Advanced Diagnostics for the Study of Linearly Polarized Emission. I. Derivation

Linearly polarized emission is described, in general, in terms of the Stokes parameters Q and U, from which the polarization intensity and polarization angle can be determined. Although the polarization intensity and polarization angle provide an intuitive description of the polarization, they are a...

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Bibliographic Details
Published in:The Astrophysical journal 2018-01, Vol.853 (1), p.9
Main Authors: Herron, C. A., Gaensler, B. M., Lewis, G. F., McClure-Griffiths, N. M.
Format: Article
Language:English
Subjects:
Astrophysics
Curvature
Emission analysis
Interferometry
Interstellar matter
Interstellar medium
Invariants
ISM: structure
Linear polarization
magnetic fields
Mathematical analysis
methods: analytical
Polarization
Radio frequency
Stokes parameters
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Summary:Linearly polarized emission is described, in general, in terms of the Stokes parameters Q and U, from which the polarization intensity and polarization angle can be determined. Although the polarization intensity and polarization angle provide an intuitive description of the polarization, they are affected by the limitations of interferometric data, such as missing single-dish data in the u-v plane, from which radio-frequency interferometric data is visualized. To negate the effects of these artifacts, it is desirable for polarization diagnostics to be rotationally and translationally invariant in the Q-U plane. One rotationally and translationally invariant quantity, the polarization gradient, has been shown to provide a unique view of spatial variations in the turbulent interstellar medium when applied to diffuse radio-frequency synchrotron emission. In this paper, we develop a formalism to derive additional rotationally and translationally invariant quantities. We present new diagnostics that can be applied to diffuse or point-like polarized emission in any waveband, including a generalization of the polarization gradient, the polarization directional curvature, polarization wavelength derivative, and polarization wavelength curvature. In Paper II, we will apply these diagnostics to observed and simulated images of diffuse radio-frequency synchrotron emission.
ISSN:0004-637X
1538-4357
DOI:10.3847/1538-4357/aaa002