Astronomy Principles and Practice Fourth Edition.pdf

234 The radiation laws
radiation is likely to be polarized, although the polarization may not be complete or perfect. This type
of radiation is said to be partially polarized.
A beam of partially polarized radiation may be thought as being made up of two combined beams,
one beam being perfectly polarized and the other being unpolarized. On a highly-resolved timescale, a
partially polarized beam of light would show variations of the ‘instantaneous’ polarization form but, on
average, one form, perhaps with a particular azimuth, would predominate. The degree of predominance
would depend on how near to perfect the partially polarized radiation is. The ratio of the strength of
the polarized component to the total strength of the beam defines the degree of polarization, p,ofthe
beam.
The most frequently met case in astrophysics is the measurement of partially linearly polarized
light. If a polarimetric analyser is rotated in such a beam, the transmitted intensity will change
according to I (1 + p cos 2 (α − β)) where α is the angle of the analyser’s axis in the instrument and β
is the vibration azimuth of the polarization relative to the instrumental frame. On a complete rotation
of the polarizer, the recorded signal will oscillate between a maximum and minimum value. If these
levels are recorded as I max and I min , it is readily shown that p can be determined from
p = I max − I min
I max + I min
. (15.31)
The degree of polarization, together with the parameters which describe the ellipse associated
with the polarized component, summarize the polarizational properties of a partially polarized beam.
This polarizational information, together with the brightness, gives a complete description of any beam
of radiation.
All the parameters which are needed to describe a general beam of radiation are capable of
carrying information about the condition of the radiating atoms which give rise to the energy, the
nature of the matter which scatters the radiation in the direction of the observer or the nature of
the matter which is in a direct line between the radiating atoms and the observer. If the observer
wishes to gain as much knowledge as possible of the outside universe, all the properties associated
with the electromagnetic radiation must be measured. Various scattering phenomena such as that
associated with free electrons or dust in extended stellar atmospheres are important means of generating
polarization. It also turns out that aligned dust grains in the interstellar medium give rise to linear
polarization by differential extinction for the radiation’s components resolved orthogonally to the axis
of the grains. Generation of polarization by the synchrotron process is revealed in the supernova
remnant known as the Crab nebula (see figure 15.13).
15.10 The Zeeman effect
Although it is not the only mechanism that gives rise to a particular spectral line behaviour
accompanied by polarizational phenomena, the Zeeman effect serves as a classical example for the
rationale of undertaking spectropolarimetric measurements.
In the middle of the 19th century, Faraday examined the emission spectrum of sodium vapour
which had been placed in a magnetic field. His apparatus, however, was insufficiently sensitive to
detect any effect caused by the field. By repeating these experiments with more sensitive equipment,
Zeeman, in 1896, demonstrated that the emission lines were broadened. Lorentz, shortly afterwards,
proposed a theory, based on the electron theory of matter, which suggested that if the broadening were
to be looked at closely, a splitting of the lines should be observed. His theory also predicted that the
light of the split lines should be polarized. When the magnetic field is in a direction along the line of
sight (a longitudinal field), two lines should be observed at wavelength positions on either side of the
position for the emission line when there is no field. These lines should be circularly polarized but
with opposite handednesses. When the field is across the line of sight (a transverse field) three lines