### Abstract

The correlation between the data obtained with two gravitational wave (GW) detectors (in Rome and in Maryland) and two neutrino detectors (LSD in Italy and Kamiokande in Japan) has been studied in more detail. If we indicate with U1 the response of the gravitational wave detectors and with U2 the response of the neutrino detectors, we find that there is a clear time correlation between U1 and U2: namely U2 comes later than U1 by an amount depending on the energy measured in the neutrino detectors (the delay decreases with the detected neutrino energy). A straightforward calculation would yield a mass for the U2 particles between 4 and 6 eV. If one further assumes that the U2 is due to neutrinos whose mass has been evaluated to be less than 0.1 eV (at 90% c.l.), we hazard the idea that a slow down during the neutrinos’ 168 000 light-year travel from SN1987A to Earth could be inferred.

## INTRODUCTION

The SN1987A has been an unique event (the first visible at naked eye supernova after the Kepler one in 1604). As a matter of fact, this is one unique instance of a known source of neutrinos hitting man made detectors, the source being located 168 000 light years away from Earth. The analysis reported in this paper deals with time correlations between different types of detectors during the SN1987A event, deepening the investigation made during several years and culminating with the result described by Galeotti and Pizzella (2016).

We are aware that the correlations found previously and those discussed in this paper do not fit most of the presently available theories. But the probability that the correlations be due to chance is extremely small, so, in our opinion, we must present to the scientific community any new result, trusting that a physical explanation will be found, as, for example, in paper of Imshennik and Ryashskaya (2004) or in the recent article of Eroshenko et al. (2019). Thus we feel we must continue in our exploration of the few available data due to the SN1987A, since it is very unlikely that another near supernova will occur in the nest decades.

In paper of Galeotti and Pizzella (2016) a new analysis of the data obtained during the SN1987A was made. A timing correlations was found that involve four set-ups located at intercontinental distances: two neutrino detectors LSD in Italy and Kamiokande (KND in the following) in Japan and two gravitational bar detectors: GEOGRAV in Rome, Italy, and Weber in Maryland, USA.

We will not make any assumption as to which particle and/or wave is responsible for the detectors’ response, so we will indicate with U1 the signal of the gravitational wave detectors and with U2 that of the neutrino detectors (see article of Aglietta et al., 1989).

Each neutrino detector produced data consisting in the energy (MeV) of the detected trigger and the time of occurrence. Among all triggers the majority are very likely due to background but the algorithm we apply is based on the idea to make use of all available data and not only those considered to be produced by neutrino interactions. In the case of the Mont Blanc neutrino detector (LSD), it is important to recall that it recorded on line, i.e. on real time, the occurrence of five interactions on February 23 at 2^{h}52^{m} UT, one day before the optical discovery of the SN1987A supernova (Galeotti and Pizzella, 2016) (in the following we refer to as the LSD 5-neutrino event).

The gravitational wave detectors provided data measuring their vibrational status with a rate of 1 Hz. Thus in one hour (for example) we have 3600 measurements for each GW detector (*E*_{R}(*t*) for the Rome detector and *E*_{MD}(*t*) for the Maryland one), whilst for the neutrino detectors we have about 100 triggers for KND and about 50 triggers for LSD.

The two GW files are combined in just one by taking the sum *E*(*t*) = *E*_{R}(*t*) + *E*_{MD}(*t*), that is the Rome and Maryland—far located detectors—sampled at the same time. We call this quantity *energy innovation*. The two files from the neutrino detectors are combined in just one by adding together the data from LSD and KND.

We stress that the data produced by each of the four detectors are completely independent.

Finally, for a given time interval Δ*T* (say one hour) we considered the sum \({{E}_{\text{G}W}}=\sum \text{}E\left( {{t}_{i}} \right)\) where the summation is extended to those energy innovations measured at times

where *t*_{ν} are the neutrino times and Δ*t* indicates a possible average delay between the arrival of signals from the GW and the neutrino detectors. This delay has been determined in previous analysis, using only the 5-neutrino (Amaldi et al., 1987) event we had found Δ*t* = 1*.*4 s, and using all data from the neutrino detectors (Aglietta et al., 1989) we found Δ*t* = 1*.*1 s. Thus in one hour *E*_{GW} consists in the sum of about 150 (*i* = 1, *…,* ∼150) selected energy innovations, among the 3600 available ones, those in delayed coincidence with the neutrino events. The value *E*_{GW} is compared, for any possible value of Δ*t*, with a large number of background values of \({{E}_{{\text{B}}}} = \sum E\left( { \ne {{t}_{i}}} \right)\) obtained by randomizing the time of all the four detectors (the two GW detectors and the two neutrino ones).

This method of analysis has been called the *net excitation method* and it has been described in details in the articles of Aglietta et al. (1989) and Aglietta et al. (1991).

