . R . - .Frascati, I t a l i a

Is t i tu to Naz ionale di .Fisica Nuc lea te - Sezione di Roma, I ta l ia

(ricevuto il 31 Marzo 1981)

S u m m a r y . - - In order to deepen the analysis of the events recorded during May 1980 by the Frasca t i antenna (see the previous paper), we have Fourier-analysed their t imes of arr ival and found the following periods of free oscillation of the Ear th : Y-(0S~1):55.03, J-(o S+1) : 5 3 . 1 2 ,

Y'(oS~) = 25.84, 3-(oTa)= 28.85 minutes : A similar analysis of da ta collected in June-Ju ly 1978 has shown the following periods: Y'(oS~ 1) = 55.23, Y-(oS3 ~) = 36.23, Y-(o S+2) = 35.30, 3-(oSo) = 20.38--20.61, ~J-(oT2) : 41.18, J (oT~3)=21 .73 , Y-(oT+a)~21.64 minutes. The probabi l i ty for these periods to be accidental in all cases is very small.

1 . - I n t r o d u c t i o n .

I n a r e c e n t w o r k (1), we d i scus sed a few v e r y l a rge s ignals r e c o r d e d d u r i n g

t h e n i g h t s M a y 6 a n d 7, 1980, b y ou r two d e t e c t o r s o p e r a t e d s i m u l t a n e o u s l y ,

(*) The main points of this paper have been presented by G. P~ZZ~LLA at the Workshop on Gravi ta t ional Radiat ion Detectors of the Tenth Texas Symposium on Relat ivist ic Astrophysics, held in Balt imore, Md., December 15-19,1980. (1) E. AMALDI, P. ]~ONIFAZI, E. COCCIA, C. COSM]~LLI, S. FI~ASCA, U. GIOVANAR])I,

309

3 1 0 1~. AMALDI, S. FRASCA~ G. V. PALLOTTINO, G. PIZZ:ELLA a I l d P. BONIFAZI

within few seconds or tens of second delays. One detector was located at the University of l~ome (M = 20.3 kg), the other at the Is t i tu to del Plasma hello Spazio of the C ~ R in Frascat i (M = 389 kg).

The delay between the two signals and the size and frequency of occur-

rence of these (( events )~ disfavour their interpretat ion in terms of gravitat ional

waves originating from extraterrestrial sources. Therefore, we tried to at- t r ibute these signals to trivial sources such as disturbances on the power lines,

variations of the atmospheric conditions, or seismic phenomena recorded by the seismological net of the I s t i tu to ~azionale di Geofisica, etc. All these

sources, however, have been excluded. I n the first paper (*) we also pointed out tha t the ~( time distribution )~ of

these <~ events ~, as they appear in the data recorded in Frascati , suggests the presence of two periods very close to those of the gravest spheroidal free oscillations of the Ea r th ~" (oS~ . ~ ' = 53.1 min and J ' = 54.7 min).

I n this second paper on the same general subject we present the first results of a search, by means of an appropriate Fourier analysis, of possible peri- odicities in the range from J - = 20 miu to J - = 100 min and their statistical significance.

2. - M e t h o d o f a n a l y s i s .

The data under consideration consist of a series of N pulses, taking place

at certain times t1r (k = 1, 2, ..., N), each of which can be described by means of an appropriate delta-function. Therefore, the funct ion we submit to Fourier analysis has the form

N

(1) /(t) = ~ a,~ (~(t -- tk), k = l

where tl~ is the measured <( initial t ime ~) of each pulse (1).

The Fourier t ransform of function (1) is

+ c o

(2) E(eo) =f/(t) exp [-- jcot] dt - -co

with

(3a) Er = ~ a~ cos optiC, k = l

= ~'~ + j F (~o)

2r

F.(~o) = ~ ak sin otk k = l

V. IAFOLLA, I. ~I[ODENA, G. V. I~ G. PizzEezA, P. RAPAGNANI, •. •ICCI, S. UCAZ~O and G. VANNARONI: Nuovo Ciyl, ento C, 4, 295 (1981).

~ A C K G R O U N D O F G R A V I T A T I O N A L W A V E A N T I E N ) T A S ~ T C . - I I 311

and

2 y ~ (3b) iF(co) [2 ~-- F~(co) ~- F~(~o), o) --~ ~ - .

For later use we introduce

27

(4) .M 2 - - IF(~ I~ A 2 ~ a~ -s k = l

Two aspects of this analysis should be considered: the first one refers to the resolution in frequency at tainable by this method, the second one is the

statistical significance of the M 2 values corresponding to possible peaks of the spectrum.

