Stars as Laboratories for Fundamental Physics - MPP Theory Group

Supernova Neutrinos 407
11.2 Predicted Neutrino Signal
11.2.1 Overall Features
One of the most important aspects of SN physics relevant to particle
astrophysics is the immense flux of neutrinos liberated after the core
collapse. This flux has been measured from SN 1987A, and with luck
will be measured again from a galactic SN in the future. Therefore,
it is important to understand the neutrino signal to be expected from
this sort of event.
On a crude level of approximation one can understand the main features
of the overall neutrino signal on the basis of very simple physical
principles. The overall amount of energy to be expected is given by the
binding energy of the compact star that formed after collapse
E b ≈ 3 G N M 2
( ) 2 ( )
M 10 km
5 R
= 1.60×1053 erg
. (11.1)
M ⊙ R
It is reasonable to expect the energy to be equipartitioned among the
different neutrino flavors and so to expect about 1 6 E b in each of the six
standard (anti)neutrino degrees of freedom. (Here and in the following
Newtonian physics is used; general relativistic corrections to energies,
temperatures, etc. as viewed from a distant observer can be as large as
several 10% due to gravitational redshifts.)
Neutrinos are trapped in the interior of the high-density neutron
star. Therefore, they are emitted from the relatively well defined surface
at a radius of 10−20 km, depending on the mass and the nuclear equation
of state. As long as the material near the surface is nondegenerate
it must support itself against the local gravitational field by normal
thermal pressure. One may apply the virial theorem (Chapter 1) which
informs us that the average kinetic energy of a typical nucleon near
the neutron-star surface must be half of its gravitational potential, i.e.
2⟨E kin ⟩ ≈ G N M m N /R (nucleon mass m N ). With a neutron-star mass
of M = 1.4 M ⊙ and a radius R = 15 km one finds ⟨E kin ⟩ ≈ 25 MeV
or T = 2 3 ⟨E kin⟩ ≈ 17 MeV. Therefore, thermal neutrinos emitted from
the neutron-star surface are characterized by a temperature of order
10 MeV.
The duration of neutrino emission is a multiple of the neutrino diffusion
time scale over the dimension of the neutron-star radius,
t diff ≈ R 2 /λ, (11.2)
where λ is a typical mean free path. A typical neutral-current weak