As reported Galeotti and Pizzella (2016), the result of this method, applied to the data of the GW and neutrino detectors and exploring the time region from 0 to 6 hours of 23 February, in intervals of 30 minutes stepped by 6 minutes, gives a strong correlation at the half an hour time interval 2^{h}36^{m} UT to 3^{h}6^{m} UT, just at the time of the LSD 5-neutrino event, with a time delay of the neutrino signals with respect to the U1 signals of 1.1 s.

The probability that this correlation was due to chance was estimated to be of the order of 4 × 10^{−7}.

Given the sensitivity of the two gravitational wave detectors, it is unlikely that U1 signals could be generated by gravitational waves from SN1987A. One cannot exclude the signals in the GW detectors be due to other causes, say still undiscovered exotic particles, unless a much larger cross-section for gravitational waves can be calculated^{Footnote 1}.

In this paper we start with investigating whether the strong correlation obtained just at the time of the LSD 5-neutrino event was not due simply to the 5-neutrino event.

We have applied the net excitation method again after having eliminated the 5-neutrino triggers from the LSD list. We get again a correlation, as shown in Fig. 1, again precisely at the half an hour period including the LSD 5-neutrino event.

This reinforces the idea that the correlation between the neutrino and GW detectors data was not simply due to the triggers recognized as neutrinos but also to same triggers believed to be background.

Since the probability that the correlation between U1 and neutrinos be due to chance was very small, we decided to investigate in greater detail the underlying data.

## DOES THE DELAY DEPEND ON THE NEUTRINO ENERGY?

The experimental result described above shows that the neutrino arrive, on average, 1.1 s after the U1 particles.

In order to study this result we must attempt to make some hypotheses. The simplest hypothesis is to assume that both particles are emitted simultaneously by the supernova and the neutrinos have a mass greater than the U1 particles, so they cover the distance SN1987A–Earth in a longer time. We assume also that the U1 particles travel with the speed of light.

It is possible to calculate the neutrino rest mass from the delay Δ*t* between a signal propagating with the speed of light and that of signals detected by LSD and Kamiokande.

For a neutrino with energy \(E\) we get

With \(D\) expressed in light-sec, for the SN 1987A we get the neutrino rest mass

We now concentrate on the half an hour time interval 2^{h}36^{m} UT to 3^{h}6^{m} UT, at the time of the LSD 5‑neutrino event, when the correlation was the highest. The total count for the U2 in the time interval

2^{h}36^{m} UT to 3^{h}6^{m} UT is 83, 32 from LSD and 51 from KND.

Interpreting the U2 signals as due to neutrinos, at a delay of 1.1 s and an average energy for the 83 events of 7.9 MeV, we get for the neutrino mass about 5 eV, too big with respect to the present upper limit of 1.1 eV (see for instance Aker et al., 2019).

The delay of 1.1 s is affected by the uncertainty on the GW timing. We have roughly estimated an error on the GW detectors timing of approximately ±0*.*5 s.

The energy distributions for the neutrinos observed in the LSD and in the KND detectors (the two detectors have different threshold energy) are shown in Fig. 2.

We apply the net excitation method separately to the LSD and to the KND data, obtaining the results depicted in Fig. 3, separately for the two neutrino detectors. From this figure we obtain the probability that the correlation between the U1 and U2 signals, when U2 follow U1 by the time Δ*t*, be due to chance by dividing the number on the ordinate scale by 10^{6}, as explained previously (i.e. the caption of Fig. 1).

We find that that the best correlation is obtained at a greater delay for low energy neutrinos, as typically the neutrino events due to LSD are.

This result shows an increase of the correlation delay for the neutrino with smaller energy.

We can verify if this is the correct interpretation of our experimental result by separating the neutrino data of each detector according to their energy. We show the result in Fig. 4 for LSD and in Fig. 5 for KND.

It is evident that the delay Δ*t* decreases with increasing neutrino energy, both for LSD and KND, in agreement with our interpretation.

## ESTIMATION FOR THE NEUTRINO MASS

Table 1 summarizes the results obtained by splitting the events according to the neutrino energies.

We remark that the four neutrino mass values shown in Table 1 have been obtained with independent sets of data. The results range from about 4.6 eV to about 5 eV with an average value of 4.8 eV.

We plot in Fig. 6 the delay Δ*t* versus 1/*E*^{2} (*E* the neutrino energy).

We notice the interception with the *y*-axis (for *E* → ∞) indicating a systematic error in our time determination. From Eq. (3) we obtain the neutrino mass

This result is just the same as previously determined.

### Different Estimation of the Neutrino Rest Mass

The results reported in Table 1 are based on the assumption that the U1 signals travel at light speed.

In order to get rid of this additional hypothesis we can just use timing difference and energy differences. From Eq. (3) we obtain

Considering Table 1 and Eq. (6) we notice that we can combine the first line with the second, third and fourth ones, the second line with the third a forth and the third line with the fourth one, obtaining six different determinations, two of them completely independent one from each other, of the neutrino mass.

Using only data of the two LSD groups we obtain *m* = 3*.*79 eV, using the two data for KND we obtain *m* = 5*.*17 eV.

The distribution of the six determinations is shown in Fig. 7.