The resolution in frequency is given by the min imum frequency separ~tion~

which is determined by the interval of t ime over which the N events ~re spread:

1 ( 5 ) ~ v - - t ; - - t~ '

corresponding to

( 6 ) n~.~. - - ~ , - -

(( resolvable peaks )) in the considered frequency range v~ -- vB = 1 / ~ - 1 / ~ .

The statistical significance can be computed as follows. Under the assump- t ion tha t the N (( events ~) are distr ibuted at r andom during the (( measuring

t ime )) tin, functions (3a) are stochastic quantities giyen by the sum of N sinu- soidal samples chosen at random.

I n our present case par t of the events is saturated and, therefore, a~ is

known only for some of them. For this as well as for other reasons we have followed the procedure of introducing in expressions (1) to (4)

(7a) a~ -~ 1

so tha t

(7b) A 2 --~ N .

for k ~ 1, 2, . . . , N ,

The random sampling of a sinusoid of ampli tude 1 is a random variable x with probabil i ty density

1 1 (s) L ( x ) - ~ V 1 - - x~

with zero mean value and variance

(9) a~ = 1 .

312 ~ . AMALDI , S. FI~ASCA, G. V. PALLOTTINO, G. PIZZ:ELLA and P. BOIN'IFAZI

B y applying the theorem of the central l imit we obtain, for the probabi l i ty densi ty funct ion of the sum of N r andom samples of sinusoid (i.e. for F and F.), the Gaussian approx ima t ion with zero mean value and var iance

N (lO) (~(N) = ~-.

Since the absolute value of the Fourier t r ans fo rm is given b y the square root of (3b) and i~c(r ) and F.(r are independent variables, the probabi l i ty densi ty funct ion of the values of the p a r a m e t e r M has the fo rm

(11) ]M(M) = ~ exp - - 2 ~ ] .

I f we consider as var iable M s instead of M, we obtain

1 (12) /M~(}/2) = ~ exp [-- Ms] .

I n conclusion, i t follows f rom either (11) or (12) tha t , under assump- t ion (7), the p robabi l i ty of observing accidental ly at a certain value of ~0 a va lue of M2>~M2(~) is given by

(13) p ( > M s) = exp [ - - M2/2a 2] = exp [-- M~],

where (9) has been used in the last equality. I f the number N of events is small, the p rob lem is only slightly more com-

pl ica ted because the Gaussian approx imat ion for the sum of AT samples has

not ye t been reached. Fo r the sake of b rev i ty we shall call the m e t h o d outlined above as Frasca ' s

method.

3. - Ana lys i s o f the exper imenta l data.

The Fourier analysis given in the previous section has been appl ied to two sets of da ta collected with the Frasca t i an tenna (M ---- 389 kg). The first set, the (( May 1980 da ta ~), is the same discussed in our previous publ icat ion for the 5 th longitudinal mode of the an tenna (v5 = 7919.43 Hz) ( table I I of ref. (1)).

I t consists of N = 10 large pulses fulfilling the condition

(14) ~s(vs) >~10 000 K ,

which have been observed during abou t 26 hours (tm = 94 080 s) in the nights May 6-7 and 7-8.

The second set, the (~ 1978 da ta ~), regards measurements t aken in the period

BACKGROUND OF GRAVITATIONAL WAVE ANTENNAS ]~TC. - II 313

June 17 to Ju ly 16, 1978 (about one month : t m ~ 661.83 h ~ 27.58 d), with the first longitudinal mode of the antenna (v, ~ 1795.93 Hz). The pulses considered below fulfil the condition

(15) { ~(vl) > 5000 K

e~(vl) > 1000 K

(for the da ta collected in June 1978),

(for the da ta collected in Ju ly 1978).

These two values have been used to reduce the number of data to be about the same during June and Ju ly 1978. They are listed in table I. l~otice t h a t between June 29 and Ju ly 4 we have improved the mechanical filters under the cryostat .

TABLE Ia) . - Z i s t o] the (~ 1978 even t s ~) observed i n F r a s e a t i . J u n e 1978.

No. B e g i n n i n g of q2 No. B e g i n n i n g of q2

e v e n t (tF)(~) (UT) (K) e v e n t (tF)(~) (UT) (K)

