Stars as Laboratories for Fundamental Physics - MPP Theory Group

188 Chapter 5
m −1
a would effectively act as a source for the local a field and so it would
be much smaller.
An inhomogeneous pseudoscalar field configuration represents an
optically active medium (Fig. 5.8c) as was noted, for example, in the
context of axionic domain wall configurations (Sikivie 1984). To lowest
order the dispersion relation for left- and right-handed circularly
polarized light is (e.g. Harari and Sikivie 1992)
k = ω ± 1 2 g aγ ˆk · ∇a, (5.35)
so that the momentum is shifted by a frequency-independent amount.
The corresponding refractive index is n = 1 ± 1 g 2 aγ ω −1 ˆk · ∇a.
Taking account of the relativistic metric in the strong gravitational
field of a pulsar, Mohanty and Nayak (1993) then found for the time delay
between circularly polarized waves which propagate approximately
along the polar axis
δt = 2 ( ) 2 2
g 4 B0R 4 11 Ω 2 cos 4 α
aγ
. (5.36)
5 575 ω 2 (G N M) 6
For the pulsar PSR 1937+21 a polarimetric analysis yields a time
delay 0.37 ± 0.67 µs and thus a 1σ upper limit of δt < 1µs (Klein
and Thorsett 1990). For typical pulsar parameters this allowed Mohanty
and Nayak (1993) to place a limit on the arion-photon coupling
of g < aγ ∼ 2×10 −11 GeV −1 .
5.5.3 Conversion of Stellar Arions in the Galactic Field
Stars are powerful sources for pseudoscalars which can be produced in
the hot interior by the Primakoff process, i.e. by the conversion γ → a
in the electric fields of the charged medium constituents. Outside of
the star, the pseudoscalars can be converted back to photons in the
galactic magnetic field so that stars would appear to be sources of
x- or γ-rays, depending on the characteristic energy of the stellar core
(Carlson 1995).
In the galaxy, photons propagate with an effective mass given by
the plasma frequency ω P which for typical electron densities of order
0.1 cm −3 is of order 10 −11 eV. As discussed in Sect. 5.4.1 the pseudoscalar
to photon conversion process is an oscillation phenomenon
with a mixing angle given by Eq. (5.28); in the present context it is
1
tan 2θ = g aγB T ω
. (5.37)
2
m 2 a − ωP
2
A typical galactic field strength is 1 µG, a typical energy at most of order
100 MeV for axions from supernovae. With g aγ < 0.6×10 −10 GeV −1