Stars as Laboratories for Fundamental Physics - MPP Theory Group

460 Chapter 12
This bound is diminished if ν e and ν ′ are nearly degenerate so that
in Eq. (7.12) δ m ≪ 1. The structure of the photon flux as a function of
δ m in Eq. (12.5) is such that for δ m < 1 the spectrum can be obtained,
in a doubly logarithmic representation such as Fig. 12.4, by shifting
it “to the left” and “upward” by the amount | log δ m | each, the shape
itself remaining unchanged (Raffelt 1985). The excluded regime in the
plane of τ γ /m νe and δ m is shown in Fig. 12.5 (left panel). Again, it
is more appropriate to express these limits in terms of µ eff and δ m by
virtue of Eq. (7.12), leading to Fig. 12.5 (right panel). As expected, for
fixed m νe the limits on µ eff quickly degrade with small δ m .
Fig. 12.5. Excluded parameters for ν e → ν ′ γ from the Sun for nearly degenerate
neutrino masses (adapted from Raffelt 1985).
A limit on τ γ /m νe similar to the solar one can be obtained from
the central bulge of the galaxy. Within 2.5 kpc it contains a luminosity
of about 2×10 10 L ⊙ and thus a neutrino luminosity similarly enhanced.
With its distance of (8.7±0.6) kpc it is about 2×10 9 times farther away
from us, leading to a much smaller local neutrino flux than that from
the Sun. However, the neutrino decay path is also 2×10 9 times larger.
Even though the neutrino flux scales with the inverse of the distance
squared from the source, the flux of decay photons scales only with the
inverse distance! Therefore, the local flux of decay photons would be
larger than the solar one by perhaps a factor of ten. The measured hard
x- and soft γ-ray flux from the central region of the galaxy is similar
in magnitude to the upper limit solar flux so that one obtains a similar
constraint on radiative decays. Because no dramatic improvement is
expected a detailed analysis is not warranted. However, a substantial
improvement is achieved by considering all hydrogen-burning stars in
the universe as a source (Sect. 12.6).