Stars as Laboratories for Fundamental Physics - MPP Theory Group

Supernova Neutrinos 401
ate neutrino sea has its Fermi surface at around 200 MeV. The lepton
number profile (lower panel of Fig. 11.2) has a step-like form, with the
step moving inward very quickly when the shock breaks through the
neutrino sphere. The quick recession of the lepton profile during the
first 0.5 s represents deleptonization during the mantle cooling phase.
After this initial phase, however, the bloated outer part of the star
has settled; it is more difficult for neutrinos to escape from this compact
object. Still, the steep gradient of lepton number drives an outward diffusion
of neutrinos which move toward regions of lower Fermi momentum
and thus, of lower degeneracy energy. Therefore, they “downscatter,”
releasing most of the previous electron and neutrino degeneracy
energy as heat. Hence near the edge of the lepton number step the
medium is heated efficiently. In Fig. 11.2 it is plainly visible that the
temperature maximum of the medium is always in the region of the
steepest lepton number gradient. 62 Therefore, the medium first heats
near the core surface, and then the temperature maximum moves inward
until it has reached the center. At this time the core is entirely
deleptonized; it continues to cool, the temperature maximum at the
center drops to obscurity.
The neutrino radiation leaving the star has typical energies in the
10 MeV range, compared with a 200 MeV neutrino Fermi energy in the
interior. Therefore, the loss of lepton number by itself is associated
with relatively little energy. Put another way, only a small excess of ν e
over ν e is needed to carry away the lepton number. The total energy
is carried away in almost equal parts by each (anti)neutrino flavor.
11.1.3 Supernova Explosions
How do supernovae explode For some time it was thought that the
outer layers of the star were ejected by the momentum transferred from
the outward neutrino flow which is released after the core collapse (Colgate
and White 1966). This scenario had to be abandoned after the
discovery of neutral-current neutrino interactions which trap these particles
so that they are released only relatively slowly. With the demise
of the neutrino explosion scenario the earlier suggestion of Colgate and
Johnson (1960) of a hydrodynamic shock wave driving the explosion became
the standard, the so-called “prompt explosion scenario” or “direct
mechanism.” It continued to malfunction, however, because in numerical
calculations the shock tended to stall because of energy dissipation
62 I thank David Seckel for explaining this point to me which is not usually stressed
in the pertinent literature.