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L. Rudnick

Publications and source records attributed to L. Rudnick.

At least 73 records · Page 4Linked to original sources

Deep VLA observations of the cluster 1RXS J0603.3+4214 in the frequency range 1-2 GHz

We report L-band VLA observations of 1RXS J0603.3+4214, a cluster that hosts a bright radio relic, known as the Toothbrush, and an elongated giant radio halo. These new observations allow us to study the surface brightness distribution down to one arcsec resolution with very high sensitivity. Our images provide an unprecedented detailed view of the Toothbrush, revealing enigmatic filamentary structures. To study the spectral index distribution, we complement our analysis with published LOFAR and GMRT observations. The bright `brush' of the Toothbrush shows a prominent narrow ridge to its north with a sharp outer edge. The spectral index at the ridge is in the range $-0.70\leqα\leq-0.80$. We suggest that the ridge is caused by projection along the line of sight. With a simple toy model for the smallest region of the ridge, we conclude that the magnetic field is below $5\,\rmμG$ and varies significantly across the shock front. Our model indicates that the actual Mach number is higher than that obtained from the injection index and agrees well with the one derived from the overall spectrum, namely ${\cal M}=3.78^{+0.3}_{-0.2}$. The radio halo shows an average spectral index of $α=-1.16\pm0.05$ and a slight gradient from north to south. The southernmost part of the halo is steeper and possibly related to a shock front. Excluding the southernmost part, the halo morphology agrees very well with the X-ray morphology. A power-law correlation is found between the radio and X-ray surface brightness

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Radio Galaxy Zoo: A Search for Hybrid Morphology Radio Galaxies

Hybrid morphology radio sources are a rare type of radio galaxy that display different Fanaroff-Riley classes on opposite sides of their nuclei. To enhance the statistical analysis of hybrid morphology radio sources, we embarked on a large-scale search of these sources within the international citizen science project, Radio Galaxy Zoo (RGZ). Here, we present 25 new candidate hybrid morphology radio galaxies. Our selected candidates are moderate power radio galaxies (L_median = 4.7x10^{24} W/(Hz sr) at redshifts 0.14 1Mpc) radio galaxies, one resides at a centre of a galaxy cluster, and one is hosted by a rare green bean galaxy. Although the origin of the hybrid morphology radio galaxies is still unclear, this type of radio source starts depicting itself as a rather diverse class. We discuss hybrid radio morphology formation in terms of the radio source environment (nurture) and intrinsically occurring phenomena (nature; activity cessation and amplification), showing that these peculiar radio galaxies can be formed by both mechanisms. While high angular resolution follow-up observations are still necessary to confirm our candidates, we demonstrate the efficacy of the Radio Galaxy Zoo in the pre-selection of these sources from all-sky radio surveys, and report the reliability of citizen scientists in identifying and classifying complex radio sources.

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Radio Galaxy Zoo: Cosmological Alignment of Radio Sources

We study the mutual alignment of radio sources within two surveys, FIRST and TGSS. This is done by producing two position angle catalogues containing the preferential directions of respectively $30\,059$ and $11\,674$ extended sources distributed over more than $7\,000$ and $17\,000$ square degrees. The identification of the sources in the FIRST sample was performed in advance by volunteers of the Radio Galaxy Zoo project, while for the TGSS sample it is the result of an automated process presented here. After taking into account systematic effects, marginal evidence of a local alignment on scales smaller than $2.5°$ is found in the FIRST sample. The probability of this happening by chance is found to be less than $2$ per cent. Further study suggests that on scales up to $1.5°$ the alignment is maximal. For one third of the sources, the Radio Galaxy Zoo volunteers identified an optical counterpart. Assuming a flat $Λ$CDM cosmology with $Ω_m = 0.31, Ω_Λ= 0.69$, we convert the maximum angular scale on which alignment is seen into a physical scale in the range $[19, 38]$ Mpc $h_{70}^{-1}$. This result supports recent evidence reported by Taylor and Jagannathan of radio jet alignment in the $1.4$ deg$^2$ ELAIS N1 field observed with the Giant Metrewave Radio Telescope. The TGSS sample is found to be too sparsely populated to manifest a similar signal.

