Stars as Laboratories for Fundamental Physics - MPP Theory Group

474 Chapter 12
The two-body decay is mostly interesting for m ν ∼ < 2m e , a limit in
which one may safely ignore all nonrelativistic corrections, including
the progenitor absorption effect. In this case
I = 1 − e−t GRS/τ ∗
t GRS /τ ∗
, (12.29)
which is unity for τ ∗ ∼ > t GRS . With typical photon energies of 3T ν ≈
20 MeV and t GRS = 223.2 s this requirement translates into m ν τ tot ∼ >
10 10 eV s.
In the relativistic limit and with I = 1 one can easily integrate
Eq. (12.27) with the Boltzmann spectrum Eq. (12.14) and finds
F ′ γ = F ν
t GRS
m ν τ γ
[
(1 − α) ε + (1 + α) ε
2 ] e −ε , (12.30)
where ε = E γ /T ν . This spectrum is shown in Fig. 12.13 for T ν = 4
and 8 MeV with m ν τ γ = 10 18 eV s. The envelopes of the shaded bands
in Fig. 12.13 correspond to α = ±1 where for each temperature the
“harder” edge corresponds to α = +1. The expected fluence for each
GRS channel of Tab. 12.1 is found by integration. The GRS fluence
limits then yield the lower bounds on m ν τ γ shown in Fig. 12.14.
Fig. 12.13. Expected fluence of photons from the decay ν → ν ′ γ of “highmass”
but relativistic SN neutrinos, 200 eV ∼ < m ν ∼
< 1 MeV, according to
Eq. (12.30) with m ν τ γ = 10 18 eV s and the indicated neutrino temperatures.
The shaded bands for each temperature are for the range −1 ≤ α ≤ +1 with
the harder edge corresponding to α = +1. Also shown are the upper limits
from the GRS channels taken from the 223.2 s column of Tab. 12.1.