1 1 7 d l h 2 m i n 2 4 s 10762 23 2 5 d 5 h 1 7 m i n 1 6 s 10 928

2 17 15 54 44 8 838 24 25 8 59 0 5 168

3 17 15 58 4 7951 25 25 10 18 59 6703

4 17 16 15 37 7582 26 25 12 32 17 6082

5 17 16 36 45 9864 27 25 15 28 26 13214

6 17 16 52 41 11 676 28 25 15 41 7 7 644

7 17 16 57 44 8771 29 25 23 50 20 8633

8 17 17 22 58 10 675 30 26 3 45 32 10 669

9 18 14 1 25 10858 31 26 15 57 27 6900

10 23 18 13 26 7770 32 26 17 23 0 2 1 2 7 2

11 23 19 35 57 5787 33 26 23 0 9 7 319

12 24 2 34 25 10623 34 28 4 41 53 9257

13 24 3 38 2 7780 35 28 5 21 12 5790

1 4 24 4 52 1 5 10669 36 28 5 46 59 7874

15 24 7 15 48 10 675 37 28 5 54 36 12 300

16 2 4 8 4 34 18268 38 28 17 41 6 5012

17 24 12 37 44 20280 39 28 19 6 47 6 879

18 24 13 40 35 15034 40 28 21 57 3 2 6319

19 24 16 42 46 15449 41 28 22 47 20 6815

20 24 19 4 32 10349 42 29 0 39 3 10 870

21 24 2 2 2 36 10335 43 29 1 16 26 6960

22 24 22 27 22 6499 44 29 6 39 45 8825

(a) Beginning of the sampling interval At = 1 s in which the event appears.

314 [E. A~IALDI~ 8. I~:RASCA~ G. V. PALLOTTII~O~ G. PIZZ:ELLA D~Ild P. BONIleAZI

T)~BLE Ib). - Li s t o] the <( 1978 events ~> observed i n _Frascati. J u l y 1978.

No. B e g i n n i n g of e* No. B e g i n n i n g of e2

e v e n t (tF)(~) (UT) (K) e v e n t (tF)(a) (UT) (K)

1 4 d 1 5 h 3 8 m i n 5 9 s 1068 22 8 d 9 h 4 1 m i n 3 0 s 1118

2 4 17 13 4 3545 23 8 l l 42 24 3 448

3 4 18 30 51 1221 24 8 12 13 47 1471

4 5 4 46 32 1777 25 8 13 17 4 1311

5 5 4 59 40 1435 26 8 14 4 52 4933

6 5 5 40 9 1342 27 8 14 33 44 4006

7 5 5 52 32 2007 28 8 17 10 39 3423

8 5 6 28 49 1441 29 8 18 17 48 3505

9 6 5 18 35 10235 30 9 6 11 20 1 662

10 6 7 26 54 1 212 31 9 8 57 4 1065

11 6 8 51 50 2 270 32 10 17 14 43 1253

12 6 11 41 16 2 168 33 10 22 1 37 11250

13 6 12 55 44 8943 34 10 22 l l 43 1498

14 6 12 59 3 3118 35 11 16 23 29 3678

15 6 18 26 22 1419 36 11 18 3 25 4594

16 6 22 14 30 12 364 37 11 23 29 41 7562

17 7 5 22 11 4 143 38 12 15 20 l l 3385

18 7 19 9 28 3 191 39 12 17 3 45 6099

19 7 23 59 56 3989 40 13 5 20 18 3534

20 8 4 46 58 1091 41 13 5 52 25 2070

21 8 8 23 32 1728

(a) Beginning of the sampling interval At = 1 s in which the event appears.

3"1. A n a l y s i s o] the (~ M a y 1980 data ~). - I n the case of a pure ly r andom dis t r ibut ion of the t imes t~, the values of M 2 should be d is t r ibuted according to (13). A tes t of this poin t is p rovided b y fig. 1, which shows a semi-logari thmic plot of the observed d is tr ibut ion of M 2. The s t ra ight line, represent ing the theoret ical expecta t ion according to (13), is in excellent agreement with the observed distribution. Therefore, in p lo t t ing the results of the Four ier t rans- forms of any set of data , we adop t a probabi l i ty scale computed by means of (13), which has the advan tage of providing a direct es t imate for the probabi l i ty t h a t a peak is due to a stat ist ical fluctuation.

The results of the Fourier t r ans fo rm of the (( 1980 events ~ are shown in fig. 2, where exp [ - - M s] is p lo t ted vs. ~ in the range f rom 20 to 100 min.

We concentrate now our a t t en t ion on the 5 peaks among all those appear ing

" AC O OUN OF RAV,TAT,ONA WAV ANteNnAS - , ,

I02k .eXpE--M

315

101

I I I I I i \ I I I i I 1~ 1 2 3 4 5 6 7 8

t,4 2

Fig. 1. - Statistical distribution of the density function of the parameter ~/2 (see definitions (4), (7)) for May 1980 data: the experimental histogram is compared to the theoretical line. N = 10.

in fig. 2 which huve, according to the ordinate scale, a p robabi l i ty Pl to be accidental < 1 0 -2. Since the n u m b e r of (( resolvable peaks )>, hr.,. , in the range (20--100) rain, amounts to 70 (see eq. (6)), the probabi l i ty of observing accidental ly a t least 5 peaks, each with a p robabi l i ty p 1 < 1 0 -2, is given b y

(16) P~ ---- 7~(70) (0"01) r (1 - 0"01)'~ : r 7"10-~

:Notice t h a t the expected n u m b e r of peaks wi th p < 1 0 -2 is ~ = 70.10 - 2 = 0.70. As we poin ted out in ref. (~), some of these periods seem to correspond to

some of the periods of the free oscillation of the Ear th . Table I I shows a com- par ison be tween our results and those obta ined b y var ious authors who have analysed the da ta provided b y s t rain und pendu lum seismographs and grav- imeters (~-~).

