160
Relic neutrinos and axions
by the new coolant but weak enough for the coolant to stream away without
undue hindrance from too many interactions. Since stellar evolution models are
well developed and successful in accounting for the observed stellar lifetimes, the
axion production cross sections and, hence, the strength of its various couplings
are constrained by the error bars on the observational data [23-27].
For example, in globular cluster stars, axions may be produced by the
Compton process
ye -. ae
(5.85)
shown in figure 5.1, or by axion bremsstrahlung
eZ -. aeZ
(5.86)
shown in figure 5.2. The production cross section for both of these and, hence,
the stellar cooling rate is proportional to g~ee where, using (5.72),(5.73), (5.65)
and (S.64),
me
(XeR - xedmame
(S.87)
gau = ge vPQ = ~3(0.62 X 1016 eV2)'
The observational data yield the constraint [23,28)
Igaeel ;S 0.5 x 10- 12
(S.88)
so that
I (XeR ~ x.L> I ma ;S 0.62 x 10- 2 eV
(S.89)
which gives ma ;S 10- 2 e V as the generic constraint on DFSZ models, taking the
unknown PQ charges to be of order unity. Of course, the mass of the hadronic
axion is unconstrained by these data.
The globular cluster data also constrain the axion-photon coupling, which
enters via the Primakoff process
y .. a
(S.90)
shown in figure 5.3, in which a photon is converted to an axion in the coherent
electromagnetic field of a nucleus or an electron. The production cross section is
proportional to g~"" where, from (S.66) and (S.64),
aem
mag"aem
(5.91)
gay" = g" '!rIll = '!r(O.62 X 1016 eV2)
and the data yield the constraint [27]
IgIIyyl ;S 0.6 x 10- 10 GeV- I •
(S.92)
Then
Igylmll ;S 0.16 eV
(S.93)