The average value is

This is again greater than the observed upper limit for the neutrino mass.

However, the consistency of the various determinations suggests that the signals of the GW detectors, whatever their nature, are produced by particles or fields traveling with velocity equal or extremely close to the speed of light.

## DIFFERENT APPROACH FOR STUDYING THE RELATIONSHIP BETWEEN DELAY AND NEUTRINO ENERGY

We have found that the neutrino energy is correlated with the neutrino delay with respect to the U1 signals, but the mass obtained from this analysis is larger than to the neutrino mass obtained by other experiments.

Before discussing this result we want to use a different method to verify that the neutrino energy be correlated with the neutrino Δ*t*.

For each one of the 83 neutrino events with energy *E*_{i} at time *t*_{ni} we consider the U1 signals preceding each neutrino time within a two second time interval and choose the time *t*_{wi} when the U1 signal is the largest, obtaining the delay Δ*t*_{i} = *t*_{ni} − *t*_{wi} between the U1 and the neutrino signals, delay which we want to correlate with the neutrino energy *E*_{i}.

We get the result shown in the Fig. 8, that, although very roughly, confirms what found previously in this work: a correlation exists between the neutrino energy and the delay Δ*t*, larger Δ*t* for smaller energy.

From the Fig. 8 we can obtain the relationship between *E* and Δ*t*. Using Eq. (3) we find, at Δ*t* = 0*.*5 s, 3.6 eV for the neutrino mass and at Δ*t* = 2 s we find 6.3 eV, not much different than the values obtained previously.

## DISCUSSION AND CONCLUSION

We think that the new analysis presented here diminish the probability that the observed correlations be due to chance.

Whilst it is difficult to consider the U1 signals due to gravitational waves, because of the small sensitivity of the bar-detectors, according to our present knowledge^{Footnote 2}, it seems reasonable to admit that a consistent fraction of the neutrino signals, obtained by neutrino detectors, be due to neutrinos.

That the values obtained for the neutrino mass of 4 to 5 eV be the neutrino mass encounters insurmountable obstacles. Indeed direct experiments on neutrinos (Aker et al., 2019) give an upper limit of 1.1 eV. If we consider upper limits due to cosmological considerations (Couchot et al., 2017; Tanabashi et al., 2018) we have upper limits for the sum over all neutrino species Σ*m*_{ν} ranging from 0.12 to 0.17 eV.

For the upper limit obtained with the tritium experiment, *m*_{ν} = 1*.*1 eV, applying Eq. (3) for the smallest neutrino energy detected by the LSD experiment, 5 MeV, we should have a delay between the U1 and neutrino signals of 0.04 s. Practically a null delay we should have if we consider the cosmological upper limit.

The obvious conclusion is that the mass obtained with our analysis cannot be the neutrino rest mass. However the statistical evidence of our analysis appears to be very high, therefore a different interpretation is in order.

The simplest interpretation is to consider that the neutrinos be emitted, during the supernova collapse, after the emission of the U1 particles, and high energy neutrinos be emitted before the low energy ones.

Another possible idea, although a very fantastic one, is that during their travel from SN1987A to Earth, 168 000 light years long voyage, the neutrinos be delayed by a time order of 1 s, higher delay for lower energy neutrinos (interaction with dark matter or special trajectory of massive particles in the spacetime?).

If we accept any of these interpretations, we recognize the important role played by the GW detectors.

Our result leads us to believe that the U1 signals be due to a real physical cause. It remains to understand the phenomenon (gravitational waves?) which induced in the GW detectors (two detectors at intercontinental distance) coincidence signals just at the time of the SN1987A occurrence, in coincidence also with two neutrino detectors located at intercontinental distances.

About the possible fantastic interpretation that the delays of the neutrino could have been due to an energy dependent slowing down during the 168 000 light years long voyage, we wish to remark that, to our knowledge, this is the first time one has information about the travel of massive particles in interstellar space.

Even if we lack a clear idea about the causes for the U1 and neutrino signals, we believe it is important to present all the experimental information.

In conclusion, a full interpretation of the observed correlations remains open. But the history of science teaches that to ignore experimental results makes our understanding of the Universe back down.

## Notes

- 1.
Giuliano Preparata calculated a much larger cross-section in his superradiance theory (Preparata, 1990).

- 2.
Not considering the larger cross-section in the Preparata superradiance theory (Preparata, 1990).

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## ACKNOWLEDGMENTS

We thank the Kamiokande, the LSD and the Rome Collaboration for having supplied to us their data. We thank Marcello Piccolo for useful discussions and suggestions, Paolo Lipari, Eligio Lisi and Francesco Vissani for suggestions on neutrino masses.

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Buccella, F., Pallottino, G.V., Galeotti, P. *et al.* Correlation of Gravitational Waves–Neutrino Detectors: The Long Neutrino Voyage from SN1987A.
*Astrophys. Bull.* **75, **110–116 (2020). https://doi.org/10.1134/S1990341320020042

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### Keywords:

- gravitational waves-neutrinos-supernovae: individual: SN1987A