Stars as Laboratories for Fundamental Physics - MPP Theory Group

402 Chapter 11
associated with the dissociation of the remaining iron shell it had to
work through before it could fly. Recall that the shock wave forms
relatively deep inside of the collapsing iron core of the progenitor star.
A possible solution is the “delayed mechanism” (Wilson 1983; Bethe
and Wilson 1985) where the shock wave lingers at a constant radius for
a few 100 ms and then takes off again (Fig. 11.1), powered both by the
accretion of material and by the energy deposition of the neutrino flow.
In this regard the dilute hot region (ρ of order 10 6 −10 8 g cm −3 , T of
order 1 MeV) below the stalled shock plays a major role at absorbing
neutrino energy. 63 Unfortunately, it is not certain that the neutrino
flux can deposit enough energy to revitalize the shock as the energy
transfer is relatively inefficient. However, if one adjusts the amount of
neutrino energy transfer to a value above a rather well defined threshold
one obtains beautiful explosions (Fig. 11.4). It should be noted that
the spectacular explosion of a SN—which at the peak of its lightcurve
outshines an entire galaxy—is only a “dirt effect” relative to the release
of neutrino energy which equals the gravitational binding energy of
the newborn neutron star of about G N M/R ≈ 3×10 53 erg with M ≈
1.4 M ⊙ and R ≈ 10 km. The total energy released in the kinetic energy
of the ejecta and in electromagnetic radiation is a few 64 10 51 erg, on the
order of 1% of the total neutron-star binding energy. Therefore, on
energetic grounds alone there is no problem at tapping the neutrino
flux for explosion energy.
A variety of schemes are currently being discussed to achieve a successful
shock revival. It is thought that convection may play a major
role at transporting energy to the surface of the bloated protoneutron
star which has formed after the break-out of the shock (e.g. Burrows
and Lattimer 1988; Wilson and Mayle 1988; Mayle and Wilson 1993;
Burrows and Fryxell 1992, 1993; Janka and Müller 1993b). It may be
that this mechanism can boost the effective neutrino luminosity for a
few hundred milliseconds, enough in some calculations to trigger an
explosion (see however Bruenn and Mezzacappa 1994). At any rate,
in the absence of a fundamental treatment of convection this method
is essentially one way of parametrizing the initial amount of neutrino
heating below the shock.
63 Goodman, Dar, and Nussinov (1987) proposed that the pair-annihilation process
νν → e + e − might be the dominant mode of energy transfer. However, Cooperstein,
van den Horn, and Baron (1987) critizised the neutrino emission parameters
of that study while Janka (1991) found that a proper treatment of the phase space
renders this process less efficient than had been originally thought.
64 This unit is sometimes referred to as 1 foe, for “ten to the fifty one ergs.”