Stars as Laboratories for Fundamental Physics - MPP Theory Group

Supernova Neutrinos 413
signal (Sect. 11.3). However, in some cases studied by Keil and Janka
(1995) with an EOS including hyperons this final collapse occurs so
late (at 8 s after bounce in one example) that black-hole formation is
difficult to exclude on the basis of the SN 1987A observations, notably
as no pulsar has yet been found there.
Needless to say, with so many parameters to play it is not difficult
to find combinations of EOS, core mass, accretion rate, and initial
temperatures which fit the observed SN 1987A signal well within the
statistical uncertainties of the observations. An example is model 55
of Burrows (1988) which is based on a “stiff EOS,” an initial baryonic
core mass of 1.3 M ⊙ , and an accretion of 0.2 M ⊙ within the first 0.5 s.
The evolution of the effective ν e luminosity and temperature is shown
in Fig. 11.7. After about 1 s the decay of the temperature is fit well by
an exponential e −t/4τ with τ ≈ 10 s while the decay of the luminosity
is poorly fit by an exponential; it decays approximately as t −1 after 1 s.
For later reference, the time-integrated flux (fluence) of this model is
shown in Fig. 11.8.
It must be stressed that the “cooling behavior” (decrease of the average
ν e energy) shown in Fig. 11.7 may not be generic at early times.
Initially the star is quite bloated, and relatively cold. Therefore, the
Fig. 11.8. Expected ν e fluence (time-integrated flux) from SN 1987A, assuming
a distance of 50 kpc, and taking Burrows’ (1988) model 55 neutrino
luminosity shown in Fig. 11.7. The solid line is for an assumed Maxwell-
Boltzmann energy spectrum for a given average neutrino energy, the dashed
line for a Fermi-Dirac spectrum with a degeneracy parameter η = 2 as
in Fig. 11.6.