Stars as Laboratories for Fundamental Physics - MPP Theory Group

Radiative Particle Decays 487
h 100 km s −1 Mpc −1 is the present-day Hubble expansion parameter and
where observationally 0.4 ∼ < h ∼ < 1.
There exist numerous measurements of the diffuse cosmic x- and
γ-radiation (for example Schönfelder, Graml, and Penningfeld 1980).
Between a few 100 keV and a few 10 MeV the isotropic flux is reasonably
well approximated by
d 2 ( ) 2
F γ
MeV
dE γ dΩ = 2×10−2 cm −2 s −1 sr −1 MeV −1 . (12.36)
E γ
Comparing this with Eq. (12.35), the most restrictive limit on τ γ is
obtained for the highest possible photon energy, E γ = E ν . The requirement
that the decay flux does not exceed the measurements at
this energy leads to the upper limit
m ν
τ γ
∼ < 1.6×10 −40 eV s
cm −3 s −1
Ṅ ν
h 2 , (12.37)
which does not depend on the assumed value for E ν because Eq. (12.35)
and (12.36) both scale with E −2 . This limit applies if the total neutrino
lifetime τ tot exceeds t U ; otherwise only a limit on the branching ratio
B γ can be found.
The most prolific stellar neutrino source in the universe are hydrogen-burning
stars which produce two ν e ’s with MeV energies for
every synthesized 4 He nucleus. Because most of the binding energy
that can be liberated by nuclear fusion is set free when single nucleons
are combined to form 4 He, most of the energy emitted by stars can
be attributed to hydrogen burning. Therefore, it is easy to translate
the optical luminosity density of the universe into an average rate of
neutrino production.
The average luminosity density of the universe in the blue (B) spectral
band is about h 2.4×10 8 L ⊙,B Mpc −3 where L ⊙,B is the solar B luminosity.
The Sun produces about 1×10 38 ν e /s and so one arrives at
Ṅ νe ≈ h 2.4×10 46 Mpc −3 s −1 = 0.8×10 −27 cm −3 s −1 . (Of course, this estimate
is relatively crude in that the neutrino luminosity scales directly
with the average bolometric luminosity of a stellar population, but not
precisely with L B .) With Eq. (12.37) this leads to a constraint for ν e
of τ γ /m > νe ∼ 5×10 12 s/eV, or µ < eff ∼ 2×10 −7 µ B m −2
eV.
The (core-collapse) supernovae in the universe are also very prominent
neutrino sources, and, more importantly, they are thought to produce
MeV neutrinos of all flavors. Such SNe do not occur in elliptical
galaxies, and their present-day rate in spirals depends sensitively