(2) H. BENIOFF, F. PRESS and S. SMITH: J. Geophys. l~es., 66, 605 (1961). (3) N . F . NEss, J. C. HA~ISON and L. B. SHCHT~" J. Geophys. Res., 66, 621 (1961). (4) G. J. F. MAC DONALD and N. F. N]ess: J. Geophys. Res., 66, 1865 (1961). (5) A comparison of our data with the results of other authors, indicated below, leads

316 E. AMALDI, S. FRASCA, G. V. PALLOTTINO~ G. 1)IZZELLA and P. BONIFAZI

lo - 4

lo - 3

o... 10 - 2 7, II &.

lo ~ 2'o I ) 5'o 60 7b 80 90 30 40 100

,~ ' (m in )

Fig. 2. - Results of Fourier analysis applied to May 1980 data: probability for the observed value of M s to be not greater than the indicated value (see eq. (13)) as a function of the period ~ = 2z/w.

F rom column 5 of table I I we see that , out of 5 peaks deduced from our

data , 4 coincide with those found for the Ea r th free oscillations. The fifth peak at 5 r = 29.4 rain reminds the peak at 5 r = 29.87 min observed by ALsoP

et al. (5), due perhaps to atmospheric pressure. I n order to evaluate the probabil i ty for such an overlapping to be ac-

cidental, we show in column 4 of table ][I the spread A f of the seismologists~

values. The probabil i ty for n out of N1 peaks to overlap accidentally with n of the

IY s seismological peaks within a period uncer ta inty A~- is given by

_~,o~-1 exp [-- ~]fik (17) p(n>no.~.) : i k! '

k=[

where %.~. means number of (~ overlapping peaks ~> and

A~ A5 r (18) <n> - - N1N2 lVl

~)max ~ ~min

essentially to the same conclusions: L. E. ALSOP, G. H. SUTTON and M. EURSIG: J. Geophys. Res., 66, 631 (1961); B. P. BOGERT: J. Geophys. Res., 66, 643 (1961); B. A. BOTT and A. MARUSSI: Geophys. J. R, Astron. Sot., 6, 299 (1962); M. BozzI ZADRO and M. CAPUTO: Nuovo Cimento, 6, 67 (1968); J. S. DERR: Bull. Seismol. Soc. Am., 59, 2079 (1969).

]~ACKGI~OUND O:F GRAVITATIOI~AL WAVE ANTENNAS ETC. - I I 3 1 7

TABnE I I . - Periods (in minutes) deduced from our data (fig. 2 and 4) and comparison with all Earth free-oscillation periods observed by the quoted seismologists with J" between 20 and 58 m i n .

M o d e (2) (a) (4) A3- M a y 1980 J u n e - J u l y 1978

e v e n t s , e v e n t s ,

v~ ~ 7819 .43 H z v 1 ~ 1795.93 H z

oS~ 1 54.7 54.98 0.3 55.03 55.23

0S~ 53.1 52 .80 0.3 53.12 - -

0S~ 2 3 5 . 9 35.87 0.03 - - 36.23

oS~ 35.2 35.24 0 .04 - - 35 .30

0S4 25.8 25.85 0 .05 25 .84 - -

oSo - - 20 .46 - - - - 20 .38 - -20 . 61 ( ' )

1S~ 24.5 24.65 - - - - - -

oT~ 42.3 - - 42.3 - -44 .8 2.5 - - 41 .18

0Ta 28.6 - - 28.4 .'--28.7 0.3 28.85 - -

oT4 21.8 - - 2 1 . 6 - - 2 1 . 9 5 0.35 - - 2 1 . 6 4 - - 2 1 . 7 3 (~)

(a) We do not known which of these two peaks can be a t t r ibu ted to the oS, oscillation. Only one of them (3" = 20.38 min) has been taken into consideration in the computa t ion of the probabili t ies of table I I I . (b) These two peaks overlap ra ther sat isfactori ly wi th two (m = 4- 3) of the 9 peaks of oT,. Both of them have been taken into account in the computa t ion of the probabi l i ty of table I I I .

A s c u s t o m a r y a m o n g s e i s m o l o g i s t s ~ i n t h i s p a p e r w e u s e t h e p e r i o d , a l t h o u g h

f o r o u r a n a l y s i s t h e f r e q u e n c y i s a m o r e a p p r o p r i a t e v a r i a b l e .

