Stars as Laboratories for Fundamental Physics - MPP Theory Group

176 Chapter 5
photon luminosity; otherwise its nuclear fuel would have been spent
before reaching an age of 4.5×10 9 yr. This requirement yields a bound
g aγ ∼ < 2.4×10 −9 GeV −1 . (5.22)
Detailed solar evolution calculations of Raffelt and Dearborn (1987)
showed that this bound was firm, but also that it could not be improved
easily (Sect. 1.3.2). The present-day properties of the Sun could
be obtained by a suitable adjustment of the unknown presolar helium
abundance.
5.2.5 Globular-Cluster Bound on g aγ
Armed with the Primakoff emission rate Eq. (5.9) it is an easy task
to derive a bound on g aγ from the energy-loss argument applied to
globular-cluster stars (Sect. 2.5). We need to require that at T ≈ 10 8 K
the axionic energy-loss rate is below 10 erg g −1 s −1 for a density of about
0.6×10 4 g cm −3 , corresponding to a classical plasma, and for about
2×10 5 g cm −3 , corresponding to degeneracy. From Fig. 5.5 it is evident
that the emission rate is a steeply falling function of density when
degeneracy effects become important. Obviously, the more restrictive
limit is found from the low-density case which is based on the heliumburning
lifetime of HB stars (Sect. 2.5.1).
In order to calculate the average energy-loss rate of the core of an
HB star one needs ⟨T 7 /ρ⟩ if in Eq. (5.9) one uses a constant κ 2 =
2.5 or F = 1.0. For a typical HB-star model (Fig. 1.4) one finds
⟨T8 7 /ρ 4 ⟩ ≈ 0.3 where T 8 = T/10 8 K and ρ 4 = ρ/10 4 g cm −3 . Therefore,
⟨ϵ a ⟩ ≈ g10 2 30 erg g −1 s −1 so that the criterion Eq. (2.40) yields a
constraint
g aγ ∼ < 0.6×10 −10 GeV −1 or f a /C aγ ∼ > 4×10 7 GeV. (5.23)
The temperature 10 8 K corresponds to 8.6 keV; a typical photon energy
is 3 T ≈ 25 keV. Therefore, this bound applies to pseudoscalars with a
mass m a ∼ < 30 keV while for larger masses it would be degraded.
5.3 Search for Cosmic Axions
One of the most interesting ramifications of the electromagnetic coupling
of pseudoscalars is the possibility to search for dark-matter axions.
It is briefly explained in Chapter 14 that axions would be produced in
the early universe by a nonthermal mechanism which excites classical