H. Junklewitz

An improved map of the galactic Faraday sky

We aim to summarize the current state of knowledge regarding Galactic Faraday rotation in an all-sky map of the Galactic Faraday depth. For this we have assembled the most extensive catalog of Faraday rotation data of compact extragalactic polarized radio sources to date. In the map-making procedure we used a recently developed algorithm that reconstructs the map and the power spectrum of a statistically isotropic and homogeneous field while taking into account uncertainties in the noise statistics. This procedure is able to identify some rotation angles that are offset by an integer multiple of π. The resulting map can be seen as an improved version of earlier such maps and is made publicly available, along with a map of its uncertainty. For the angular power spectrum we find a power law behavior C� ∝ � −2.17 for a Faraday sky where an overall variance profile as a function of Galactic latitude has been removed, in agreement with earlier work. We show that this is in accordance with a 3D Fourier power spectrum P(k) ∝ k −2.17 of the underlying

Estimating extragalactic Faraday rotation

Observations of Faraday rotation for extragalactic sources probe magnetic fields both inside and outside the Milky Way. Building on our earlier estimate of the Galactic contribution, we set out to estimate the extragalactic contributions. We discuss the problems involved; in particular, we point out that taking the difference between the observed values and the Galactic foreground reconstruction is not a good estimate for the extragalactic contributions. We point out a degeneracy between the contributions to the observed values due to extragalactic magnetic fields and observational noise and comment on the dangers of over-interpreting an estimate without taking into account its uncertainty information. To overcome these difficulties, we develop an extended reconstruction algorithm based on the assumption that the observational uncertainties are accurately described for a subset of the data, which can overcome the degeneracy with the extragalactic contributions. We present a probabilistic derivation of the algorithm and demonstrate its performance using a simulation, yielding a high quality reconstruction of the Galactic Faraday rotation foreground, a precise estimate of the typical extragalactic contribution, and a well-defined probabilistic description of the extragalactic contribution for each data point. We then apply this reconstruction technique to a catalog of Faraday rotation observations for extragalactic sources. The analysis is done for several different scenarios, for which we consider the error bars of different subsets of the data to accurately describe the observational uncertainties. By comparing the results, we argue that a split that singles out only data near the Galactic poles is the most robust approach. We find that the dispersion of extragalactic contributions to observed Faraday depths is most likely lower than 7 rad/m(2), in agreement with earlier results, and that the extragalactic contribution to an individual data point is poorly constrained by the data in most cases.

NIFTY – Numerical Information Field Theory - A versatile PYTHON library for signal inference

NIFTy, “Numerical Information Field Theory”, is a software package designed to enable the development of signal inference algorithms that operate regardless of the underlying spatial grid and its resolution. Its object-oriented framework is written in Python, although it accesses libraries written in Cython, C++, and C for eciency. NIFTy oers a toolkit that abstracts discretized representations of continuous spaces, fields in these spaces, and operators acting on fields into classes. Thereby, the correct normalization of operations on fields is taken care of automatically without concerning the user. This allows for an abstract formulation and programming of inference algorithms, including those derived within information field theory. Thus, NIFTy permits its user to rapidly prototype algorithms in 1D, and then apply the developed code in higher-dimensional settings of real world problems. The set of spaces on which NIFTy operates comprises point sets, n-dimensional regular grids, spherical spaces, their harmonic counterparts, and product spaces constructed as combinations of those. The functionality and diversity of the package is demonstrated by a Wiener filter code example that successfully runs without modification regardless of the space on which the inference problem is defined.

RESOLVE: A new algorithm for aperture synthesis imaging of extended emission in radio astronomy

We present resolve, a new algorithm for radio aperture synthesis imaging of extended and diffuse emission in total intensity. The algorithm is derived using Bayesian statistical inference techniques, estimating the surface brightness in the sky assuming a priori log-normal statistics. resolve estimates the measured sky brightness in total intensity, and the spatial correlation structure in the sky, which is used to guide the algorithm to an optimal reconstruction of extended and diffuse sources. During this process, the algorithm succeeds in deconvolving the effects of the radio interferometric point spread function. Additionally, resolve provides a map with an uncertainty estimate of the reconstructed surface brightness. Furthermore, with resolve we introduce a new, optimal visibility weighting scheme that can be viewed as an extension to robust weighting. In tests using simulated observations, the algorithm shows improved performance against two standard imaging approaches for extended sources, Multiscale-CLEAN and the Maximum Entropy Method.

Probing magnetic helicity with synchrotron radiation and Faraday rotation

We present a first application of the recently proposed LITMUS test for magnetic helicity, as well as a thorough study of its applicability under different circumstances. In order to apply this test to the galactic magnetic field, the newly developed critical filter formalism is used to produce an all-sky map of the Faraday depth. The test does not detect helicity in the galactic magnetic field. To understand the significance of this finding, we made an applicability study, showing that a definite conclusion about the absence of magnetic helicity in the galactic field has not yet been reached. This study is conducted by applying the test to simulated observational data. We consider simulations in a flat sky approximation and all-sky simulations, both with assumptions of constant electron densities and realistic distributions of thermal and cosmic ray electrons. Our results suggest that the LITMUS test does indeed perform very well in cases where constant electron densities can be assumed, both in the flat-sky limit and in the galactic setting. Non-trivial distributions of thermal and cosmic ray electrons, however, may complicate the scenario to the point where helicity in the magnetic field can escape detection.