F o r o u r (~ 1 9 8 0 e v e n t s ~; w e h a v e

5V1 -~ 5 ~ N2 ---- 9 .

TABL]~ I I I . - .Number no.p. of our peaks overlapping, within A:~', those observed by seismologists and values of the corresponding probabilities to occur accidentally (eq . (17)) .

A J " ( m i n ) ( n ) (") no.p. (~) p ( ~ no.~.)

1980 e v e n t s 0.2 0.11 3 2 . 0 - 1 0 -4

0.3 0.17 4 3.0" 10 -5

0.4 0.22 4 8.2" 10 -5

1978 e v e n t s 0.2 0 .43 4 1.0" 10 -a

0.3 0 .64 4 4 . 2 . 1 0 -a

0.4 0 .86 6 2.7- 10 -4

(a) Here (n) is computed by means of eq. (18). (b) Number of ~ overlapping peaks *: i.e. periods deduced from our da ta overlapping wi th peaks observed by seismologists.

21 - II Nuovo Cimento C.

3 1 8 ~E. A~IALDI, S. FRASCA~ G. V. PALLOTTIIWO~ G. I~IZZI~LLA and e . :BO1WIFAZI

I n table I I I we give the probabil i t ies compu ted b y means of (17) and (18) for the reasonable set of values of A3-: 0.2, 0.3 and 0.4 rain.

At this po in t i t appears in order to notice t h a t these probabil i t ies p(>no.~.) in all cases t u r n out to be of the order of 10 -4 and t h a t t hey are complete ly

independent of the probabi l i ty P5 given b y (16). Fu r the rmore , bo th P5 and p(>no. , . ) are independent of the probabi l i ty considered in ref. (1) for the coin- cidences between the Frasca t i and l~ome detectors.

The same analysis applied to the events recorded a t the 1st longitudinal mode do not show such ~ clear evidence of periods over lapping those of the free oscillations of the Ear th .

3"2. A n a l y s i s o / the (( 1 9 7 8 d a t a ~. - W e pass now to a discussion of the (( 1978 da ta ~) whose t imes of arr ival are given in table I . They regard only the 1st longitudinal mode, because higher modes were not recorded in 1978.

The results of the Fourier analysis are shown in fig. 3 and 4, which are similar

10 ~

10

10

1 10

10 0

1 0 - 1 I I I I I I t I 0 1 2 3 4. 5 6 7 8

M:'

Fig. 3. - The same as fig. 1 for the (~ 1978 data)). Zr= 85.

B A C K G R O U N D O F G R A V I T A T I O N A L W A V E A N T E N N A S : E T C . - I I 319

,0-5[ 10"-4 /

i ,:,o-2h., Ill I.i J ,,I,w , _,t1 11 Jll,J.i.l,i. ll.[ l,Ill,/Jl, / i i 6 J 10 o

20 4-0 50 60 7 0 8 ,g"(min)

100

Fig. 4. - The same as fig. 2 for the (( 1978 dat~)).

to fig. 1 and 2. The peaks wi th a probabi l i ty to be accidental ly smaller t h a n 0.5.10 -3 are 19, they are l isted in table IV. I n this case the n u m b e r of resolvable peaks (eq. (6)) a m m o u n t s to 1509, corresponding to an expec ted value g----

0.5.10-3.1509 ~ 7.55. The probabi l i ty t ha t o u r 19 peaks are due to statis- t ical f luctuations can be computed b y using the b inomial formula (see eq. (16)),

which in our case gives

(19) 1~o9[1509\

P19 = ~ L r ) (0"005)~(1-0"005)15~ 3"1"10-4"

I n conclusion, it is reasonable to expect t h a t some 8 - -5 of our 19 peaks do really overlap with those observed b y the seismologists, bu t there is a probabil i ty smaller t h a n the value (19) t h a t all of t h e m originate f rom stat is t ical

fluctuations. A comparison with the seismologist results is shown in table I I , f rom which

we see t h a t 7 of our peaks overlap with well-known periods of free oscillation of the Ear th . I n the lower pa r t of t a b l e / I I we show the n u m b e r of over lapping periods (no.,.) a f te r exclusion of oT2 because of its large unce r t a in ty (A J---- = 2.5 min). I n the same table we give also the corresponding probabil i t ies p (>no.,.) computed for a few values of A J - a round 0.3 min. I n all considered cases this p robabi l i ty is be tween 10 -a and 10 -4.

The different aspects of fig. 2 and 4 can be unders tood b y considering t h a t

~ 2 0 :E. A M A L D I , S. :FRASCA~ G. V. P A L L O T T I N O , G. P I Z Z E L L A and L B O N I F A Z I

TABLE IV (~). - Results of the t'ourier analysis el the 1978 events and corresponding probabilities (eq. (13)).