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Deep Chandra observations of the stripped galaxy group falling into Abell 2142

In the local Universe, the growth of massive galaxy clusters mainly operates through the continuous accretion of group-scale systems. The infalling group in Abell 2142 is the poster child of such an accreting group, and as such, it is an ideal target to study the astrophysical processes induced by structure formation. We present the results of a deep (200 ks) observation of this structure with Chandra, which highlights the complexity of this system in exquisite detail. In the core of the group, the spatial resolution of Chandra reveals the presence of a leading edge and a complex AGN-induced activity. The morphology of the stripped gas tail appears straight in the innermost 250 kpc, suggesting that magnetic draping efficiently shields the gas from its surroundings. However, beyond $\sim300$ kpc from the core, the tail flares and the morphology becomes strongly irregular, which could be explained by a breaking of the drape, e.g. because of turbulent motions. The power spectrum of surface-brightness fluctuations is relatively flat ($P_{2D}\propto k^{-2.3}$), which indicates that thermal conduction is strongly inhibited even beyond the region where magnetic draping is effective. The amplitude of density fluctuations in the tail is consistent with a mild level of turbulence with a Mach number $M_{3D}\sim0.1-0.25$. Overall, our results show that the processes leading to the thermalization and mixing of the infalling gas are slow and relatively inefficient.

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The two-component giant radio halo in the galaxy cluster Abell 2142

We report on a spectral study at radio frequencies of the giant radio halo in A2142 (z=0.0909), which we performed to explore its nature and origin. A2142 is not a major merger and the presence of a giant radio halo is somewhat surprising. We performed deep radio observations with the GMRT at 608 MHz, 322 MHz, and 234 MHz and with the VLA in the 1-2 GHz band. We obtained high-quality images at all frequencies in a wide range of resolutions. The radio halo is well detected at all frequencies and extends out to the most distant cold front in A2142. We studied the spectral index in two regions: the central part of the halo and a second region in the direction of the most distant south-eastern cold front, selected to follow the bright part of the halo and X-ray emission. We complemented our observations with a preliminary LOFAR image at 118 MHz and with the re-analysis of archival VLA data at 1.4 GHz. The two components of the radio halo show different observational properties. The central brightest part has higher surface brightess and a spectrum whose steepness is similar to those of the known radio halos, i.e. $α^{\rm 1.78~GHz}_{\rm 118~MHz}=1.33\pm 0.08$. The ridge, which fades into the larger scale emission, is broader in size and has considerably lower surface brightess and a moderately steeper spectrum, i.e. $α^{\rm 1.78~GHz}_{\rm 118~MHz}\sim 1.5$. We propose that the brightest part of the radio halo is powered by the central sloshing in A2142, similar to what has been suggested for mini-halos, or by secondary electrons generated by hadronic collisions in the ICM. On the other hand, the steeper ridge may probe particle re-acceleration by turbulence generated either by stirring the gas and magnetic fields on a larger scale or by less energetic mechanisms, such as continuous infall of galaxy groups or an off-axis merger.

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Observed Faraday Effects in Damped Lyman-Alpha Absorbers and Lyman Limit Systems: The Magnetised Environment of Galactic Building Blocks at Redshift=2

Protogalactic environments are typically identified using quasar absorption lines, and these galactic building blocks can manifest as Damped Lyman-Alpha Absorbers (DLAs) and Lyman Limit Systems (LLSs). We use radio observations of Faraday effects to test whether DLAs and LLSs host a magnetised medium, by combining DLA and LLS detections throughout the literature with 1.4 GHz polarization data from the NRAO VLA Sky Survey (NVSS). We obtain a control, a DLA, and a LLS sample consisting of 114, 19, and 27 lines-of-sight respectively - all of which are polarized at $\ge8σ$ to ensure Rician bias is negligible. Using a Bayesian framework, we are unable to detect either coherent or random magnetic fields in DLAs: the regular coherent magnetic fields within the DLAs must be $\le2.8$ $μ$G, and the lack of depolarization is consistent with the weakly magnetised gas in DLAs being non-turbulent and quiescent. However, we find mild suggestive evidence that LLSs have coherent magnetic fields: after controlling for the redshift-distribution of our data, we find a 71.5% probability that LLSs have a higher RM than a control sample. We also find strong evidence that LLSs host random magnetic fields, with a 95.5% probability that LLS lines-of-sight have lower polarized fractions than a control sample. The regular coherent magnetic fields within the LLSs must be $\le2.4$ $μ$G, and the magnetised gas must be highly turbulent with a typical scale on the order of $\approx5$-20 pc, which is similar to that of the Milky Way. This is consistent with the standard dynamo pedagogy, whereby magnetic fields in protogalaxies increase in coherence and strength as a function of cosmic time. Our results are consistent with a hierarchical galaxy formation scenario, with the DLAs, LLSs, and strong magnesium II (MgII) systems exploring three different stages of magnetic field evolution in galaxies.

