Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
Taking into account the differential number of neutrinos dnνα(p) for a certain momentum
p and integrating over all momenta one can write the effective neutrino-
neutrino Hamiltonian:
Hνν = √
2GF
α
ρνα(p ′ )dnνα(p ′ ) − ρνα(p ′ )dn¯να(p ′
) dp ′
(5.7)
This formula is valid for an isotropic and homogeneous neutrino distribution,
which physically corresponds to the Early Universe environment. For a non
homogeneous but still isotropic environment, one has to add a geometric factor
(1 − ˆp · ˆp ′ ) 1 taking into account the fact that neutrinos interact with each
other with a certain angle of interaction. For such an environment, the neutrinoneutrino
Hamiltonian is:
Hνν = √
2GF ρνα(p ′ )(1 − ˆp · ˆp ′ )dnνα(p ′ ) − ρνα(p ′ )(1 − ˆp · ˆp ′ )dn¯να(p ′
) dp ′
α
5.1.2 The Neutrino Bulb Model
(5.8)
Before studying the various and rich behaviours of the neutrino-neutrino interactions
that occur inside the supernova, we have to establish the model to use.
This model must be precise enough to correctly take into account the relevant
physics that take place near the neutrino sphere, but in the same time not too
complex in order to be computationally doable. In [52], Duan & al. introduce
the Neutrino Bulb Model (NBM) that we use. Let us present the hypothesis
and limits of this model where approximations about the physical and geometric
conditions of the post-shock supernova made. This model is characterized by the
following assumptions:
1. The neutron star emits neutrinos uniformly and isotropically from the surface
of the neutrino sphere of radius Rν;
2. At any point outside the neutrino sphere, the physical conditions, such as
baryon density nB, temperature T, etc..., depend only on the distance r
from this point to the center of the neutron star;
3. Neutrinos are emitted from the neutrino sphere surface in pure flavor eigenstates
and with Fermi-Dirac type energy spectra.
The neutrino bulb model, as illustrated in Fig. 5.2, has two fundamental symmetries.
Since there is a spherical symmetry, one only needs to study the physical
conditions (in our case: the neutrino states) along one radial direction, the z–axis
1 Here a hatted vector ˆn denotes the direction of vector n, and is defined as ˆn ≡ n/|n|.
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