Stars as Laboratories for Fundamental Physics - MPP Theory Group

432 Chapter 11
11.4.2 Prompt ν e Burst
The prompt ν e burst from a core collapse SN can be detected, in principle,
by the forward-peaked signal from the elastic ν e e → eν e scattering
in a water Cherenkov detector. In the Kamiokande SN 1987A observations,
the first event could have been caused by the prompt ν e burst,
but naturally one event contains no statistically significant information.
It could have been caused by ν e p → ne + and simply happen to point
in the forward direction. Therefore, the main interest in the prompt ν e
burst is the possibility that it could be observed from a future galactic
SN by the Superkamiokande or SNO detectors which would yield statistically
significant signatures. A possible oscillation of the ν e burst
into other flavors would reduce the number of forward events because
of the reduced ν-e scattering cross section of non-ν e flavors (Fig. 11.10).
If the neutrino mass hierarchy is normal where the lightest mass
eigenstate is the dominant ν e admixture, the medium-induced neutrino
refractive index in the stellar mantle and envelope can cause a “mass
inversion” and thus level crossing between, say, ν e and ν µ in analogy
to the solar MSW effect. Therefore, one may expect resonant flavor
conversion of the prompt ν e burst in a collapsing star as shown by a
number of authors; 67 I follow the analysis of Nötzold (1987).
When the shock wave breaks through the neutrino sphere and liberates
the prompt ν e burst, the overlaying part of the progenitor star
has not yet noticed the collapse of its core so that the density profile is
given by that of the progenitor star. The electron density is reasonably
well approximated by a simple power law for which Nötzold (1987) used
n e ≈ 10 34 cm −3 r −3
7 , (11.11)
where r 7 ≡ r/10 7 cm. Note that 10 7 cm = 100 km is the approximate
radius of the shell from where the ν e ’s originate. According to the
discussion in Sect. 6.7.1 the electron density causes an energy shift
between ν e and ν µ or ν τ of ∆V = √ 2G F n e = 1.3×10 −3 eV r7 −3 . Comparing
this with the energy shift ∆m 2 ν/2p ν of neutrinos with momentum
p ν one finds an effective medium-induced effect of ∆m 2 eff = 2p ν ∆V =
3×10 4 eV 2 p 10 r7 −3 where p 10 = p ν /10 MeV.
However, because the prompt ν e burst itself constitutes a large local
ν e density, the neutrino-induced refractive index may be more important
than the standard electron-induced contribution. The total num-
67 Mikheev and Smirnov (1986), Arafune et al. (1987a,b), Lagage et al. (1987),
Minakata et al. (1987), Nötzold (1987), Walker and Schramm (1987), Kuo and
Pantaleone (1988), Minakata and Nunokawa (1988), and Rosen (1988).