Using supernova neutrinos to monitor the collapse, to search for gravity waves and to probe neutrino masses

Introduction Core collapse supernovae (type II, Ib and Ic) occur when the progenitor has a mass > 8 M ⊙ and originate compact remnants: neutron stars, black holes and possibly hybrid (=quark core) stars. The formation of such an object requires to carry away a huge binding energy, several times 10 53 erg. It is well known that the role of carriers is played mainly by neutrinos; but more importantly for us, and according to the standard scenario of core collapse supernova explosion 1,2 , neutrinos play also a fundamental role in driving the explosion. They deposit energy that can revive the shock, which will eventually cause the expulsion of the external layers of the star.

The current scenario of neutrino emission is based on two main phases of neutrino emission. The first one, called accretion phase, entails 10-20% of the total energy. It is characterized by a very high neutrino luminosity and is directly related to the matter which is accreted over the proto-neutron star through the stalled supernova shock wave. The other phase is called cooling phase; the neutrinos escape slowly from the proto-neutron star, releasing the remaining 80-90% of the energy. Only two analyses of SN1987A data included both emission phases: the analysis of 2001 by Loredo and Lamb 4 and the recent one due to our group 3 . The most relevant modification of this last analysis is the improvement of the model of νe emission Fig. 1. Directions of events events in a Cherenkov detector of 32 kton: the ∼ 300 elastic scattering events are visible over the ∼ 5000 inverse beta decay events, expected from the galactic center. [We use the Lambert projection: the points of the unit sphere-i.e., the possible directions-identified by n = (s θ c φ , s θ s φ , c θ ), are mapped into the circle of radius 2, whose points are identified by

that we are going to describe in some detail in the following. a Remarkably, both these analyses claim an evidence of the phase of accretion in the SN1987A data.

Detecting Supernova Neutrinos Before describing the model, we recall how many events we expect from the most important detection reaction, the inverse beta decay (IBD): νe + p → e + + n. The number of events is: N ev = N p × F νe × σ νep . The cross section for a νe with average energy Ē = 15 MeV is

The νe fluence (time integrated flux) can be written by

, where E b = 3•10 53 erg is the gravitational binding energy, D is the distance of the supernova and “6” are the neutrino types. For 1 kton detector, there are N p ≈ 1 kton × 10 9 × 6 • 10 23 × 2/18× 10 32 protons. So the number of expected events is about 10. This rough estimation agrees with the number of events observed: 16 in Kamiokande-II 8 (2140 tons), 8 in IMB 9 (6800 tons) and 5 in Baksan 10 (200 tons): 29 events in 30 seconds, that include a few background events.

Other reactions are expected to yield less events in water Cherenkov (as Kamiokande-II, IMB, Super-Kamiokande) or scintillators (as Baksan, LVD, Kam-LAND). This is true, e.g., for the elastic scattering reaction, where the cross section

F m e E is much smaller since E ≫ m e . However the electrons are scattered by supernova neutrinos in the same direction of the incoming neutrinos, for the same a Other features of the new analysis: (i) energy, time and direction of each event are taken into account; (ii) the correct background 7 , finite detection efficiency and energy resolution are described; (iii) dead times and live time fraction are included; (iv) only the relative times are used and the delay of the detector response, called offset times, is accounted for; (v) frequentist techniques of inference are applied with an unbiased likelihood 6 ; and (vi) the full 30 s analysis window is considered. An updated cross section of IBD 5 is used, an improved description of the neutrino spectrum is introduced and neutrino oscillations are accounted for in a suitable approximation.

reason, E ≫ m e . In other words, elastic scatterings will allow ’neutrino imaging’ as is illustrated in the figure, where we show the directions of arrival of the supernova events. The cluster of events in the center, due to elastic scattering, is well visible over the background of inverse beta decay events, which are only mildly directional. The statistical analysis shows that the direction of the supernova is determined with an accuracy of few degrees. See 11,12,6 for further discussion.

We close this introductory note remarking that supernova neutrinos are a special target of neutrino astronomy. Indeed, despite the rarity of the observable core collapses, these neutrino can be certainly detected as demonstrated by SN1987A; moreover, they will permit to shed light on many open theoretical problems, regarding several fields: astrophysics, nuclear physics and particle physics.

We describe now the model for the neutrino flux. Each emission phase is characterized by its intensity, its duration and the average energy of the emitted neutrinos. So, we have 6 as

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