Stars as Laboratories for Fundamental Physics - MPP Theory Group

Two-Photon Coupling of Low-Mass Bosons 177
axion field oscillations, i.e. a highly degenerate axion Bose condensate
that would play the role of “cold dark matter,” and notably provide the
unseen mass necessary to explain the rotation curves of spiral galaxies
such as our own (e.g. Kolb and Turner 1990). Because there are
uncertainties with regard to details of the primordial axion production
mechanism the exact value of the relevant axion mass is not known.
However, typically it is of order 10 −5 eV so that it is a reasonable speculation
that the mass of our galaxy is dominated by very low-mass
bosons. As these particles are bound to the galaxy they must be nonrelativistic;
a typical velocity dispersion corresponding to the galactic
gravitational potential is around 10 −3 in units of the speed of light.
Sikivie (1983) proposed to search for galactic axions by means of a
Primakoff-like method. The a → γ conversion of nonrelativistic axions
in the µeV mass range produces photons in the microwave (GHz) range.
Therefore, the idea is to place a microwave cavity in a strong magnetic
field and wait for cavity modes to be excited by the axion field. In
this context one may view the electromagnetic modes of the cavity and
the free axion field modes as oscillators which are coupled by virtue of
the interaction Eq. (5.1) where B is the external static field while E is
from an electromagnetic cavity mode. Then, power is transferred from
the axion field to the cavity excitations by virtue of the oscillator beats
induced by the coupling; detailed calculations of the conversion rate
were performed by Sikivie (1985) and Krauss et al. (1985).
It is worth noting that with a mass of 10 −5 eV and a velocity of
10 −3 a typical axion momentum is 10 −8 eV which corresponds to a
wave length of about 20 m. Thus on laboratory scales the axion field
is homogeneous. This does not apply to free microwaves—their energy
and momentum are the same (ω γ = |k γ |); for 10 −5 eV their wave
length is 2 cm. The role of the resonant cavity is to overcome this momentum
mismatch: on resonance the fundamental cavity frequency is
degenerate with nonrelativistic axions of a certain mass for which the
energy transfer is maximized. In a search experiment the cavity must
be stepped through a range of resonant frequencies which defines the
range of axion masses to which a given experimental setup is sensitive.
Two pilot experiments of this sort were completed several years ago
(Wuensch et al. 1989; Hagmann et al. 1990). Assuming an axionic darkmatter
density at the Earth of 5×10 −25 g cm −3 = 300 MeV cm −3 allowed
these groups to exclude the range of masses and coupling constants
shown in Fig. 5.7. The solid line indicates the relationship between g aγ
and m a in axion models where E/N = 8/3 or ξ = 1 in Eq. (14.24), i.e.
where g aγ = (m a /µeV) (0.69×10 16 GeV) −1 .