Stars as Laboratories for Fundamental Physics - MPP Theory Group

Radiative Particle Decays 463
emission at T νe ≈ 4 MeV so that the fluence 73 of ν’s plus ν’s per flavor
was about
F ν = 1.4×10 10 cm −2 (4 MeV/T ν ) , (12.12)
taking ⟨E ν ⟩ = 3T ν . Approximately the same result is thought to apply
to ν µ and ν τ with about 1.3−1.7 times the temperature, although for
those flavors there is no direct measurement.
Because SN 1987A occurred in the Large Magellanic Cloud (LMC)
at an approximate distance of d LMC = 50 kpc = 1.5×10 23 cm an enormous
decay path was available for the neutrinos from this measured
source. A very restrictive upper limit photon flux was provided by the
gamma ray spectrometer on the solar maximum mission (SMM) satellite
which was operational at the time of the neutrino signal and did
not register any excess γ counts above the normal background. In order
to use this result one needs to compute the expected γ signal from
neutrino decay. Because one is dealing with a short neutrino burst the
previous results for stationary sources do not apply directly: the time
structure of the expected photon burst must be taken into account.
This is easy when the mass of the parent neutrino is below about
40 eV; the pulse dispersion is then not much larger than the duration
of the observed ν e burst. Because for low-mass neutrinos the decay
photons have essentially the same time structure as the neutrino burst
one considers the γ fluence for a time interval of about 10 s around the
first neutrino arrival. The non-ν e flavors could be heavier if they violate
the cosmological mass limit of a few 10 eV. Then the photon pulse will
be correspondingly stretched, a case to be studied in Sect. 12.4.4 below.
If the neutrino masses are not degenerate so that in Eq. (12.5)
δ m = 1 the expected differential fluence is
F ′ γ(E γ ) = F ν
m ν
τ γ
∫ ∞ (
d LMC dE ν 1 − α + 2α E )
γ Φν (E ν )
,
E γ E ν Eν
2
(12.13)
where Φ ν (E ν ) ≡ F ′ ν(E ν )/F ν is a normalized spectrum (units MeV −1 ).
For this expression CP conservation was assumed so that ν’s and ν’s are
characterized by the same values of τ γ and α as discussed in Sect. 12.2.1.
73 With fluence one means the time-integrated flux. In this book I use the symbol
F for a differential particle flux (cm −2 s −1 MeV −1 ), the symbol F for a fluence
(cm −2 ), and F ′ = dF/dE for a “differential fluence” which includes spectral information
(cm −2 MeV −1 ).