Stars as Laboratories for Fundamental Physics - MPP Theory Group

488 Chapter 12
on the Hubble type, varying from 0.2 h 2 SNu for Sa spirals to about
5 h 2 SNu for Sd (van den Bergh and Tammann 1991) where the supernova
unit is defined by 1 SNu ≡ 1 SN per century per 10 10 L ⊙,B .
Adopting 1 h 2 SNu as a representative value and about 5×10 57 neutrinos
plus antineutrinos of a given flavor per SN yields for each flavor
Ṅ ν ≈ h 3 1.3×10 −27 cm −3 s −1 , a rate almost identical to that from
hydrogen-burning stars. 79 The radiative lifetime limit is then also identical,
except that it applies to neutrinos of all flavors.
All of these bounds are weaker than those from SN 1987A. Therefore,
decaying stellar neutrinos cannot actually contribute to the observed
x- and γ-ray background.
12.7 Cosmological Bounds
12.7.1 Neutrinos
Within the big-bang scenario a cosmic background sea of neutrinos is
an inevitable consequence of the hot early universe. Its contribution to
the cosmic energy density was already used in Sect. 7.1.5 to derive extremely
restrictive neutrino mass limits. If neutrinos decay radiatively,
further constraints can be obtained. For one, the decay photons can
show up directly as a diffuse, isotropic cosmic background radiation.
If the decays occur before recombination, i.e. before the universe became
transparent to radiation, but so late that the photons could not
be thermalized entirely, they contribute to a spectral distortion of the
cosmic microwave background radiation (CMBR). The resulting limits
were discussed, for example, by Kolb and Turner (1990) who found
that those areas of masses and lifetimes are excluded that are hatched
in Fig. 12.20. It was assumed that neutrinos decay only radiatively.
The contribution of the neutrinos and their decay products to the
mass density of the universe leads to the constraints shown in Fig. 7.2
which are based on the present-day value of Ωh 2 and on the expansion
79 Multiplying this rate with the age of the universe of about 3×10 17 s and the
speed of light of 3×10 10 cm/s, and using h = 0.5 one finds an estimated present-day
flux at Earth of about 1 cm −2 s −1 . In a recent detailed study, Totani and Sato
(1995) find a flux which is larger than this crude estimate by as much as a factor
of 30. The Kamiokande II detector has set an upper limit on the cosmic background
flux of ν e of about 10 3 cm −2 s −1 for effective temperatures in the 3−4 MeV range
(Zhang et al. 1988). It is conceivable that this background will be measured by
the Superkamiokande detector. Note that at the Kamiokande site the ν e flux from
power reactors is roughly 1000 times larger than the background flux, except that
it falls off sharply beyond about 10 MeV.