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

Chapter 4
Pacman - A new RM Map Making
Algorithm
The statistical analysis of RM measurements in terms of correlation functions and
equivalently power spectra requires that the RM’s are unambiguously determined as
discussed in the last chapter. Thus, any ambiguous RM can lead to misinterpretation
of the data investigated. This ambiguity results from the observational fact that
the polarisation angles are only determined up to additions of ±nπ. In this chapter,
a new map making algorithm - called Pacman - is described. Instead of solving
the nπ-ambiguity for each data point independently, the proposed algorithm solves
the nπ-ambiguity for a high signal-to-noise region and uses this information to assist
computations in adjacent low signal-to-noise areas.
This work is submitted to Mon. Not. Roy. Astron. Soc. as two papers (Dolag et al.
2004; Vogt et al. 2004). My part in this work was the contribution to the development
of the algorithm, the data handling, the statistical characterisation and tests of the various
RM maps and describing the algorithm in the two scienfic publications. Pacman
was implemented by Klaus Dolag.
4.1 Introduction
For the calculation of rotation measures (RM) and intrinsic polarisation angles (ϕ 0 )
using the relationship ϕ = RM λ 2 + ϕ 0 (see Eq. (1.42)), a least squares fit is normally
applied to the polarisation angle data. Since the measured polarisation angle ϕ is
constrained only to values between 0 and π leaving the freedom of additions of ± nπ,
where n is an integer, the determination of RM and ϕ 0 is ambiguous, causing the so
called nπ-ambiguity. Therefore, a least squares fit has to be applied to all possible nπcombinations
of the polarisation angle data at each data point of the polarised radio
source while searching for the nπ-combination for which χ 2 is minimal.
In principle, χ 2 can be decreased to infinitely small numbers by increasing RM
substantially. Vallée & Kronberg (1975) and Haves (1975) suggested to avoid this
problem by introducing an artificial upper limit for |RM| ≤ RM max . Since this is
a biased approach, Ruzmaikin & Sokoloff (1979) proposed to assume that no nπambiguity
exists between the measurements of two closely spaced wavelengths taken
from a whole wavelength data set. The standard error of the polarisation measurements
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