Stars as Laboratories for Fundamental Physics - MPP Theory Group

426 Chapter 11
neutrino-sphere radius of 18 km and the inferred total binding energy
of 3.08×10 53 erg correspond much better to theoretical expectations.
Perhaps this finding can be taken as a hint that the delayed-explosion
scenario with a significant matter accretion phase is favored by the SN
1987A data over a prompt-explosion picture.
In Loredo and Lamb’s best-fit two-component model the Kelvin-
Helmholtz signal is described by a “displaced power law” cooling model
with a neutrino sphere of fixed radius R and thermal neutrino emission
with T (t) = T 0 /(1 + t/3τ). It turns out that the luminosity, which is
proportional to T 4 , follows a surprisingly similar curve to the exponential
e −t/τ so that the parameter τ has practically the same meaning
as before. ⟨E νe ⟩ for the time-integrated flux is given by 2.13 T 0 , very
similar to 2.36 T 0 for the exponential. In Fig. 11.16 the 68% and 95%
credible regions are shown in the T 0 -τ-plane. While the best-fit value
is not too different from the single-component exponential model of
Fig. 11.15, the 95% credible region is much larger, including the lowest
values of the typical theoretical ⟨E νe ⟩ predictions quoted in Eq. (11.4).
11.3.4 Neutrino Mass and Pulse Duration
Zatsepin (1968) was the first to point out that the ν e burst expected
from stellar collapse offers a possibility to measure or constrain small
neutrino masses. Because a neutrino with mass m ν travels slower than
the speed of light its arrival at Earth will be delayed by
∆t = 2.57 s
( D
50 kpc
) (10 MeV
E ν
) 2 ( ) mν 2
. (11.9)
10 eV
Because the measured ν e ’s from SN 1987A were registered within a few
seconds and had energies in the 10 MeV range, the m νe mass is limited
to less than about 10 eV.
A detailed study must proceed along the lines of the maximumlikelihood
analysis of Loredo and Lamb (1989, 1995) quoted in the
previous section where the detector background is included, and such
parameters as the unknown offset times between the detectors are left
unconstrained. Including the possibility that some of the registered
events are due to background is particularly important because the
neutrino mass limit is very sensitive to the early low-energy events at
Kamiokande which have a relatively high chance of being due to background.
Loredo and Lamb (1989) found a vanishing best-fit neutrino
mass and a 95% CL upper limit of m νe < 23 eV. This bound is less
restrictive than limits found by previous authors on the basis of less