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Rainer Beck

Publications and source records attributed to Rainer Beck.

At least 37 records · Page 2Linked to original sources

Extragalactic Magnetism with SOFIA (Legacy Program) -- I: The magnetic field in the multi-phase interstellar medium of M51

The recent availability of high-resolution far-infrared (FIR) polarization observations of galaxies using HAWC+/SOFIA has facilitated studies of extragalactic magnetic fields in the cold and dense molecular disks.We investigate if any significant structural differences are detectable in the kpc-scale magnetic field of the grand design face-on spiral galaxy M51 when traced within the diffuse (radio) and the dense and cold (FIR) interstellar medium (ISM). Our analysis reveals a complex scenario where radio and FIR polarization observations do not necessarily trace the same magnetic field structure. We find that the magnetic field in the arms is wrapped tighter at 154um than at 3 and 6 cm; statistically significant lower values for the magnetic pitch angle are measured at FIR in the outskirts (R > 7 kpc) of the galaxy. This difference is not detected in the interarm region. We find strong correlations of the polarization fraction and total intensity at FIR and radio with the gas column density and 12CO(1-0) velocity dispersion. We conclude that the arms show a relative increase of small-scale turbulent B-fields at regions with increasing column density and dispersion velocities of the molecular gas. No correlations are found with HI neutral gas. The star formation rate shows a clear correlation with the radio polarized intensity, which is not found in FIR, pointing to a small-scale dynamo-driven B-field amplification scenario. This work shows that multi-wavelength polarization observations are key to disentangling the interlocked relation between star formation, magnetic fields, and gas kinematics in the multi-phase ISM.

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Spectro-polarimetric observations of the CIZA J2242.8+5301 northern radio relic: no evidence of high-frequency steepening

Observations of radio relics at very high frequency (>10 GHz) can help to understand how particles age and are (re-)accelerated in galaxy cluster outskirts and how magnetic fields are amplified in these environments. In this work, we present new single-dish 18.6 GHz Sardinia Radio Telescope and 14.25 GHz Effelsberg observations of the well known northern radio relic of CIZA J2242.8+5301. We detected the relic which shows a length of $\sim$1.8 Mpc and a flux density equal to $\rm S_{14.25\,GHz}=(9.5\pm3.9)\,mJy$ and $\rm S_{18.6\,GHz}=(7.67\pm0.90)\,mJy$ at 14.25 GHz and 18.6 GHz respectively. The resulting best-fit model of the relic spectrum from 145 MHz to 18.6 GHz is a power-law spectrum with spectral index $α=1.12\pm0.03$: no evidence of steepening has been found in the new data presented in this work. For the first time, polarisation properties have been derived at 18.6 GHz, revealing an averaged polarisation fraction of $\sim40\%$ and a magnetic field aligned with the 'filaments' or 'sheets' of the relic.

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Magnetism Science with the Square Kilometre Array

The Square Kilometre Array (SKA) will answer fundamental questions about the origin, evolution, properties, and influence of magnetic fields throughout the Universe. Magnetic fields can illuminate and influence phenomena as diverse as star formation, galactic dynamics, fast radio bursts, active galactic nuclei, large-scale structure, and Dark Matter annihilation. Preparations for the SKA are swiftly continuing worldwide, and the community is making tremendous observational progress in the field of cosmic magnetism using data from a powerful international suite of SKA pathfinder and precursor telescopes. In this contribution, we revisit community plans for magnetism research using the SKA, in the light of these recent rapid developments. We focus in particular on the impact that new radio telescope instrumentation is generating, thus advancing our understanding of key SKA magnetism science areas, as well as the new techniques that are required for processing and interpreting the data. We discuss these recent developments in the context of the ultimate scientific goals for the SKA era.