No. of peak 3- (min) p ( > M 2) Peaks No. 3- (rain) p ( > M) ~

1 20.38 0.002 4 11 36.23 0.004 5

2 20.61 0.003 8 12 36.30 0.000 79

3 21.64 0.0014 13 37.31 0.000 31

4 21.73 0.000 15 14 41.18 0.001 1

5 27.68 0.003 0 15 55.24 0.001 2

6 29.88 0.003 6 16 56.85 0.004 0

7 29.93 0.001 5 17 65.31 0.004 2

8 33.07 0.000 034 18 73.57 0.002 7

9 35.24 0.004 4 19 77.70 0.005 0

10 35.30 0.000 86

(a) ~,Ve h a v e u s e d fo r t h e * 1978 e v e n t s ~ t h e p e a k t h r e s h o l d 0 . 5 . 1 0 -z i n s t e a d of 1" 10-" a d o p t e d fo r t h e ~ 1980 e%~cnts ~ i n o r d e r t o r e d u c e t h e n u m b e r of p e a k s to be c o m p a r e d w i t h t h e s e i s m o l o g i s t s ' r e s u l t s . ~Vith a p e a k t h r e s h o l d e q u a l t o 1" 10 -2 t h e n u m b e r of p e a k s i n c r e a s e s f r o m 19 t o 27, b u t a l so t h e n u m b e r of e x p e c t e d a c c i d e n t a l p e a k s i nc reases , so t h a t t h e g e n e m d c o n c l u s i o n s r e m a i n e s s e n t i a l l y u n c h a n g e d .

t h e t w o sets of d a t a of 1980 a n d 1.978 h a v e been co l l ec t ed in 26 h o u r s a n d

26 days .

There fo re , t h e f ree osc i l la t ions of t h e E a r t h wh ich h a v e pe r iods n o t l o n g e r

t h a n a b o u t one h o u r a n d ~ d e c a y t i m e T--~ Q/o) of a few d a y s a re s m o o t h e d

o u t in t h e (( 1978 d a t a ~.

W e m u s t a d d t h a t , b y choos ing s h o r t e r i n t e r v a l s of m e a s u r i n g t i m e , some

p e a k s b e c o m e m o r e p r o m i n e n t . F o r e x a m p l e , if we l i m i t our ana lys i s to t h e

(~ J u n e 1978 d a t a ~) we o b t a i n two p e a k s , a t ~ - = 21.73 m i ~ a n d ~ - -~ 21.64 m i n

w i t h p r o b a b i l i t y of be ing acc iden ta l , r e s p e c t i v e l y , of 1 .3 .10 -5 a n d 8 .10 -4.

T h e s e p e a k s (fig. 5) c o r r e s p o n d v e r y wel l w i t h t hose o b t a i n e d b y s p l i t t i n g t h e

p e r i o d of t h e oT4 f ree osc i l l a t ion as a n effect of t h e Coriolis forces. B o t h of

t h e m d i s a p p e a r d u r i n g J u l y , 1978. Such a b e h a v i o u r is in a g r e e m e n t w i t h t h e

Q-va lue ( ~ 400) g iven in ref . (4).

3"3. Could the peaks ]ound / tom the .Fourier analysis be arti/acts generated in the data processing? - T h e re su l t s of t h e d a t a ana lys i s p r e s e n t e d in sub-

sect . 3"1 a n d 3"2 ( t ab le I I ) f r o m t h e b e g i n n i n g were for us a m a t t e r of su rpr i se .

There fo re , we e x p l o r e d t h e p o s s i b i l i t y t h a t t h e p e a k s a p p e a r i n g in t h e F o u r i e r

s p e c t r a of fig. 2, 4 a n d 5 w i t h a v e r y s m a l l s t a t i s t i c a l p r o b a b i l i t y ( p < 1 0 -2)

c o u l d b e a r t i f a c t s g e n e r a t e d in t h e a d o p t e d d a t a - p r o c e s s i n g p rocedure .

W e m e n t i o n he re t h e r e su l t s of t h r e e t e s t s a l t h o u g h t h e y c onc e rn e i t he r

t r i v i a l c o m p u t e r p r o g r a m s (a) a n d b)) or a choice w i t h p h y s i c a l i m p l i c a t i o n s

wh ich a r e s t i l l ou t of our g r a s p (e)).

