Stars as Laboratories for Fundamental Physics - MPP Theory Group

Two-Photon Coupling of Low-Mass Bosons 185
a more restrictive limit of g aγ < 3.6×10 −7 GeV −1 for m < a ∼ 7×10 −4 eV.
For a larger mass an a-γ oscillation pattern develops on the length scale
of the optical cavity, leading to an “oscillating limit” as a function of
m a . In this regime the ellipticity measurement was superior.
New experimental efforts in the birefringence category include a
proposal by Cooper and Stedman (1995) to use ring lasers. A laser
experiment which is actually in the process of being built is PVLAS
(Bakalov et al. 1994) which will be able to improve previous laboratory
limits on g aγ by a factor of 40, i.e. it is expected to be sensitive in
the regime g > aγ ∼ 1×10 −8 GeV −1 as long as m < a ∼ 10 −3 eV. While such
strong couplings are astrophysically excluded it is intriguing that this
experiment should be able to detect for the first time the standard QED
birefringence effect of Fig. 5.8a.
5.5 Astrophysical Magnetic Fields
5.5.1 Transitions in Magnetic Fields of Stars
Certain stars have very strong magnetic fields. For example, neutron
stars frequently have fields of 10 12 −10 13 G (e.g. Mészáros 1992), and
even white dwarfs can have fields of up to 10 9 G. Therefore, one may
think that axions produced in the hot interior of neutron stars at a temperature
of, say, 50 keV would convert to γ-rays in the magnetosphere
(Morris 1986). However, the vacuum refractive term suppresses the
conversion rate because the photon momentum for a given frequency
is k γ = n ∥,⊥ ω > ω with the refractive indices Eq. (5.31) while for the
axions k a = ω − m 2 a/2ω < ω. Therefore, in the presence of a magnetic
field axions and photons are less degenerate so that it is more difficult
for them to oscillate into each other.
In principle, the refractive index can be cancelled by the presence
of a plasma where the photon forward scattering on electrons induces a
negative n−1, i.e. something like a photon effective mass. In the aligned
rotator model for a magnetized neutron star a self-consistent solution of
the Maxwell equations with currents requires the presence of an electron
density of about n e = 7×10 10 cm −3 B 12 Ps
−1 where B 12 is the magnetic
field along the rotation axis in units of 10 12 G and P s is the pulsar period
in seconds (Goldreich and Julian 1969). The corresponding plasma
frequency is ωP 2 = 4παn e /m e = 0.97×10 −10 eV 2 B 12 Ps
−1 . This implies
k − ω = −ωP/2ω 2 = −5×10 −14 eV B 12 Ps
−1 ωkeV −1 with ω keV = ω/keV, to
be compared with ∆ ∥ = (n ∥ − 1) ω = 0.92×10 −4 eV B12ω 2 keV which is
much larger, allowing one to ignore the plasma term.