Neutrinos from the recent LMC supernova

Sir—The supernova explosion that was observed recently¹ in the nearby Large Magellanic Cloud (LMC) provides a unique opportunity to test the theory of neutron star formation in Type II supernova explosions. In particular, one can investigate the prediction that almost all of the gravitational binding energy of the residue neutron star (~3×10⁵³ erg) was radiated within a few seconds in the form of ~10⁵⁸ neutrinos with average energy ~10–15 Me V. Here, we calculate the expected neutrino signals in terrestrial detectors which, according to the standard supernova theory^2–10, should have been observed during a short period (~1 s) before the onset of the optical supernova. (A measurement of the time delay between the first neutrino and optical pulses would be of great importance for our understanding of supernovae.) We also show how information on the fundamental properties of neutrinos (their life-times, masses and mixings, and their magnetic moments) can be obtained from neutrino observations of the LMC supernova. The number of neutrino-induced events in a terrestrial detector due to differential fluxes df/dE of neutrinos of types is given by

where n_i is the number of particles of type j (atomic nuclei and electrons) in the target and s(j) are their cross-sections for relevant reactions which depend on the neutrino type and on the neutrino energy.

Recently Wilson⁷ and Wilson et al.¹⁰ have calculated the collapse of massive stars of 10, 15 and 25 M and found that the predicted time-averaged neutrino signal does not vary greatly from star to star. In Table 1 we list the neutrino fluxes at the source as calculated by Wilson for a supernova explosion of a 25 M star with a 1.6 M iron core and the fluxes expected at a distance of 50 kpc from the supernova.

We have calculated the event rates in existing solar neutrino detectors using the spectra and fluxes of Wilson^7,10 and neutrino cross-sections from Bahcall (ref. 11 and unpublished data). Kamiokande II¹², which contains 3 kt of water, should experience about 50 events with a positron recoil energy in excess of 10 Me V. The events should all be concentrated within a few seconds at an epoch that was a short time before the onset of the optical supernova on 24 February 1987. The high time resolution of the detector and the bunching in time of the real events should make the signal stand out above noise by a large factor. The 140-t liquid-scintillator detectors of the University of Pennsylvania¹³ in the Homestake mine and the 90-t scintillator detector in the Mont Blanc Tunnel¹⁴ should have seen about 3 events each if the standard supernova theory is correct. This signal is marginally detectable because of the high time resolution of the experiments. A comparison of the arrival times for neutrino events seen in different detectors will provide a crucial test of the physical reality of the observations; the neutrinos should arrive essentially simultaneously at all terrestrial detectors. For the ³⁷Cl tank of Davis¹⁵, only one additional ³⁷Ar atom is expected to be produced, a signal which would not be detectable.

Standard supernova theory may be wrong. It is more difficult to calculate how a star explodes than to estimate how the Sun shines and we do have the solar neutrino problem. To show the power of observations with existing neutrino detectors, we assume that 3×10⁵³ ergs are emitted as thermal neutrinos (temperature T) and that the energy is distributed equally among all neutrino flavours. We find the following total number of events for the three different classes of neutrino detector mentioned above:

(The last relation overestimates the detection rate for temperatures above 5 Me V; it is too large by a factor of about 2 at T = 10 Me V). A thermal spectrum with a typical energy of T~10–15 Me V would produce an event rate for the ³⁷Cl experiment that is an order of magnitude larger than the standard supernova model.

A number of authors, motivated by the solar neutrino problem¹⁶, have suggested recently that the neutrino has properties not included in the simplest electroweak model. Explanations of the solar neutrino problem of this type include neutrino decay¹⁷, resonant neutrino oscillations¹⁸ and a large neutrino magnetic moment (L.B. Okun et al., preprint ITEP, 1986). The LMC supernova can be used to test these suggestions.

If the ~10 Me V ⁸B solar neutrinos decay significantly during their flight from the Sun to Earth, then essentially no neutrinos will survive the flight from the LMC supernova at a distance of 50 kpc. Consequently, the neutrino decay hypothesis which may explain the solar neutrino problem predicts no neutrino signals in underground neutrino detectors from the recent LMC supernova. If neutrinos are detected, their life times in the laboratory frame must exceed 10⁵ years.

Neutrino oscillations increase the expected signals because the average energy of the n_ms and n_ts is about twice that of the n_es (see Table 1). Electron neutrinos generate most of the signals and the interaction cross-sections increase with incident neutrino energy. If the n_ms and n_ts oscillate into n_es (and vice versa) after leaving the neutron star (for example, through the MSW¹⁸ effect on positrons and electrons in the outer layers of the star) then the incident n_es will have higher energies and higher cross-sections and consequently will have more events in terrestrial detectors. Complete interchange between n_es and n_ts or n_ms will increase the signals in water and liquid scintillators by about a factor of two but will still produce only ~1 event in Davis's solar neutrino experiment.

