Stars as Laboratories for Fundamental Physics - MPP Theory Group

Two-Photon Coupling of Low-Mass Bosons 175
erate limit, the emission rate drops precipitously, an important feature
which will be taken advantage of in Sect. 5.2.5 below.
5.2.4 Solar Axion Spectrum
As a first practical application it is easy to calculate the expected flux
of axions at Earth from the Primakoff conversion in the Sun where the
classical approximation is well justified. To this end van Bibber et al.
(1989) have integrated Eq. (5.9) over a standard solar model which
yields an axion luminosity
L a = g 2 10 1.7×10 −3 L ⊙ , (5.20)
with L ⊙ the solar luminosity and g 10 ≡ g aγ × 10 10 GeV. (Recalling that
g aγ = (α/πf a ) C aγ this corresponds to f a /C aγ = 2.3×10 7 GeV.) The
differential flux at Earth is well approximated by the formula
dF a
dω a
= g 2 10 4.02×10 10 cm −2 s −1 keV −1 (ω a /keV) 3
e ωa/1.08 keV − 1
(5.21)
which is shown in Fig. 5.6. The average axion energy is ⟨ω a ⟩ = 4.2 keV.
The total flux at Earth is F a = g 2 10 3.54×10 11 cm −2 s −1 .
The “standard Sun” is about halfway through its main-sequence
evolution. Therefore, the solar axion luminosity must not exceed its
Fig. 5.6. Axion flux at Earth according to Eq. (5.25) from the Primakoff
conversion of photons in the Sun.