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Radio Galaxy Zoo: discovery of a poor cluster through a giant wide-angle tail radio galaxy

We have discovered a previously unreported poor cluster of galaxies (RGZ-CL J0823.2+0333) through an unusual giant wide-angle tail radio galaxy found in the Radio Galaxy Zoo project. We obtained a spectroscopic redshift of $z=0.0897$ for the E0-type host galaxy, 2MASX J08231289+0333016, leading to M$_r = -22.6$ and a $1.4\,$GHz radio luminosity density of $L_{\rm 1.4} = 5.5\times10^{24}$ W Hz$^{-1}$. These radio and optical luminosities are typical for wide-angle tailed radio galaxies near the borderline between Fanaroff-Riley (FR) classes I and II. The projected largest angular size of $\approx8\,$arcmin corresponds to $800\,$kpc and the full length of the source along the curved jets/trails is $1.1\,$Mpc in projection. X-ray data from the XMM-Newton archive yield an upper limit on the X-ray luminosity of the thermal emission surrounding RGZ J082312.9+033301,at $1.2-2.6\times10^{43}$ erg s$^{-1}$ for assumed intra-cluster medium temperatures of $1.0-5.0\,$keV. Our analysis of the environment surrounding RGZ J082312.9+033301 indicates that RGZ J082312.9+033301 lies within a poor cluster. The observed radio morphology suggests that (a) the host galaxy is moving at a significant velocity with respect to an ambient medium like that of at least a poor cluster, and that (b) the source may have had two ignition events of the active galactic nucleus with $10^7\,$yrs in between. This reinforces the idea that an association between RGZ J082312.9+033301, and the newly discovered poor cluster exists.

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LOFAR, VLA, and Chandra observations of the Toothbrush galaxy cluster

We present deep LOFAR observations between 120-181 MHz of the "Toothbrush" (RX J0603.3+4214), a cluster that contains one of the brightest radio relic sources known. Our LOFAR observations exploit a new and novel calibration scheme to probe 10 times deeper than any previous study in this relatively unexplored part of the spectrum. The LOFAR observations, when combined with VLA, GMRT, and Chandra X-ray data, provide new information about the nature of cluster merger shocks and their role in re-accelerating relativistic particles. We derive a spectral index of $α= -0.8 \pm 0.1$ at the northern edge of the main radio relic, steepening towards the south to $α\approx - 2$. The spectral index of the radio halo is remarkably uniform ($α= -1.16$, with an intrinsic scatter of $\leq 0.04$). The observed radio relic spectral index gives a Mach number of $\mathcal{M} = 2.8^{+0.5}_{-0.3}$, assuming diffusive shock acceleration (DSA). However, the gas density jump at the northern edge of the large radio relic implies a much weaker shock ($\mathcal{M} \approx 1.2$, with an upper limit of $\mathcal{M} \approx 1.5$). The discrepancy between the Mach numbers calculated from the radio and X-rays can be explained if either (i) the relic traces a complex shock surface along the line of sight, or (ii) if the radio relic emission is produced by a re-accelerated population of fossil particles from a radio galaxy. Our results highlight the need for additional theoretical work and numerical simulations of particle acceleration and re-acceleration at cluster merger shocks.

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LOFAR facet calibration

LOFAR, the Low-Frequency Array, is a powerful new radio telescope operating between 10 and 240 MHz. LOFAR allows detailed sensitive high-resolution studies of the low-frequency radio sky. At the same time LOFAR also provides excellent short baseline coverage to map diffuse extended emission. However, producing high-quality deep images is challenging due to the presence of direction dependent calibration errors, caused by imperfect knowledge of the station beam shapes and the ionosphere. Furthermore, the large data volume and presence of station clock errors present additional difficulties. In this paper we present a new calibration scheme, which we name facet calibration, to obtain deep high-resolution LOFAR High Band Antenna images using the Dutch part of the array. This scheme solves and corrects the direction dependent errors in a number of facets that cover the observed field of view. Facet calibration provides close to thermal noise limited images for a typical 8 hr observing run at $\sim$ 5arcsec resolution, meeting the specifications of the LOFAR Tier-1 northern survey.