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CHANG-ES XXII: Coherent Magnetic Fields in the Halos of Spiral Galaxies

Context. The magnetic field in spiral galaxies is known to have a large-scale spiral structure along the galactic disk and is observed as X-shaped in the halo of some galaxies. While the disk field can be well explained by dynamo action, the 3-dimensional structure of the halo field and its physical nature is still unclear. Aims. As first steps towards understanding the halo fields, we want to clarify whether the observed X-shaped field is a wide-spread pattern in the halos of spiral galaxies and whether these halo fields are just turbulent fields ordered by compression or shear (anisotropic turbulent fields), or have a large-scale regular structure. Methods. The analysis of the Faraday rotation in the halo is the tool to discern anisotropic turbulent fields from large-scale magnetic fields. This, however, has been challenging until recently because of the faint halo emission in linear polarization. Our sensitive VLA broadband observations C-band and L-band of 35 spiral galaxies seen edge-on (called CHANG-ES) allowed us to perform RM-synthesis in their halos and to analyze the results. We further accomplished a stacking of the observed polarization maps of 28 CHANG-ES galaxies at C-band. Results. Though the stacked edge-on galaxies were of different Hubble types, star formation and interaction activities, the stacked image clearly reveals an X-shaped structure of the apparent magnetic field. We detected a large-scale (coherent) halo field in all 16 galaxies that have extended polarized intensity in their halos. We detected large-scale field reversals in all of their halos. In six galaxies they are along lines about vertical to the galactic midplane (vertical RMTL) with about 2 kpc separation. Only in NGC 3044 and possibly in NGC 3448 we observed vertical giant magnetic ropes (GMRs) similar to those detected recently in NGC 4631.

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Synthesizing Observations and Theory to Understand Galactic Magnetic Fields: Progress and Challenges

Constraining dynamo theories of magnetic field origin by observation is indispensable but challenging, in part because the basic quantities measured by observers and predicted by modelers are different. We clarify these differences and sketch out ways to bridge the divide. Based on archival and previously unpublished data, we then compile various important properties of galactic magnetic fields for nearby spiral galaxies. We consistently compute strengths of total, ordered, and regular fields, pitch angles of ordered and regular fields, and we summarize the present knowledge on azimuthal modes, field parities, and the properties of non-axisymmetric spiral features called magnetic arms. We review related aspects of dynamo theory, with a focus on mean-field models and their predictions for large-scale magnetic fields in galactic discs and halos. Further, we measure the velocity dispersion of HI gas in arm and inter-arm regions in three galaxies, M 51, M 74, and NGC 6496, since spiral modulation of the root-mean-square turbulent speed has been proposed as a driver of non-axisymmetry in large-scale dynamos. We find no evidence for such a modulation and place upper limits on its strength, helping to narrow down the list of mechanisms to explain magnetic arms. Successes and remaining challenges of dynamo models with respect to explaining observations are briefly summarized, and possible strategies are suggested. With new instruments like the Square Kilometre Array (SKA), large data sets of magnetic and non-magnetic properties from thousands of galaxies will become available, to be compared with theory.

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An In-depth Investigation of Faraday Depth Spectrum Using Synthetic Observations of Turbulent MHD Simulations

In this paper we present a detailed analysis of the Faraday depth (FD) spectrum and its clean components obtained through the application of the commonly used technique of Faraday rotation measure synthesis to analyze spectro-polarimetric data. In order to directly compare the Faraday depth spectrum with physical properties of a magneto-ionic medium, we generated synthetic broad-bandwidth spectro-polarimetric observations from magnetohydrodynamic (MHD) simulations of a transonic, isothermal, compressible turbulent medium. We find that correlated magnetic field structures give rise to a combination of spiky, localized peaks at certain FD values, and broad structures in the FD spectrum. Although the majority of these spiky FD structures appear narrow, giving an impression of a Faraday thin medium, we show that they arise from strong synchrotron emissivity at that FD. Strong emissivity at a FD can arise because of both strong spatially-local polarized synchrotron emissivity at a FD or accumulation of weaker emissions along the distance through a medium that have Faraday depths within half the width of the rotation measure spread function. Such a complex Faraday depth spectrum is a natural consequence of MHD turbulence when the lines of sight pass through a few turbulent cells. This therefore complicates the convention of attributing narrow FD peaks to presence of a Faraday rotating medium along the line of sight. Our work shows that it is difficult to extract the FD along a line of sight from the Faraday depth spectrum using standard methods for a turbulent medium in which synchrotron emission and Faraday rotation occur simultaneously.