Dar¹⁹ has shown that if the neutrino magnetic moment is in the range 10⁻¹⁰ to 10⁻¹² Bohr magnetons (which explains the solar neutrino problem (L.B. Okun et al. preprint ITEP, 1986)), then relatively-high-energy neutrinos with a thermal spectrum can escape from a supernova explosion as a result of magnetic interactions with electrons. A conservative assumption, within this non-standard picture, is that the n_e neutrinos are emitted with a temperature in excess of 10 Me V (and with about half the fluxes assumed for the thermal case cited above) (see ref. 19). The event rates for this model can be obtained from equation (2) by substituting the relevant temperature and dividing by two (to correct for smaller fluxes).

The collapse event produces a fluence of ~3×10⁵⁸ (m_i/T)^3/2e^−m/T of neutrinos of flavours i with mass m_i. This flux contains a significant amount of energy if the neutrino mass, m_i, is less than a few hundred MeV. If these massive neutrinos are unstable and decay electromagnetically (see refs 20–22), for example, via n_H→n_e+e⁺+e⁻ or other electromagnetic decay modes, ~10⁵³f(m_i/T)^3/2e^−m_i/T ergs will be produced in electron–positron pairs and g-rays between the Earth and the supernova (f = 1 if the neutrino life time, t, is shorter than 5×10¹²s, the flight time from the supernova to the Earth, and f = t/5×10¹² otherwise). In order to observe an electromagnetic signal from this decay, it must take place outside the collapsing star (t10³s). If more than 10⁻¹²/[f(m_i/T)^3/2e^−m_i/T] of this energy is converted to g-rays, within one second (either by direct decay or by rapid electron–positron annihilation), we should detect a g-ray burst coincident with the n-signal. The absence of such a burst coincident with the &n;-signal can be used to eliminate electromagnetic decay modes of neutrinos with masses in the range of one to a few hundred Me V and lifetimes larger than ~10³s.

Higher-energy neutrinos will arrive at the Earth before lower-energy neutrinos if the neutrino has a finite mass. However, this time delay, ~0.01(m_n/1 eV)²(10 Me V/E_n)²s, is too small to be observable for the LMC supernova.

A yet unknown, but potentially significant, fraction of the released energy might be emitted as gravitational radiation. The gravitational wave emission depends strongly on the asymmetry of the collapse and in particular on the amount of rotation of the core. Even with the most optimistic assumptions about gravitational radiation emission, E_gr = 0.01 M_core0.016 M, and h = Dl/l0.7×10⁻¹⁸, the LMC supernova is just below the sensitivity of current detectors. However, it is interesting to ask whether gravitational radiation would have been seen by next generation detectors (such as the proposed Caltech/MIT interferometer) with a sensitivity of 10⁻²¹. At low angular momentum, the gravitiational radiation emissivity scales²³ like J⁴. Therefore, the LMC supernova would have been detected even if the core was rotating only at 1/30 of its breakup speed, which is as slow as the Crab pulsar today.

Note added in proof: Since this paper was received on 2 March the neutrino burst was found by the Kamiokande experimental group, with properties generally consistent with the calculated expectations.

J.N. BAHCALL
The Institute for Advanced Study,
Princeton, New Jersey 08540, USA

A. DAR^*
Department of Physics and Space,
Technion, Haifa, Israel

T. PIRAN^*
Racah Institute for Physics,
Hebrew University, Jerusalem, Israel

^*Present address: The Institute for Advanced Study, Princeton, New Jersey 08540, USA.

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Upper limit on the mass of the electron neutrino

J. N. Bahcall & S. L. Glashow
The Institute for Advanced Study, Princeton, New Jersey, USA
Harvard University, Cambridge, Masachusetts 02138, USA

The historic detection by the Kamiokande-II collaboration¹ and the IMB collaboration² of neutrinos from the Large Magellanic Cloud (LMC) supernova provides the first opportunity to determine the mass, , of the electron neutrino from astronomical observations. Here we show that , is less than 11 eV, provided only that propagation effects have not conspired to sharpen, by more than a factor of two the narrow pulse-width of neutrinos, observed by the Kamiokande-II collaboration from the LMC supernova. This result improves on the laboratory limit on , and confirms the view that electron neutrinos do not constitute the major component of the matter density of the Universe.

Many authors have discussed the fact that higher energy neutrinos from a distant supernova will arrive at Earth before lower energy neutrinos if the neutrino has a finite mass^3,4. For the recently observed LMC supernova, the additional travel time, Dt, that is required for a neutrino of energy E because it has a mass , where d is distance to the LMC:

For any given neutrino mass, one can calculate from equation (1) the emission time (offset by the light travel time) at the star for each neutrino that causes an observable event. The data contain no further information. How does one decide if the calculated departure times are 'acceptable'? Previous authors have not discussed this question.

Without some assumption about what is physically or astronomically plausible, one cannot proceed further. We do not have any a priori knowledge of the departure times of the neutrinos. Whatever the neutrino mass, the complicated nuclear and hydrodynamic processes occurring in the explosive formation of the neutron star might somehow yield a sequence of emission times in just such a way as to produce the sharply peaked time structure seen at Kamioka. Indeed, our analysis is based solely on the assumption that the narrow (in time) observed pulse is not an accident resulting from propagation effects.