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The ASKAP/EMU Source Finding Data Challenge

The Evolutionary Map of the Universe (EMU) is a proposed radio continuum survey of the Southern Hemisphere up to declination +30 deg., with the Australian Square Kilometre Array Pathfinder (ASKAP). EMU will use an automated source identification and measurement approach that is demonstrably optimal, to maximise the reliability, utility and robustness of the resulting radio source catalogues. As part of the process of achieving this aim, a "Data Challenge" has been conducted, providing international teams the opportunity to test a variety of source finders on a set of simulated images. The aim is to quantify the accuracy of existing automated source finding and measurement approaches, and to identify potential limitations. The Challenge attracted nine independent teams, who tested eleven different source finding tools. In addition, the Challenge initiators also tested the current ASKAPsoft source-finding tool to establish how it could benefit from incorporating successful features of the other tools. Here we present the results of the Data Challenge, identifying the successes and limitations for this broad variety of the current generation of radio source finding tools. As expected, most finders demonstrate completeness levels close to 100% at 10sigma dropping to levels around 10% by 5sigma. The reliability is typically close to 100% at 10sigma, with performance to lower sensitivities varying greatly between finders. All finders demonstrate the usual trade-off between completeness and reliability, whereby maintaining a high completeness at low signal-to-noise comes at the expense of reduced reliability, and vice-versa. We conclude with a series of recommendations for improving the performance of the ASKAPsoft source-finding tool.

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Radio Galaxy Zoo: host galaxies and radio morphologies derived from visual inspection

We present results from the first twelve months of operation of Radio Galaxy Zoo, which upon completion will enable visual inspection of over 170,000 radio sources to determine the host galaxy of the radio emission and the radio morphology. Radio Galaxy Zoo uses $1.4\,$GHz radio images from both the Faint Images of the Radio Sky at Twenty Centimeters (FIRST) and the Australia Telescope Large Area Survey (ATLAS) in combination with mid-infrared images at $3.4\,μ$m from the {\it Wide-field Infrared Survey Explorer} (WISE) and at $3.6\,μ$m from the {\it Spitzer Space Telescope}. We present the early analysis of the WISE mid-infrared colours of the host galaxies. For images in which there is $>\,75\%$ consensus among the Radio Galaxy Zoo cross-identifications, the project participants are as effective as the science experts at identifying the host galaxies. The majority of the identified host galaxies reside in the mid-infrared colour space dominated by elliptical galaxies, quasi-stellar objects (QSOs), and luminous infrared radio galaxies (LIRGs). We also find a distinct population of Radio Galaxy Zoo host galaxies residing in a redder mid-infrared colour space consisting of star-forming galaxies and/or dust-enhanced non star-forming galaxies consistent with a scenario of merger-driven active galactic nuclei (AGN) formation. The completion of the full Radio Galaxy Zoo project will measure the relative populations of these hosts as a function of radio morphology and power while providing an avenue for the identification of rare and extreme radio structures. Currently, we are investigating candidates for radio galaxies with extreme morphologies, such as giant radio galaxies, late-type host galaxies with extended radio emission, and hybrid morphology radio sources.

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Cluster magnetic fields through the study of polarized radio halos in the SKA era

Galaxy clusters are unique laboratories to investigate turbulent fluid motions and large scale magnetic fields. Synchrotron radio halos at the center of merging galaxy clusters provide the most spectacular and direct evidence of the presence of relativistic particles and magnetic fields associated with the intracluster medium. The study of polarized emission from radio halos is extremely important to constrain the properties of intracluster magnetic fields and the physics of the acceleration and transport of the relativistic particles. However, detecting this polarized signal is a very hard task with the current radio facilities.We use cosmological magneto-hydrodynamical simulations to predict the expected polarized surface brightness of radio halos at 1.4 GHz. We compare these expectations with the sensitivity and the resolution reachable with the SKA1. This allows us to evaluate the potential for studying intracluster magnetic fields in the surveys planned for SKA1.

