Proc. Neutrino Astrophysics - MPP Theory Group

Quasilinear Diffusion of Neutrinos in Plasma
S.J. Hardy
Max-Planck-Institut für Astrophysik,
Karl-Schwarzschild-Str. 1, 85748 Garching, Germany
Introduction
It has been recognized for some years that a neutrino propagating in a plasma acquires an
induced charge [1]. This charge is due to the forward scattering interactions between the
neutrino and the electrons in the plasma. As these scatterings are electroweak interactions,
the induced charge is rather small, for example, 10 −31 C, for the dense plasma near the core of
a type II supernova (SN). Though weak, this charge allows neutrinos in a plasma to undergo
processes which would usually be restricted to charged particles, such as Cherenkov emission
or absorption of a photon.
The electromagnetic interactions of a neutrino in a plasma have been considered in a
variety of physical and astrophysical scenarios (for a review, see [2]). Some recent work by
Bingham et al. [3] proposed a “neutrino beam instability” where an intense flux of beamed
neutrinos propagating through a plasma leads to the production of an exponentially growing
number of photons in the plasma through stimulated Cherenkov emission. This form of instability,
caused by electron or photon beams, is well known in plasma physics. The proposed
application of the neutrino process was as a reheating mechanism for the plasma behind the
stalled shock of a type II SN. While such an instability is possible in principle, it has recently
been shown [4] that this does not occur in type II SNe.
More recently, Tsytovich et al. [5] have proposed an alternative mechanism whereby the
neutrinos from a type II SN may diffuse slightly in momentum space by propagating through
a pre-existing saturated thermal distribution of photons. The diffusion mechanism, known as
quasilinear diffusion, is based on the averaged effect of the individual interactions that occur
between the photons and the neutrinos. Again, the analogous effect involving electrons is well
known is plasma physics [6]. In their initial calculation, Tsytovich et al. obtained a timescale
for angular diffusion of the neutrinos from the core of the SN of τang ≈ 10 −4 s, this corresponds
to a scattering length of approximately 30km, independent of energy, which would be of great
interest for neutrino transport near the shock of a type II SN. The calculation reported here
represents a more rigorous calculation of this process and application of the results to a model
calculation of the plasma properties of a type II SN. It is concluded that this process is only
likely to be of importance to low energy neutrinos (below 10keV) and is unlikely to have any
bearing on the explosion of a type II SN.
Quasilinear Diffusion Rate
Given the nature of the plasma behind the shock of a type II SN, it is reasonable to assume a
high level of plasma turbulence. Within the weak turbulence approximation, this turbulence
is represented by a distribution of longitudinal photons in the plasma. The strongest level of
plasma turbulence allowed would be where the energy density associated with the longitudinal
photons is equal to the energy density associated with the thermal motion of the plasma.
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