BACKGROU-ND OF G R A V I T A T I O N A L W A V ~ A N T E N N A S ~ T C . - I I

10 -5

321

10 - 4

10 -3

~10 -2

10 -1 I I I

I0 ol 20

, II . t l . . i ,I A

, ~ ( m i n )

I 22

Fig. 5. - Similar to fig. 2 (and 4) for the (( June 1978 da ta >) for 20 min < 3 - < 22 min.

a) M a y a d i s t r i b u t i o n of 10 e v e n t s chosen a t r a n d o m g ive r ise to a F o u r i e r

s p e c t r u m w i t h p e a k s in some w a y s im i l a r to t h o s e of fig. 2 ? T h e a n s w e r was no.

b) M a y t h e t i m e w i n d o w a d o p t e d in t h e F o u r i e r ana lys i s p r o d u c e F o u r i e r

p e a k s s imi l a r to t h o s e o b s e r v e d in fig. 2 a n d 4? W e h a v e ver i f i ed t h a t no effect

of t h i s t y p e a p p e a r s in our case.

c) W e h a v e e x p l o r e d t h e consequences of a s s u m p t i o n (7a) b y c h o o s i n g

t h e ak (k --~ 1, 2, . . . , 10) a t r a n d o m in a r a n g e of v a l u e s b e t w e e n 1 a n d 10. T h e

pe r i ods of t h e p e a k s of i n t e r e s t in th i s d i scuss ion d i d n o t change .

4 . - C o n c l u s i o n s .

W e h a v e co l l ec ted in t a b l e V t h e v a r i o u s p r o b a b i l i t i e s c o m p u t e 4 a b o v e

for ou r o b s e r v a t i o n s to b e p u r e l y a c c i d e n t a l . T a b l e s I I a n d V s u m m a r i z e ou r

resu l t s . T h e y a p p e a r to p r o v i d e e v i d e n c e in f a v o u r of a c o r r e l a t i o n b e t w e e n 8

or 9 w e l l - k n o w n free osc i l l a t ions of t h e E a r t h a n d t h e (~events~> (i.e. l a rge pu lses )

r e c o r d e d b y t h e F r a s c a t i a n t e n n a a t t w o d i f fe ren t f r equenc i e s :

~1 ~ 1795.93 I t z in 1978 , r5 ~ 7819.43 I-Iz in 1980 .

A p o i n t wh ich r e m a i n s obscu re is w h y in (< M a y 1980 d a t a >) we obse rve

some of t h e s e pe r iod ic i t i e s a t u~ : 7819.43 Hz, b u t n o t a t ul : 1795.93 t t z .

The r e a s o n m a y s i m p l y be t h a t t h e r e su l t s of F r a s c a ' s m e t h o d can ea s i l y b e

322 E. AMALDI, S. Iel~ASCA, G. V. PALLOTTINO, G. PIZZELLA and P. BONIFAZI

TABLE V. - Summary o] probabilities ]or our observations to be accidental (~).

Probability Probability Probability of ob- of of observing serving no.p. peaks Frascati- at least n overlapping with Rome peaks each with periodsoffreeoscil- accidental probability p <P0 lation of the Earth <( coin- (p(n > no.p.), cidences >> table I I I )

( P O = 10 -2 ; n = 5) (no.r~.= 3 . ' 4 )

May 1980 data 10 -4 7- 10 -4 2.0.10 4--3.0.10 -~ (ref. (1)) (eq. (16))

(Po= 0.5" 10-2; u = 19) (no.p. = 4--6)

1978 data 3.1.10 -4 4.2.10-a--2.7 �9 10 -4 (eq. (19))

(a) The d a t a s h o w n in the th ree co lumns are i n d e p e n d e n t of each other ,

upset by a small contaminat ion of spurious pulses. We can also imagine various

physieM reasons for such a behaviour. These, however, can be dear ly formulated only in the frame of a reasonable physical mechanism providing the link be-

twee~ the slow oscillations of the Ea r th and the excitatiorz of our antenna. Unfor tunate ly we do not ye t dispose of such a mechanism and this makes

us unhappy. We have already suggested, as a possible explanation, tha t the

observed correlation between the Ear th oscillations and the pulses of our arz-

tenna depends on a few specific features of our detector, such as the structure of its suspension and/or of the mechanical filters designed for decoupling the

bar from the ground. These were different in some respect in 1978 and 1980. I n our previous paper we have tentat ively proposed three possible classes

of mechanisms. Although we do not yet dispose of experimental results which allow the choice of one of them, or at least a step towards a clarification of this fundamentM point, we consider as a working assumption the excitation of our

antenna to be due to vibrations (of acoustical or ultracousticM nature) generated locally in the crust of the E a r t h by cricks of the rocks due to their compression

and/or traction. We should recall tha t the ampli tude of oscillation of the ends of our bar (L = 150 cm) corresponding to Q2 = 10000 K amounts to 10 -14 cm.

This value indicates that , with respect to the seismologists, we operate in a

different range not only of frequency but also of amplitude. I t is, however, not easy to compare the data provided by the two classes of instruments.

