708 Encyclopedia of the Solar System
FIGURE 13 Images and spectra of H 2 CO in comet C/1995 O1 (Hale–Bopp) taken with the BIMA array and
ARO 12 m telescope on different days and in different transitions, as indicated in each panel. Panel b shows a
contour map from BIMA at 72.8 GHz (in bold; from spectrum in panel a), superposed on the ARO 225.7 GHz
image (from spectrum in panel c). The synthesized beam for BIMA is shown in the lower left, and that of ARO
appears in the lower right. (S. N. Milam et al., Formaldehyde in comets C/1995 O1 (Hale–Bopp), C/2002 T7
(LINEAR), and C/2001 Q4 (NEAT): Investigating the cometary origin of H 2 CO,Astrophys.J. 649 ,
1169–1177.)withqthe elemental charge,Bthe magnetic field strength,
methe electron mass, andcthe speed of light. Propagation
of the radiation depends on the interaction of the radia-
tion with the local plasma, or charged particle population.
The oscillation of these particles, as caused by the elec-
tromagnetic properties of the plasma, leads to a complex
interaction between the propagating radiation (the electro-
magnetic waves) and the local plasma. For example, the
radiation can escape its region of origin only if the lo-
cal cyclotron frequency is larger than the electron plasma
frequency:
νe=(
4 πNeq^2
me) 1 / 2
(7)withNethe electron density. Hence, the plasma frequency
is the frequency at which electrons oscillate about their
equilibrium positions in the absence of a magnetic field.
This similarly sets the limit for propagation through Earth’s
ionosphere at∼10 MHz. If the local cyclotron frequency
is less than the electron plasma frequency, the waves are
locally trapped and amplified, until it reaches a region from
where it can escape. The cyclotron maser instability also
requires a large ratio ofνL/νe. The auroral regions in plane-
tary magnetospheres are characterized by such conditions.
The mode of propagation (or polarization) of auroral radio
emissions is in the so-called extraordinary (X) sense, and
the polarization (direction of the electric vector of the ra-
diation) depends upon the direction of the magnetic field.
The emission is right-handed circularly polarized (RH) if
the field at the source is directed toward the observer and
left-handed circularly polarized (LH) if the field points away
from the observer.^1
Cyclotron radiation is emitted in a dipole pattern, where
the lobes are bent in the forward direction. The result-
ing emission is like a hollow cone pattern, as displayed in
Fig. 15. The radiation intensity is zero along the axis of the(^1) Circular polarization is in the RH sense when the electric vector of the
radiation in a plane perpendicular to the magnetic field direction rotates
in the same sense as a RH screw advancing in the direction of
propagation. Thus, rotation is counterclockwise when propagation is
toward and viewed by the observer. RH polarization is defined as
positive; LH, as negative. In some cases, the radio emissions propagate in
the ordinary (O) magneto-ionic mode. In this mode the polarization is
reversed. The theory of the cyclotron maser instability does admit the
possibility of emission in the ordinary mode. However, it is less common.