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CHANG-ES XIV: Cosmic-ray propagation and magnetic field strengths in the radio halo of NGC 4631

NGC 4631 is an interacting galaxy that exhibits one of the largest, gaseous halos observed among edge-on galaxies. We aim to examine the synchrotron and cosmic-ray propagation properties of its disk and halo emission with new radio continuum data. Radio continuum observations of NGC 4631 were performed with the Karl G. Jansky Very Large Array at C-band (5.99 GHz) in the C and D array configurations, and at L-band (1.57 GHz) in the B, C, and D array configurations. Complementary observations of NGC 4631 with the Effelsberg telescope were performed at 1.42 and 4.85 GHz. The interferometric total intensity data were combined with the single-dish Effelsberg data in order to recover the missing large-scale total power emission. The thermal and nonthermal components of the total radio emission were separated by estimating the thermal contribution through the extinction-corrected H$α$ emission. The H$α$ radiation was corrected for extinction using a linear combination of the observed H$α$ and 24 $μ$m data. NGC 4631 has a global thermal fraction at 5.99 (1.57) GHz of 14$\pm$3% (5.4$\pm$1.1%). The mean scale heights of the total emission in the radio halo (thick disk) at 5.99 (1.57) GHz are $1.79\pm0.54$ kpc ($1.75\pm0.27$ kpc) and have about the same values for the synchrotron emission. The total magnetic field of NGC 4631 has a mean strength of $\rm{\langle B_{eq}\rangle} \simeq 9 \rm{μG}$ in the disk, and a mean strength of $\rm{\langle B_{eq}\rangle}~\simeq 7~\rm{μG}$ in the halo. We also studied a double-lobed background radio galaxy southwest of NGC 4631, which is an FR~II radio galaxy according to the distribution of spectral index across the lobes. From the halo scale heights we estimated that the radio halo is escape-dominated with convective cosmic ray propagation, and conclude that there is a galactic wind in the halo of NGC 4631.

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CHANG-ES XV: Large-scale magnetic field reversals in the radio halo of NGC 4631

NGC 4631 is an interacting galaxy which exhibits one of the largest gaseous halos observed among edge-on galaxies. We aim to examine the synchrotron and polarization properties of its disk and halo emission with new radio continuum data. Radio continuum observations of NGC 4631 were performed with the Karl G. Jansky Very Large Array at C-band (5.99 GHz) in the C & D array configurations, and at L-band (1.57 GHz) in the B, C, & D array configurations. The Rotation Measure Synthesis algorithm was utilized to derive the polarization properties. We detected linearly polarized emission at C-band and L-band. The magnetic field in the halo is characterized by strong vertical components above and below the central region of the galaxy. The magnetic field in the disk is only clearly seen in the eastern side of NGC 4631, where it is parallel to the plane of the major axis of the galaxy. We detected for the first time a large-scale, smooth Faraday depth pattern in a halo of an external spiral galaxy, which implies the existence of a regular (coherent) magnetic field. A quasi-periodic pattern in Faraday depth with field reversals was found in the northern halo of the galaxy. The field reversals in the northern halo of NGC 4631, together with the observed polarization angles, indicate giant magnetic ropes (GMRs) with alternating directions. To our knowledge, this is the first time such reversals are observed in an external galaxy.

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CHANG-ES XVI: An in-depth view of the cosmic-ray transport in the edge-on spiral galaxies NGC 891 and NGC 4565

Cosmic-ray electrons (CREs) originating from the star-forming discs of spiral galaxies frequently form extended radio haloes that are best observable in edge-on galaxies. For the present study we selected two nearby edge-on galaxies from the CHANG-ES survey, NGC 891 and 4565, which differ largely in halo size and SFR. To figure out how such differences are related to the CRE transport in disc and halo, we use wide-band 1.5 and 6 GHz VLA observations obtained in the B, C, and D configurations, and combine the 6 GHz images with Effelsberg observations to correct for missing short spacings. We study the spatially resolved non-thermal spectral index distribution in terms of CRE spectral ageing, compute total magnetic field strengths assuming energy equipartition between CRs and magnetic fields, and also determine synchrotron scale heights. Based on the vertical profiles of synchrotron intensity and spectral index, we create purely advective and purely diffusive CRE transport models by numerically solving the 1D diffusion-loss equation. In particular, we investigate for the first time the radial dependence of synchrotron and magnetic field scale heights, advection speeds and diffusion coefficients in these two galaxies. We find the spectral index distribution of NGC 891 to be mostly consistent with continuous CRE injection, while in NGC 4565 the local synchrotron spectra are more in line with discrete-epoch CRE injection (JP or KP models). This implies that CRE injection timescales are lower than the synchrotron cooling timescales. The scale height of NGC 891 increases with radius, indicating that synchrotron losses are significant. NGC 891 is probably dominated by advective CRE transport at a velocity of $\gtrsim150\,\mathrm{km\,s^{-1}}$. In contrast, NGC 4565 is diffusion-dominated up to $z=1$ kpc or higher, with a diffusion coefficient of $\geq2\times10^{28}\,\mathrm{cm^2\,s^{-1}}$.

