Stars as Laboratories for Fundamental Physics - MPP Theory Group

486 Chapter 12
Fig. 12.19. Excluded areas of the ν τ mass and lifetime if the standard-model
decay ν τ → ν e e + e − is the only available channel. The laboratory results
refer to the bounds on sin 2 2θ e3 of Fig. 12.3, translated into a limit on τ e + e −
by virtue of Eq. (7.9). The SN 1987A bound is that from Fig. 12.18 while
the cosmological one is from Fig. 7.2. The excluded range indicated by the
vertical arrow refers to the argument of Sect. 12.5.1.
12.6 Neutrinos from All Stars
All stars in the universe contribute to a diffuse cosmic background flux
of MeV neutrinos. If they decayed radiatively they would produce a
cosmic x- and γ-ray background which must not exceed the measured
levels. Because the entire radius of the visible universe is available as a
decay path, one can derive rather restrictive limits on τ γ (Cowsik 1977).
In order to derive such limits I assume that neutrinos of energy E ν
are produced with a constant rate Ṅν (cm −3 s −1 ). Assuming a zerocurvature
model of the universe, Kolb and Turner (1989) found for the
resulting isotropic flux of decay photons
d 2 F γ
dE γ dΩ = m ν
τ γ
1
4π
9
2 1/2 5
Ṅ ν t 2 U
Eν 3/2 Eγ
1/2
, (12.35)
where t U is the age of the universe. Moreover, it was assumed that
in ν → ν ′ γ the daughter neutrino is massless, and that the decays
are isotropic in the parent frame (anisotropy parameter α = 0). In
a flat universe one has t U = 2 3 H−1 0 = h −1 2.05×10 17 s where H 0 =