Probing magnetic turbulence by synchrotron polarimetry: statistics and structure of magnetic fields from Stokes correlators

Abstract

We describe a technique for probing the statistical properties of cosmic magnetic fields based on radio polarimetry data. Second-order magnetic field statistics like the power spectrum cannot always distinguish between magnetic fields with essentially different spatial structure. Synchrotron polarimetry naturally allows certain 4th-order magnetic field statistics to be inferred from observational data, which lifts this degeneracy and can thereby help us gain a better picture of the structure of the cosmic fields and test theoretical scenarios describing magnetic turbulence. In this work we show that a 4th-order correlator of physical interest, the tension-force spectrum, can be recovered from the polarized synchrotron emission data. We develop an estimator for this quantity based on polarized-emission observations in the Faraday-rotation-free frequency regime. We consider two cases: a statistically isotropic field distribution, and a statistically isotropic field superimposed on a weak mean field. In both cases the tension force power spectrum is measurable; in the latter case, the magnetic power spectrum may also be obtainable. The method is exact in the idealized case of a homogeneous relativistic-electron distribution that has a power-law energy spectrum with a spectral index p=3, and assumes statistical isotropy of the turbulent field. We carry out tests of our method using synthetic data generated from numerically simulated magnetic fields. We show that the method is valid, that it is not prohibitively sensitive to the value of the electron spectral index, and that the observed tension-force spectrum allows one to distinguish between, e.g., a randomly tangled magnetic field (a default assumption in many studies) and a field organized in folded flux sheets or filaments.

Published on MNRAS 2009

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• Statistical Description of Synchrotron Intensity Fluctuations: Studies of Astrophysical Magnetic Turbulence
• Studying Galactic interstellar turbulence through fluctuations in synchrotron emission: First LOFAR Galactic foreground detection
• Spectrum and Anisotropy of Turbulence from Multi-Frequency Measurement of Synchrotron Polarization
• Magnetic power spectra from Faraday rotation maps - REALMAF and its use on Hydra A
• RESOLVE: A new algorithm for aperture synthesis imaging of extended emission in radio astronomy
• Visibility based angular power spectrum estimation in low frequency radio interferometric observations
• Universality of the Small-Scale Dynamo Mechanism
• Polarimetric studies of magnetic turbulence with interferometer
• Faraday signature of magnetic helicity from reduced depolarization
• The angular power spectrum measurement of the Galactic synchrotron emission in two fields of the TGSS survey
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• Faraday caustics: Singularities in the Faraday spectrum and their utility as probes of magnetic field properties
• Tracing Magnetic Field with Synchrotron Polarization Gradients: Parameter Study
• Tracing magnetic fields by the synergies of synchrotron emission gradients
• Imprints of magnetic power and helicity spectra on radio polarimetry statistics
• Studying the local magnetic field and anisotropy of magnetic turbulence by synchrotron polarization derivative
• An Image-based Tapered Gridded Estimator (ITGE) for the angular power spectrum
• Validating a novel angular power spectrum estimator using simulated low frequency radio-interferometric data
• Gradient measurement of synchrotron polarization diagnostic: Application to spatially separated emission and Faraday rotation regions
• Polarization properties of turbulent synchrotron bubbles: an approach based on Chandrasekhar-Kendall functions
• Studying the properties of compressible MHD turbulence by synchrotron fluctuation statistics
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• Measurement of the scaling slope of compressible magnetohydrodynamic turbulence by synchrotron radiation statistics
• On the saturation mechanism of the fluctuation dynamo at ${\text{Pr}}_{\mathrm{M}}\ge 1$