Shocks and cold fronts in merging and massive galaxy clusters: new detections with Chandra

A number of merging galaxy clusters shows the presence of shocks and cold fronts, i.e. sharp discontinuities in surface brightness and temperature. The observation of these features requires an X-ray telescope with high spatial resolution like Chandra, and allows to study important aspects concerning the physics of the intra-cluster medium (ICM), such as its thermal conduction and viscosity, as well as to provide information on the physical conditions leading to the acceleration of cosmic rays and magnetic field amplification in the cluster environment. In this work we search for new discontinuities in 15 merging and massive clusters observed with Chandra by using different imaging and spectral techniques of X-ray observations. Our analysis led to the discovery of 22 edges: six shocks, eight cold fronts and eight with uncertain origin. All the six shocks detected have $\mathcal{M} < 2$ derived from density and temperature jumps. This work contributed to increase the number of discontinuities detected in clusters and shows the potential of combining diverse approaches aimed to identify edges in the ICM. A radio follow-up of the shocks discovered in this paper will be useful to study the connection between weak shocks and radio relics.Comment: Matched to the MNRAS published version, minor grammar and typo fixe

Comparison between a vector multiport network analyzer and the national S-parameter measurement system

A multiport vector network analyzer based on a new calibration concept, has been compared with the P-port S-parameter National measurement system at IENGF. The measurements were performed on precision 7 mm standard components and exhibited an optimum agreement. These results open the possibility to use the new multiport network analyzer for certification measurements of multiport device

Accuracy of a multiport network analyzer

The accuracy of a multiport vector network analyzer, which uses a new calibration concept, has been compared with a 2-port network analyzer that implements the classical TRL procedure. The accuracy assessment is based on the analysis of the error propagation due to the connectors repeatability, both of the used standards and the measurands. The comparison, performed in the 2-18 GHz band on devices fitted with APC-7 mm connectors, proved the high accuracy reached by a multiport system which can qualify for metrological applications

Magnetic Field Evolution in Giant Radio Relics using the example of CIZA J2242.8+5301

Giant radio relics are the arc-shaped diffuse radio emission regions observed in the outskirts of some merging galaxy clusters. They are believed to trace shock-waves in the intra-cluster medium. Recent observations demonstrated that some prominent radio relics exhibit a steepening above 2 GHz in their radio spectrum. This challenges standard theoretical models because shock acceleration is expected to accelerate electrons to very high energies with a power-law distribution in momentum. In this work we attempt to reconcile these data with the shock-acceleration scenario. We propose that the spectral steepening may be caused by the highest energy electrons emitting preferentially in lower magnetic fields than the bulk of synchrotron bright electrons in relics. Here, we focus on a model with an increasing mag- netic field behind the shock front, which quickly saturates and then declines. We derive the time-evolution of cosmic-ray electron spectra in time variable magnetic fields and an expanding medium. We then apply the formalism on the large radio relic in the cluster CIZA J2242.8+5301 (the Sausage relic). We show that under favourable circumstances of magnetic field amplification downstream, our model can explain the observed radio spectrum, the brightness profile and the spectral index profile of the relic. A possible interpretation for the required amplification of the magnetic field downstream is a dynamo acting behind the shock with an injection scale of magnetic turbulence of about 10 kpc. Our models require injection efficiencies of CRe - which are in tension with simple diffusive shock acceleration from the thermal pool. We show that this problem can likely be alleviated considering pre-existing CRe.Comment: 18 pages, 3 tables, 14 figure

On eigenspaces of some compound complex unit gain graphs

Let T be the multiplicative group of complex units, and let L (Φ) denote the Laplacian matrix of a nonempty T-gain graph Φ = (Γ, T, γ). The gain line graph L (Φ) and the gain subdivision graph S (Φ) are defined up to switching equivalence. We discuss how the eigenspaces determined by the adjacency eigenvalues of L (Φ) and S (Φ) are related with those of L (Φ)

Line graphs of complex unit gain graphs with least eigenvalue -2

Let T be the multiplicative group of complex units, and let L(φ) denote a line graph of a T-gain graph φ. Similarly to what happens in the context of signed graphs, the real number min Spec(A(L(φ)), that is, the smallest eigenvalue of the adjacency matrix of L(φ), is not less than -2. The structural conditions on φ ensuring that min Spec(A(L(φ)) = -2 are identified. When such conditions are fulfilled, bases of the -2-eigenspace are constructed with the aid of the star complement technique

Modular localization and Wigner particles

We propose a framework for the free field construction of algebras of local observables which uses as an input the Bisognano-Wichmann relations and a representation of the Poincare' group on the one-particle Hilbert space. The abstract real Hilbert subspace version of the Tomita-Takesaki theory enables us to bypass some limitations of the Wigner formalism by introducing an intrinsic spacetime localization. Our approach works also for continuous spin representations to which we associate a net of von Neumann algebras on spacelike cones with the Reeh-Schlieder property. The positivity of the energy in the representation turns out to be equivalent to the isotony of the net, in the spirit of Borchers theorem. Our procedure extends to other spacetimes homogeneous under a group of geometric transformations as in the case of conformal symmetries and de Sitter spacetime.Comment: 22 pages, LaTeX. Some errors have been corrected. To appear on Rev. Math. Phy

The turbulent pressure support in galaxy clusters revisited

Due to their late formation in cosmic history, clusters of galaxies are not fully in hydrostatic equilibrium and the gravitational pull of their mass at a given radius is expected not to be entirely balanced by the thermal gas pressure. Turbulence may supply additional pressure, and recent (X-ray and SZ) hydrostatic mass reconstructions claim a pressure support of $\sim 5-15\%$ of the total pressure at $R_{\rm 200}$. In this work we show that, after carefully disentangling bulk from small-scale turbulent motions in high-resolution simulations of galaxy clusters, we can constrain which fraction of the gas kinetic energy effectively provides pressure support in the cluster's gravitational potential. While the ubiquitous presence of radial inflows in the cluster can lead to significant bias in the estimate of the non-thermal pressure support, we report that only a part of this energy effectively acts as a source of pressure, providing a support of the order of $\sim 10\%$ of the total pressure at $R_{\rm 200}$.Comment: 5 pages, 5 pages, accepted, to appear in MNRAS Letter

New scaling relations in cluster radio halos and the re-acceleration model

In this paper we derive new expected scaling relations for clusters with giant radio halos in the framework of the re-acceleration scenario in a simplified, but physically motivated, form, namely: radio power (P_R) vs size of the radio emitting region (R_H), and P_R vs total cluster mass (M_H) contained in the emitting region and cluster velocity dispersion (sigma_H) in this region. We search for these correlations by analyzing the most recent radio and X-ray data available in the literature for a well known sample of clusters with giant radio halos. In particular we find a good correlation between P_R and R_H and a very tight ``geometrical'' scaling between M_H and R_H. From these correlations P_R is also expected to scale with M_H and sigma_H and this is confirmed by our analysis. We show that all the observed trends can be well reconciled with expectations in the case of a slight variation of the mean magnetic field strength in the radio halo volume with M_H. A byproduct correlation between R_H and sigma_H is also found, and can be further tested by optical studies. In addition, we find that observationally R_H scales non-linearly with the virial radius of the host cluster, and this immediately means that the fraction of the cluster volume which is radio emitting increases with cluster mass and thus that the non-thermal component in clusters is not self-similar.Comment: 11 pages, 12 figures, accepted for publication in MNRA