Stars as Laboratories for Fundamental Physics - MPP Theory Group

514 Chapter 13
ν e ’s are detected. These expectations are borne out by the numerical
results shown in Fig. 13.6. A doubling of the number of flavors is
probably excluded by the observed signal duration.
13.7 Neutrino Opacity
The cooling time scale of a young SN core is determined by the neutrino
opacities which in turn are dominated by the neutral-current scattering
ν + N → N + ν of neutrinos on nucleons. Apart from final-state Pauli
blocking effects these opacities are given in terms of the scattering cross
section σ = (G 2 F/π) (CV 2 + 3CA) 2 Eν 2 where the neutral-current nucleon
weak-coupling constants C V,A were given in Appendix B. Therefore, the
neutrino opacities are dominated by the axial-vector, i.e. the nucleon
spin-dependent interaction. In Sect. 4.6.7 it was discussed that a naive
application of perturbation theory in a nuclear medium likely is not
appropriate because of the large spin fluctuation rate implied by this
method. It would indicate that the spin of a given nucleon fluctuates
so fast in a SN core that a neutrino would “see” on average a nearly
vanishing contribution. This would lead to a decrease of a typical axialvector
scattering rate as estimated in Fig. 4.9.
To test if such a suppression effect is compatible with the SN 1987A
neutrino signal, Keil, Janka, and Raffelt (1995) calculated a series of
protoneutron star cooling sequences with modified neutrino opacities.
To this end they substituted CA 2 → F CA 2 in the numerical subroutine
which evaluates the opacities where
F = (1 − a) +
a
(13.12)
1 + b
with
b = 1
12
( ) 2
(
Γσ
≈
T
) 2
ρ 10 MeV
. (13.13)
3×10 13 g cm −3 T
Here, a = 1 represents full suppression while smaller values of a allow
one to dial a lesser reduction of the opacities.
The predicted neutrino signal at IMB and Kamiokande II was,
again, characterized by the total number of expected events N IMB and
N KII as well as the signal durations t IMB and t KII which represent the
time at which 90% of the total number of expected events have been accrued.
In Fig. 13.7 these quantities are shown as a function of a where
the suppression effect was implemented for both, neutral- and chargedcurrent
axial-vector interactions. The results marked with open circles