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Unravelling the origin of large-scale magnetic fields in galaxy clusters and beyond through Faraday Rotation Measures with the SKA

We investigate the possibility for the SKA to detect and study the magnetic fields in galaxy clusters and in the less dense environments surrounding them using Faraday Rotation Measures. To this end, we produce 3-dimensional magnetic field models for galaxy clusters of different masses and in different stages of their evolution, and derive mock rotation measure observations of background radiogalaxies. According to our results, already in phase I, we will be able to infer the magnetic field properties in galaxy clusters as a function of the cluster mass, down to $10^{13}$ solar-masses. Moreover, using cosmological simulations to model the gas density, we have computed the expected rotation measure through shock-fronts that occur in the intra-cluster medium during cluster mergers. The enhancement in the rotation measure due to the density jump will permit to constraint the magnetic field strength and structure after the shock passage. SKA observations of polarised sources located behind galaxy clusters will answer several questions about the magnetic field strength and structure in galaxy clusters, and its evolution with cosmic time.

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Comparison of algorithms for determination of rotation measure and Faraday structure I. 1100 - 1400 MHz

(abridged) We run a Faraday structure determination data challenge to benchmark the currently available algorithms including Faraday synthesis (previously called RM synthesis in the literature), wavelet, compressive sampling and $QU$-fitting. The frequency set is similar to POSSUM/GALFACTS with a 300 MHz bandwidth from 1.1 to 1.4 GHz. We define three figures of merit motivated by the underlying science: a) an average RM weighted by polarized intensity, RMwtd, b) the separation $Δϕ$ of two Faraday components and c) the reduced chi-squared. Based on the current test data of signal to noise ratio of about 32, we find that: (1) When only one Faraday thin component is present, most methods perform as expected, with occasional failures where two components are incorrectly found; (2) For two Faraday thin components, QU-fitting routines perform the best, with errors close to the theoretical ones for RMwtd, but with significantly higher errors for $Δϕ$. All other methods including standard Faraday synthesis frequently identify only one component when $Δϕ$ is below or near the width of the Faraday point spread function; (3) No methods, as currently implemented, work well for Faraday thick components due to the narrow bandwidth; (4) There exist combinations of two Faraday components which produce a large range of acceptable fits and hence large uncertainties in the derived single RMs; in these cases, different RMs lead to the same Q, U behavior, so no method can recover a unique input model.

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The stripping of a galaxy group diving into the massive cluster A2142

Structure formation in the current Universe operates through the accretion of group-scale systems onto massive clusters. The detection and study of such accreting systems is crucial to understand the build-up of the most massive virialized structures we see today. We report the discovery with XMM-Newton of an irregular X-ray substructure in the outskirts of the massive galaxy cluster Abell 2142. The tip of the X-ray emission coincides with a concentration of galaxies. The bulk of the X-ray emission of this substructure appears to be lagging behind the galaxies and extends over a projected scale of at least 800 kpc. The temperature of the gas in this region is 1.4 keV, which is a factor of ~4 lower than the surrounding medium and is typical of the virialized plasma of a galaxy group with a mass of a few 10^13M_sun. For this reason, we interpret this structure as a galaxy group in the process of being accreted onto the main dark-matter halo. The X-ray structure trailing behind the group is due to gas stripped from its original dark-matter halo as it moves through the intracluster medium (ICM). This is the longest X-ray trail reported to date. For an infall velocity of ~1,200 km s-1 we estimate that the stripped gas has been surviving in the presence of the hot ICM for at least 600 Myr, which exceeds the Spitzer conduction timescale in the medium by a factor of >~400. Such a strong suppression of conductivity is likely related to a tangled magnetic field with small coherence length and to plasma microinstabilities. The long survival time of the low-entropy intragroup medium suggests that the infalling material can eventually settle within the core of the main cluster.

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Is the Sunyaev-Zeldovich effect responsible for the observed steepening in the spectrum of the Coma radio halo ?