Before describing our method, we will summarize what is known about the energies and arrival times of the observed Kamiokande-II events. In both these water detectors, the dominant events are^1,2,5 absorption by protons and n_e, scattering by electrons.

The first eight neutrino events arrived within less than 2 seconds, followed by a period of 7 seconds in which no neutrinos were detected. There were then three less certain neutrino events in the next 3 seconds. In the initial two-second pulse, five of the eight events were observed in the first 0.5 s. The events corresponded to measured positron (or electron) energies ranging from 7.5 MeV to 35 MeV, with typical uncertainties of the order of 20%. (In deriving mass limits, we have converted the observed (positron or electron) energies to neutrino energies by supposing that each event was due to absorption on protons by antineutrinos. The IMB events reported so far are all relatively high in energy (20 MeV) and are therefore less useful in setting limits on the neutrino mass.

If the observed pulse duration were caused solely by the mass of the neutrino, then the higher energy events would have arrived first. This was not observed. The time-ordered sequence of positron (or electron) energies was (all in MeV) 20, 13.5, 7.5, 9.2, 12.8, 35.4, 21.0, 19.8, 8.6, 13.0 and 8.9. Two of the lowest energy events (7.5 MeV and 9.2 MeV) preceded by 1.2 s three higher energy events (35 MeV, 21 MeV and 19.8 MeV). We conclude that the duration of the pulse at the source was at least 1.2 s and could have been (for zero neutrino mass) as long as the entire observed pulse.

The only assumption that we will make is that propagation effects did not sharpen the pulse width of the observed neutrino events by more than a factor of two. Thus the eight events which were detected at Earth in the initial two seconds of the pulse are presumed not to have been spread out at the source by more than four seconds. The choice of a factor of two is arbitrary but we believe that it is conservative and, if the reader prefers a different numerical factor, he can make the appropriate scaling using Table 1 (below). Stated differently, we assume that the effects of propagation on the arrival times have not been such as to produce by accident a short pulse from what was initially a much more diffuse signal.

Table 1 shows as a function of assumed neutrino mass the computed duration, at the neutron star, of both the first eight events (D₈) and all the reported events (D₁₁). For = 0, these quantities are equal to the observed values of 2 s and 13 s. The inferred durations at the star increase monotonically with assumed mass because the observed events do not have the relation between energy and arrival time that is implied by equation (1). Using the best estimates given by the Kamiokande collaboration for all of the energies we find that if exceeds 9.0 eV, then the 2 s initial pulse that is observed on Earth would have been longer than 4 s at the neutron star. We have also recalculated the upper limit by varying the nominal energies within their quoted errors. In all cases, the pulse width at the source is at least twice the value measured at Earth if 11 eV. We conclude therefore that

The strength of this limit derives from the lower energy events (7.5 MeV, 9.2 MeV and 12.8 MeV), all of which are observed to move at large angles with respect to the direction of the LMC (108, 70 and 135 degrees respectively). The measured directions show that these three events are not due to electron-neutrino scattering, which is strongly forward peaked.

A neutrino mass of 27 eV is required, according to Table 1, to make the entire set of eleven observed events twice as long (25 s) at the source than is observed at Earth. We reject this possibility as physically implausible because it implies that the initial pulse (observed to be 1.9 s in duration at the Earth, and surely a physically significant phenomenon) was compressed in time by more than an order of magnitude (from 22.4 s at the star).

There are other ways, most of them more complicated, of analysing the Kamiokande-II data. One can, of course, obtain more stringent limits provided one is willing to introduce stronger assumptions regarding what is astronomically or physically plausible. For example, if one could justify the claim that the five events observed in the first 0.5 seconds had a distinct astrophysical origin, one could lower the upper limit to 7.5 eV including the measurement errors.

Conservatively, we conclude that the mass of the electron neutrino must be less than or equal to 11 eV. This limit is stronger than has been achieved by 50 years of measurements on terrestrial systems.

Larger detectors sensitive to lower energy neutrinos should be able to observe, with much higher event rates, subsequent supernovae explosions in the Galaxy. Supernovae in the Galaxy could be as frequent as one a decade⁶ if they occur in obscured regions and are therefore not associated with observable optical supernovae. The next observation of neutrinos from a supernova explosion will provide an independent measurement of the neutrino mass and will exclude the extremely unlikely possibility that the LMC distance, the detected neutrino energies and the departure times all conspired to sharpen greatly the neutrino signal from the collapse. With larger detectors, it should be possible to set even better limits on (or measure) the mass of the electron neutrino. The higher event rates will permit experimentalists to determine characteristics of the ambient material at the time the neutron star is being formed. In the extended periods between observable explosions, the detectors can be used to measure accurately the arrival times, energies and directions of solar neutrinos.

We thank the Kamiokande-II collaboration and the IMB collaboration for sharing with us their epochal data. This work was supported in part by the NSF.

Received Friday 13 March; accepted 23 March 1987.

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