Stars as Laboratories for Fundamental Physics - MPP Theory Group

Two-Photon Coupling of Low-Mass Bosons 187
there can be a strong and potentially observable circular birefringence
effect along the polar direction if massless pseudoscalars exist. The
masslessness of the pseudoscalars is crucial for this scenario and so axions
(Chapter 14) which generically must have a mass do not fulfill this
requirement. Therefore, I use “arions” as a generic example which are
like axions in all respects except that they are true Nambu-Goldstone
bosons of a global chiral U(1) symmetry and thus strictly massless
(Anselm and Uraltsev 1982a,b; Anselm 1982).
The main idea of the pulsar birefringence scenario is that in the
oblique rotator model a strong E · B density exists in the pulsar magnetosphere
which serves as a source for the arion field. Therefore, a
pulsar would be surrounded by a strong classical arion field density
which constitutes an optically active “medium,” causing a time delay
between the two circular polarization states of the pulsed radio emission
from the polar cap region. As a Feynman graph, this situation is
represented by Fig. 5.8d.
In detail, Mohanty and Nayak (1993) considered the oblique rotator
model where the pulsar magnetic dipole axis is tilted with regard
to its rotation axis by an angle α. The instantaneous rotating
magnetic dipole field is B = (B 0 R 3 /r 3 ) [3ˆr (ˆr · ˆµ) − ˆµ], where B 0
is the magnetic field strength at the poles of the pulsar surface (radius
R) and ˆµ is the instantaneous magnetic dipole direction with
the angle α relative to the angular velocity vector Ω. The time average
of the electric field which is induced by the rotating magnetic
dipole, and which matches the boundary condition that the electric
field component parallel to the pulsar surface vanishes, is found to be
⟨E⟩ = B 0 R 5 Ω cos α r −4 [3 (sin 2 θ − 2) ˆr − 2 sin θ cos θ ˆθ] where θ is the
3
polar angle relative to the rotation axis. The time-averaged value for
the pseudoscalar field density is
⟨E · B⟩ = −B 2 0ΩR 8 r −7 cos α cos 3 θ. (5.33)
It appears as a source for the arion field on the r.h.s. of Eq. (5.24). Taking
account of the relativistic space-time metric outside of the pulsar,
Mohanty and Nayak (1993) found for the resulting arion field
2 B
a = −g
0R 2 8 Ω cos α cos θ
aγ + O(r −3 ), (5.34)
575 (G N M) 3 r 2
where G N is Newton’s constant and M the pulsar mass. The entire
magnetosphere contributes coherently to this result. If the pseudoscalars
had a mass, only the density E · B within a distance of about