We should also recall t ha t years ago at least two groups (6,7) looked for cor-

(6) R. fl-. ADAMYANTA, A. D. ALEKSEEV and N. I. KOSONITSYN : 2. Eksp. Teor. Fiz. .Pis'ma Red., 15, 277 (1972) (English translation: J E T P Lett., 15, 194 (1972)). (7) J . A . TYSON, G. C. MAc L]~NNAN and L. J. LANZEROTTI: Phys. Rev. Lett., 30, 1006 (1973).

BACKGROUND OF GRAVITATIONAL WAVE ANTENNAS ETC. - I I 323

r e l a t i ons b e t w e e n t h e d a t a r e c o r d e d b y WEBEg w i t h his g r a v i t a t i o n a l - w a v e

a n t e n n a s a n d v a r i o u s g e o p h y s i c a l effects . T h e i r r e su l t s show some c o r r e l a t i on ,

b u t do n o t re~ch a suf f ic ient ly h igh conf idence l im i t .

W e c o n t i n u e to col lec t n e w e x p e r i m e n t a l i n f o r m a t i o n in t h e h o p e of suc-

ceed ing in c l a r i f y ing a t l e a s t some of t h e a b o v e - m e n t i o n e d p r o b l e m s . W e

a lso sugges t t h a t o t h e r g roups w o r k i n g w i t h g r a v i t a t i o n a l - w a v e d e t e c t o r s

d e v o t e p a r t of t h e i r ef for t to i n v e s t i g a t e w h e t h e r t h e b a c k g r o u n d of t h e i r in-

s t r u m e n t s is or is n o t in p a r t c o r r e l a t e d w i t h t h e v a r i o u s E a r t h m o v e m e n t s .

Th is w o r k has been s u p p o r t e d f i n a n c i a l l y b y t h e C~II~ for t h e F r a s e a t i

a n t e n n a , b y t h e I ~ T F ~ for t h e d a t a ana lys i s .

W e express ou r t h a n k s to Mr. A. SOgCE for his v a l u a b l e c o n t r i b u t i o n in t h e

d a t a ana lys i s .

�9 R I A S S U 2 ~ T O

Per approfondire l 'anal is i degli eventi registrat i dal l ' antenna di Fasea t i nel Maggie 1980 (vedi lavoro precedente) si ~ appl icata l 'anal is i di Four ier ai lore tempi di arr ive e si sono t rovat i i seguenti periodi di oseillazione l ibera della Terra: Y'(oS21)= 55.03, Y'(oS+X)=53.12, Y-(oS~)=25.84, ~ (oTa)= 28.85 minuti . Una simile analisi dei dat i regis t ra t i nel periodo Giugno-Luglio 1978 ha mostrato i seguenti periodi: Y-(oS2 ~) = 55.23, J-(oS3 z) = 36.23, Y-(oS +~) = 35.30, ~-(oSo) = 20.38--20.61, ~q'(oT~) = 41.18, ~q'(oT~ s) = 21.73, ~-(oT +s) = 21.64 minuti . La probabil i t~ che questi periodi siano accidentali ~ molto piccola in t u t t i i casi.

BO3MO~HOe 3eMHoe Hp0HcXO~,~eHHe ~ 0 H a aHTeHH FpaBHTatgflOHHbLX Bo.Ym. - I I

Pe3ioMe (*). - - ~n~ TOrO, ~ITOdbI yrnydrlTb arian,3 COdblTH~, 3aperHcTpHpoBaHrmIX B Te~erme Ma~ 1980 rona c noMombro aHTeHHbI Be ~pac~aTa (CM. npe~b~nymym CTaTLrO), MI, I npOBO~M Cyp~e-aHann3 BpeMeH npnd/,ITrI~t crirnanoB. Hony~amTc~ cnenymmne nepHo~r,i CBOdO~H~XX ocam~rm~rn~ 3eMnn: ~(o8~I)~--55.03, 3-(oS+1)~53.12, 3-(oS4)~25.84, J-(oTz)~-28.85 MnHyT. Aaanornqrmn~ aHanH3 ~aHrmlX, codpaHHbIX B nmHe-nrone 1978 ro~a, noKa3~BaeT cne~tymmne nepno~bi 3-(oS~ ~) --~ 55.23, 3-(oS~ 2) = 36.23, ~r(oS+2) ~- 35.30, J-(oSo) - - 20.38 --20.61, 3-(oT2) = 41.18, J-(oT~) = 21.73, ~r(oT+3) = 21.64 ~mnyT. Bepo~- THOCTb TOrO, qTO aTH n e p n o ~ ~B~rOTCZ cnyqa~H~Mn, BO Bcex cnyqaax oaaa~maexca olielLb M a n o ~ .

(*) Hepeee3eno pebatalueft.

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Background of gravitational-wave antennas of possible terrestrial origin.-II