Faraday caustics - Singularities in the Faraday spectrum and their utility as probes of magnetic field properties

We describe singularities in the distribution of polarized intensity as a function of Faraday depth (i.e. the Faraday spectrum) that arise due to line of sight (LOS) magnetic field reversals. We call th ese features Faraday caustics due to their similarity to opt ical caustics. They appear sharply spiked in the Faraday spectrum with a tail that extends to one side. The direction in which the tail ext ends depends on the way in which the LOS magnetic field reversal occurs (eit her changing from oncoming to retreating or vice versa). We describe how surfaces of Faraday caustics relate to boundaries between regions where the LOS magnetic field has opposite polarity . Examples from simulations of the polarized synchrotron emission from the Milky Way are provided. We derive the probability or luminosity distribution of Faraday caustics produced in a Gaussian magnetic field distribution as a function of their strength, F , and find that for strong Faraday caustics P(F )∝ F −3 . If fully resolved, this distribution is also shown to depen d on the Taylor microscale which relates to the largest scale over which dissipation is impor tant in turbulent flow.

Imprints of magnetic power and helicity spectra on radio polarimetry statistics

The statistical properties of turbulent magnetic fields in radio-synchrotron sources should be imprinted on the statistics of polarimetric observables. In search of these imprints, i.e. characteristic modifications of the polarimetry statistics caused by magnetic field properties, we calculate correlation and cross-correlation functions from a set of observables that contain total intensity I, polarized intensity P, and Faraday depth φ. The correlation functions are evaluated for all combinations of observables up to fourth order in magnetic field B. We derive these analytically as far as possible and from first principles using only some basic assumptions, such as Gaussian statistics for the underlying magnetic field in the observed region and statistical homogeneity. We further assume some simplifications to reduce the complexity of the calculations, because for a start we were interested in a proof of concept. Using this statistical approach, we show that it is possible to gain information about the helical part of the magnetic power spectrum via the

A new approach to multifrequency synthesis in radio interferometry

We present a new approach to multifrequency synthesis in radio astronomy. Using Bayesian inference techniques, the new technique estimates the sky brightness and the spectral index simultaneously. In principle, the bandwidth of a wide-band observation can be fully exploited for sensitivity and resolution, currently only limited by higher order e ects like spectral curvature. Employing this new approach, we further present a multifrequency extension to the imaging algorithmresolve. This method also delivers a reconstruction of the most probable spectral index spatial correlation structure across the source and an estimate of the spectral index uncertainty, although at a comparably high computational cost. In simulations, this new algorithm can outperform current multifrequency imaging techniques.

Using rotation measure grids to detect cosmological magnetic fields: A Bayesian approach

Determining magnetic field properties in different environments of the cosmic large-scale structure as well as their evolution over redshift is a fundamental step toward uncovering the origin of cosmic magnetic fields. Radio observations permit the study of extragalactic magnetic fields via measurements of the Faraday depth of extragalactic radio sources. Our aim is to investigate how much different extragalactic environments contribute to the Faraday depth variance of these sources. We develop a Bayesian algorithm to distinguish statistically Faraday depth variance contributions intrinsic to the source from those due to the medium between the source and the observer. In our algorithm the Galactic foreground and measurement noise are taken into account as the uncertainty correlations of the Galactic model. Additionally, our algorithm allows for the investigation of possible redshift evolution of the extragalactic contribution. This work presents the derivation of the algorithm and tests performed on mock observations. Because cosmic magnetism is one of the key science projects of the new generation of radio interferometers, we have predicted the performance of our algorithm on mock data collected with these instruments. According to our tests, high-quality catalogs of a few thousands of sources should already enable us to investigate magnetic fields in the cosmic structure.

Statistical methods for the analysis of rotation measure grids in large scale structures in the SKA era

Determining magnetic field properties in different environments of the cosmic large-scale structure as well as their evolution over redshift is a fundamental step toward uncovering the origin of cosmic magnetic fields. Radio observations permit the study of extragalactic magnetic fields via measurements of the Faraday depth of extragalactic radio sources. Our aim is to investigate how much different extragalactic environments contribute to the Faraday depth variance of these sources. We develop a Bayesian algorithm to distinguish statistically Faraday depth variance contributions intrinsic to the source from those due to the medium between the source and the observer. In our algorithm the Galactic foreground and the measurement noise are taken into account as the uncertainty correlations of the galactic model. Additionally, our algorithm allows for the investigation of possible redshift evolution of the extragalactic contribution. This work presents the derivation of the algorithm and tests performed on mock observations. With cosmic magnetism being one of the key science projects of the new generation of radio interferometers we have made predictions for the algorithms performance on data from the next generation of radio interferometers. Applications to real data are left for future work.