Stars as Laboratories for Fundamental Physics - MPP Theory Group

Particle Dispersion and Decays in Media 235
In Sect. 2.2.3 it has been discussed that neutrino emission cools
hot white dwarfs so fast that there is a clear depression of the whitedwarf
luminosity function at the hot and bright end relative to the
simple Mestel law which takes only surface photon emission into account.
This depression would be enhanced by additional cooling caused
by dipole moments or millicharges, allowing one to derive a limit of
about µ 12 < 10, although even for µ 12 ≈ 3 a nonnegligible effect
is apparent.
A more restrictive and probably more reliable limit can be derived
from the properties of globular-cluster stars (Raffelt 1990b). To this
end one may use the simple criteria derived in Sect. 2.5 which state
that a novel energy-loss rate is constrained by ⟨ϵ x ⟩ < ∼ 10 erg g −1 s −1 for
the average core-conditions of a horizontal branch star, and for those of
a low-mass red giant before the helium flash. In both cases T ≈ 10 8 K.
For this temperature, the plasma loss rates are shown in Fig. 6.14 as
a function of density. The anomalous rates were obtained from the
standard one according to Eq. (6.94), taking Q 1 /Q 3 = Q 2 /Q 3 = 1 and
using the zero-temperature plasma frequency given in Eq. (D.12) as a
function of density.
The first criterion of Sect. 2.5, based on the helium-burning lifetime
of HB stars, requires calculating the energy loss rate at an average
density which is below 10 4 g cm −3 . Therefore, the medium is so dilute
Fig. 6.14. Neutrino energy-loss rate in helium at T = 10 8 K. Solid line:
Total standard rate. Long dashes: Standard plasma rate. Short dashes:
Plasma rate induced by a dipole moment µ ν = 2×10 −12 µ B . Dots: Plasma
rate induced by a neutrino “millicharge” e ν = 10 −14 e.