The spectrum of the radio halo in the Coma cluster is measured over almost two decades in frequency. The current radio data show a steepening of the spectrum at higher frequencies, which has implications for models of the radio halo origin. There is an on-going debate on the possibility that the observed steepening is not intrinsic to the emitted radiation, but is instead caused by the SZ effect. Recently, the Planck satellite measured the SZ signal and its spatial distribution in the Coma cluster allowing to test this hypothesis. Using the Planck results, we calculated the modification of the radio halo spectrum by the SZ effect in three different ways. With the first two methods we measured the SZ-decrement within the aperture radii used for flux measurements of the halo at the different frequencies. First we adopted the global compilation of data from Thierbach et al. and a reference aperture radius consistent with those used by the various authors. Second we used the available brightness profiles of the halo at different frequencies to derive the spectrum within two fixed apertures, and derived the SZ-decrement using these apertures. As a third method we used the quasi-linear correlation between the y and the radio-halo brightness at 330 MHz discovered by Planck to derive the modification of the radio spectrum by the SZ-decrement in a way that is almost independent of the adopted aperture radius. We found that the spectral modification induced by the SZ-decrement is 4-5 times smaller than that necessary to explain the observed steepening. Consequently a break or cut-off in the spectrum of the emitting electrons is necessary to explain current data. We also show that, if a steepening is absent from the emitted spectrum, future deep observations at 5 GHz with single dishes are expected to measure a halo flux in a 40 arcmin radius that would be 7-8 times higher than currently seen.

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The "toothbrush-relic": evidence for a coherent linear 2-Mpc scale shock wave in a massive merging galaxy cluster?

Some merging galaxy clusters host diffuse extended radio emission, so-called radio halos and relics. Here we present observations between 147 MHz and 4.9 GHz of a new radio-selected galaxy cluster 1RXS J0603.3+4214 (z=0.225). The cluster is also detected as an extended X-ray source in the RASS. It hosts a large bright 1.9 Mpc radio relic, an elongated ~2 Mpc radio halo, and two smaller radio relics. The large radio relic has a peculiar linear morphology. For this relic we observe a clear spectral index gradient, in the direction towards the cluster center. We performed Rotation Measure (RM) Synthesis between 1.2 and 1.7 GHz. The results suggest that for the west part of the large relic some of the Faraday rotation is caused by ICM and is not only due to galactic foregrounds. We also carried out a detailed spectral analysis of this radio relic and created radio color-color diagrams. We find (i) an injection spectral index of -0.6 to -0.7, (ii) steepening spectral index and increasing spectral curvature in the post-shock region, and (iii) an overall power-law spectrum between 74 MHz and 4.9 GHz with α=-1.10 \pm 0.02. Mixing of emission in the beam from regions with different spectral ages is probably the dominant factor that determines the shape of the radio spectra. Changes in the magnetic field, total electron content, or adiabatic gains/losses do not play a major role. A model in which particles are (re)accelerated in a first order Fermi process at the front of the relic provides the best match to the observed spectra. We speculate that in the post-shock region particles are re-accelerated by merger induced turbulence to form the radio halo as the relic and halo are connected. The 1RXS J0603.3+4214 merger is probably more complex than the "simple'" binary merger events that are thought to give rise to symmetric double radio relics.

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Probing the origin of giant radio halos through radio and gamma-ray data : the case of the Coma cluster

We combine all available information about the spectral shape and morphology of the radio halo of the Coma cluster with the gamma-ray upper limits obtained by the Fermi-LAT and with the magnetic field strength derived from Faraday rotation measures (RM). We explore the possibility that the radio halo is due to synchrotron emission of secondary electrons generated via p-p collisions in the intra-cluster-medium (ICM). First we investigate the case of pure secondary models. We use the observed spatial distribution of the halo's radio brightness to constrain the amount of cosmic rays (CRs) and their spatial distribution in the cluster that are required by the model. Under the canonical assumption that the spectrum of CRs is a power-law in momentum and that the spectrum of secondaries is stationary, we find that the combination of the steep spectrum of CRs necessary to explain the spectrum of the halo and their very broad spatial distribution (and large energy density) result in a gamma-ray emission in excess of present limits, unless the cluster magnetic field is sufficiently large. However such a field appears inconsistent with constraints from RM. Second we investigate more complex models based on secondary particles in which CR protons and their secondaries are all reaccelerated by MHD turbulence. We show that under these conditions it is possible to reproduce the radio data and to predict gamma-rays in agreement with the Fermi-LAT limits without tension with constraints on the cluster magnetic field. Reacceleration of secondaries by MHD turbulence also requires a spatial distribution of CRs much flatter than that of the ICM, if both the turbulent and magnetic field energy densities scale with that of the ICM. However broader spatial distributions of turbulence and field and/or the reacceleration of additional primary electrons in the ICM greatly alleviate this requirement.

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