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Revisiting the Equipartition Assumption in Star-forming Galaxies

Energy equipartition between cosmic rays and magnetic fields is often assumed to infer magnetic field properties from the synchrotron observations of star-forming galaxies. However, there is no compelling physical reason to expect the same. We aim to explore the validity of the energy equipartition assumption. After describing popular arguments in favour of the assumption, we first discuss observational results which support it at large scales and how certain observations show significant deviations from equipartition at scales smaller than $\approx 1 \, {\rm kpc}$, probably related to the propagation length of the cosmic rays. Then we test the energy equipartition assumption using test-particle and MHD simulations. From the results of the simulations, we find that the energy equipartition assumption is not valid at scales smaller than the driving scale of the ISM turbulence ($\approx 100 \, {\rm pc}$ in spiral galaxies), which can be regarded as the lower limit for the scale beyond which equipartition is valid. We suggest that one must be aware of the dynamical scales in the system before assuming energy equipartition to extract magnetic field information from synchrotron observations. Finally, we present ideas for future observations and simulations to investigate in more detail under which conditions the equipartition assumption is valid or not.

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CHANG-ES: XVIII---The CHANG-ES Survey and Selected Results

The CHANG-ES (Continuum Halos in Nearby Galaxies) survey of 35 nearby edge-on galaxies is revealing new and sometimes unexpected and startling results in their radio continuum emission. The observations were in wide bandwidths centered at 1.6 and 6.0 GHz. Unique to this survey is full polarization data showing magnetic field structures in unprecedented detail, resolution and sensitivity for such a large sample. A wide range of new results are reported here, some never before seen in any galaxy. We see circular polarization and variability in active galactic nuclei (AGNs), in-disk discrete features, disk-halo structures sometimes only seen in polarization, and broad-scale halos with reversing magnetic fields, among others. This paper summarizes some of the CHANG-ES results seen thus far. Released images can be found at https://www.queensu.ca/changes.

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Magnetic arms of NGC6946 traced in the Faraday cubes at low radio frequencies

Magnetic fields in galaxies exist on various spatial scales. Large-scale magnetic fields are thought to be generated by the $α-Ω$ dynamo. Small-scale galactic magnetic fields (1 kpc and below) can be generated by tangling the large-scale field or by the small-scale turbulent dynamo. The analysis of field structures with the help of polarized radio continuum emission is hampered by the effect of Faraday dispersion (due to fluctuations in magnetic field and/or thermal electron density) that shifts signals from large to small scales. At long observation wavelengths large-scale magnetic fields may become invisible, as in the case of spectro-polarimetric data cube of the spiral galaxy NGC~6946 observed with the Westerbork Radio Synthesis Telescope in the wavelength range 17-23 cm. The application of RM Synthesis alone does not overcome this problem. We propose to decompose the Faraday data cube into data cubes at different spatial scales by a wavelet transform. Signatures of the `magnetic arms' observed in NGC~6946 at shorter wavelengths become visible. Our method allows us to search for large-scale field patterns in data cubes at long wavelengths, as provided by new-generation radio telescopes.

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CHANG-ES X: Spatially-resolved Separation of Thermal Contribution from Radio Continuum Emission in Edge-on Galaxies

