Stars as Laboratories for Fundamental Physics - MPP Theory Group

424 Chapter 11
η = 0 are taken for the instantaneous spectra. The time-integrated
spectrum of the exponential cooling model looks quite similar to the
time-integrated spectrum shown in Fig. 11.8.
Loredo and Lamb also used α ≡ (R/10 km) (50 kpc/D) g 1/2 as a fit
parameter where D is the distance to SN 1987A and g a statistical
weight factor which is unity if only left-handed, massless or low-mass
neutrinos of the three sequential flavors are emitted. The registration
time of the first neutrino in each detector is taken as a free parameter
relative to the arrival time of the first neutrinos. In the 1995 analysis,
Loredo and Lamb included the Baksan signal without “event 0”
which is attributed to background because it precedes the main bunch
by 5 s.
The following six parameters are then allowed to float freely in order
to achieve a maximum-likelihood result: T 0 , τ, α, t off (IMB), t off (KII),
and t off (BST). All best-fit offset times are found to be zero. The other
best-fit values are α = 4.02, τ = 4.37 s, and T 0 = 3.81 MeV. This
initial temperature of the exponential cooling model corresponds to an
average neutrino energy of the time-integrated flux of ⟨E νe ⟩ = 9.0 MeV.
In Fig. 11.15, the 68% and 95% credible regions are shown in the T 0 -τplane
where T 0 has been translated into ⟨E νe ⟩ which is of greater direct
relevance.
Fig. 11.15. Two-dimensional marginal distribution for the parameters τ and
⟨E νe ⟩ = 2.36 T 0 of the exponential cooling model. (Curves courtesy of Tom
Loredo, taken from Loredo and Lamb 1995.)