Investigations of Faraday Rotation Maps of Extended Radio Sources ...

12 CHAPTER 1. INTRODUCTION
where a 0 = e 3 /(2πm 2 ec 4 ) is a constant, the wavelength λ = c/ν. The proportionality
constant between the polarisation angle and the wavelength squared is called rotation
measure (RM):
∫ d
RM = a 0 dl n e B ‖ , (1.41)
and thus,
0
ϕ = RMλ 2 + ϕ 0 . (1.42)
By convention, RM is positive (negative) for a magnetic field directed toward (away
from) the observer. In order to determine the RM values for a given source, one usually
observes the linearly polarised source at at least three different wavelengths. The
RM value is then determined for each point of the source using Eq. (1.42) employing
a least-squares fit. One major difficulty involved in performing this fit is that the polarisation
angle is observationally only constrained to values between 0 and π leaving
a freedom of additions of ±nπ which leads to the so called nπ-ambiguity. This problem
is illustrated in Fig. 1.1. In this work, a method is proposed in order to solve this
problem (see Chapter 4).
φ
φ 01
RM1
φ
02
RM2
2
2
λ λ
φ 1
03
RM3
2
2 λ
3
λ
2
Figure 1.1: The so-called nπ-ambiguity arising in the determination of the RM is
illustrated. The RM is the slope of the linear regression expressed by Eq. (1.42).
Clearly, additions of ±π change the slope significantly. This plot is adapted from
Ruzmaikin & Sokoloff (1979); Giovannini (2004).
As mentioned in Sect. 1.2.3, the observed degree of polarisation of radiation differs
from the expected value meaning that it is substantially depolarised between its
origin and the observer. One depolarising effect mentioned is Faraday depolarisation