We analyze the application of star formation rate (SFR) calibrations using H$α$ and 22 micron infrared imaging data in predicting the thermal radio component for a test sample of 3 edge-on galaxies (NGC 891, NGC 3044, and NGC 4631) in the Continuum Halos in Nearby Galaxies -- an EVLA Survey (CHANG-ES). We use a mixture of H$α$ and 24 micron calibration from Calzetti et al. (2007), and a linear 22 micron only calibration from Jarrett et al. (2013) on the test sample. We apply these relations on a pixel-to-pixel basis to create thermal prediction maps in the two CHANG-ES bands: L- and C-band (1.5 GHz and 6.0 GHz, respectively). We analyze the resulting non-thermal spectral index maps, and find a characteristic steepening of the non-thermal spectral index with vertical distance from the disk after application of all methods. We find possible evidence of extinction in the 22 micron data as compared to 70 micron Spitzer Multband Imaging Photometer (MIPS) imaging in NGC 891. We analyze a larger sample of edge-on and face-on galaxy 25 micron to 100 micron flux ratios, and find that the ratios for edge-ons are systematically lower by a factor of 1.36, a result we attribute to excess extinction in the mid-IR in edge-ons. We introduce a new calibration for correcting the H$α$ luminosity for dust when galaxies are edge-on or very dusty.

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CHANG-ES IX: Radio scale heights and scale lengths of a consistent sample of 13 spiral galaxies seen edge-on and their correlations

The vertical halo scale height is a crucial parameter to understand the transport of cosmic-ray electrons (CRE) and their energy loss mechanisms in spiral galaxies. Until now, the radio scale height could only be determined for a few edge-on galaxies because of missing sensitivity at high resolution. We developed a sophisticated method for the scale height determination of edge-on galaxies. With this we determined the scale heights and radial scale lengths for a sample of 13 galaxies from the CHANG-ES radio continuum survey in two frequency bands. The sample average value for the radio scale heights of the halo are 1.1 +/- 0.3kpc in C-band and 1.4 +/- 0.7kpc in L-band. From the frequency dependence analysis of the halo scale heights we found that the wind velocities (estimated using the adiabatic loss time) are above the escape velocity. We found that the halo scale heights increase linearly with the radio diameters. In order to exclude the diameter dependence, we defined a normalized scale height which is quite similar for all sample galaxies at both frequency bands and does not depend on the star formation rate or the magnetic field strength. However, the normalized scale height shows a tight anticorrelation with the mass surface density. The sample galaxies with smaller scale lengths are more spherical in the radio emission, while those with larger scale lengths are flatter. The radio scale height depends mainly on the radio diameter of the galaxy. The sample galaxies are consistent with an escape-dominated radio halo with convective cosmic ray propagation, indicating that galactic winds are a widespread phenomenon in spiral galaxies. While a higher star formation rate or star formation surface density does not lead to a higher wind velocity, we deceleration of CRE outflow, e.g. a lowering of the wind velocity from the galactic disk.

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The NOD3 software package: A graphical user interface-supported reduction package for single-dish radio continuum and polarisation observations

The venerable NOD2 data reduction software package for single-dish radio continuum observations, developed for use at the 100-m Effelsberg radio telescope, has been successfully applied over many decades. Modern computing facilities call for a new design. We aim to develop an interactive software tool with a graphical user interface (GUI) for the reduction of single-dish radio continuum maps. Special effort is given on the reduction of distortions along the scanning direction (scanning effects) by combining maps scanned in orthogonal directions or dual- or multiple-horn observations that need to be processed in a restoration procedure. The package should also process polarisation data and offer the possibility to include special tasks written by the individual user. Based on the ideas of the NOD2 package we developed NOD3, which includes all necessary tasks from the raw maps to the final maps in total intensity and linear polarisation. Furthermore, plot routines and several methods for map analysis are available. The NOD3 package is written in Python which allows to extend the package by additional tasks. The required data format for the input maps is FITS. NOD3 is a sophisticated tool to process and analyse maps from single-dish observations that are affected by 'scanning effects' due to clouds, receiver instabilities, or radio-frequency interference (RFI). The 'basket-weaving' tool combines orthogonally scanned maps to a final map that is almost free of scanning effects. The new restoration tool for dual-beam observations reduces the noise by a factor of about two compared to the NOD2 version. Combining single-dish with interferometer data in the map plane ensures the full recovery of the total flux density.

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New insights into the interstellar medium of the dwarf galaxy IC 10: connection between magnetic fields, the radio--infrared correlation and star formation

We present the highest sensitivity and angular resolution study at 0.32 GHz of the dwarf irregular galaxy IC\,10, observed using the Giant Metrewave Radio Telescope, probing $\sim45$ pc spatial scales. We find the galaxy-averaged radio continuum spectrum to be relatively flat, with a spectral index $α= -0.34\pm0.01$ ($S_ν\propto ν^α$), mainly due to a high contribution from free--free emission. At 0.32 GHz, some of the H{\sc ii} regions show evidence of free--free absorption as they become optically thick below $\sim0.41$ GHz with corresponding free electron densities of $\sim11-22~\rm cm^{-3}$. After removing the free--free emission, we studied the radio--infrared relations on 55, 110 and 165 pc spatial scales. We find that on all scales the non-thermal emission at 0.32 and 6.2 GHz correlates better with far-infrared (FIR) emission at $70\,μ$m than mid-infrared emission at $24\,μ$m. The dispersion of the radio--FIR relation arises due to variations in both magnetic field and dust temperature, and decreases systematically with increasing spatial scale. The effect of cosmic ray transport is negligible as cosmic ray electrons were only injected $\lesssim5$ Myr ago. The average magnetic field strength ($B$) of $12~μ$G in the disc is comparable to that of large star-forming galaxies. The local magnetic field is strongly correlated with local star formation rate ($\mathrm{SFR}$) as $B \propto \mathrm{SFR}^{0.35\pm0.03}$, indicating a star-burst driven fluctuation dynamo to be efficient ($\sim10$ per cent) in amplifying the field in IC\,10. The high spatial resolution observations presented here suggest that the high efficiency of magnetic field amplification and strong coupling with SFR likely sets up the radio--FIR correlation in cosmologically young galaxies.

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A new method to suppress the bias in polarized intensity

Computing polarised intensities from noisy data in Stokes U and Q suffers from a positive bias that should be suppressed. To develop a correction method that, when applied to maps, should provide a distribution of polarised intensity that closely follows the signal from the source. We propose a new method to suppress the bias by estimating the polarisation angle of the source signal in a noisy environment with help of a modified median filter. We then determine the polarised intensity, including the noise, by projection of the observed values of Stokes U and Q onto the direction of this polarisation angle. We show that our new method represents the true signal very well. If the noise distribution in the maps of U and Q is Gaussian, then in the corrected map of polarised intensity it is also Gaussian. Smoothing to larger Gaussian beamsizes, to improve the signal-to-noise ratio, can be done directly with our method in the map of the polarised intensity. Our method also works in case of non-Gaussian noise distributions. The maps of the corrected polarised intensities and polarisation angles are reliable even in regions with weak signals and provide integrated flux densities and degrees of polarisation without the cumulative effect of the bias, which especially affects faint sources. Features at low intensity levels like 'depolarisation canals' are smoother than in the maps using the previous methods, which has broader implications, for example on the interpretation of interstellar turbulence.

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Relics in galaxy clusters at high radio frequencies

We observed three radio relics in galaxy clusters and one radio relic candidate at 4.85 and 8.35 GHz in total emission and linearly polarized emission with the Effelsberg 100-m telescope and one radio relic candidate in X-rays with the Chandra telescope. The radio spectra of the integrated emission below 8.35 GHz can be well fitted by single power laws for all four relics. The flat spectra (spectral indices of 0.9 and 1.0) for the "Sausage" relic in cluster CIZA J2242+53 and the "Toothbrush" relic in cluster 1RXS 06+42 indicate that models describing the origin of relics have to include effects beyond the assumptions of diffuse shock acceleration. The spectra of the radio relics in ZwCl 0008+52 and in Abell 1612 are steep, as expected from weak shocks (Mach number $\approx 2.4$). We find polarization degrees of more than 50 % in the two prominent Mpc-sized radio relics, the Sausage and the Toothbrush. The high degree of polarization indicates that the magnetic field vectors are almost perfectly aligned along the relic structure. The polarization degrees correspond to Mach numbers of $>2.2$. Polarized emission is also detected in the radio relics in ZwCl 0008+52 and, for the first time, in Abell 1612. Abell 1612 shows a complex X-ray surface brightness distribution, indicating a recent major merger. No Faraday depolarization is detected between 4.85 GHz and 8.35 GHz, except for one component of the Toothbrush relic. Faraday depolarization between 1.38 GHz and 8.35 GHz varies with distance from the center of the host cluster 1RXS 06+42, which can be explained by a decrease in electron density and/or in strength of a turbulent magnetic field. Faraday rotation measures show large-scale gradients along the relics, which cannot be explained by variations in the Milky Way foreground. Large-scale regular fields appear to be present in intergalactic space around galaxy clusters.

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