The knowledge of the dynamical state of galaxy clusters allows to alleviate systematics when observational data from these objects are applied in cosmological studies. Evidence of correlation between the state and the morphology of the clusters is well studied. The morphology can be inferred by images of the surface brightness in the X-ray band and of the thermal component of the Sunyaev-Zel’dovich (tSZ) effect in the millimetre range. For this purpose, we apply, for the first time, the Zernike polynomial decomposition, a common analytic approach mostly used in adaptive optics to recover aberrated radiation wavefronts at the telescopes pupil plane. With this novel way we expect to correctly infer the morphology of clusters and so possibly, their dynamical state. To verify the reliability of this new approach we use more than 300 synthetic clusters selected in THE THREE HUNDRED project at different redshifts ranging from 0 up to 1.03. Mock maps of the tSZ, quantified with the Compton parameter, y-maps, are modelled with Zernike polynomials inside R500, the cluster reference radius. We verify that it is possible to discriminate the morphology of each cluster by estimating the contribution of the different polynomials to the fit of the map. The results of this new method are correlated with those of a previous analysis made on the same catalogue, using two parameters that combine either morphological or dynamical-state probes. We underline that instrumental angular resolution of the maps has an impact mainly when we extend this approach to high-redshift clusters.

The cosmic microwave background (CMB) is one of the most powerful tools for cosmology. Its polarization could have imprinted the sign of an inflationary background of gravitational waves, which is supposed to have originated at 10−38/10−35 seconds after the Big Bang. Detecting this background is extremely difficult because of the weakness of the signal (if any) left on the CMB polarization and because of the need to control the systematic effects. Additionally, the presence of astrophysical foregrounds, the possibility of leakage from curl-free to curl-like components, including gravitational lensing, and the instrumental noise and systematics, require sensitive detectors and smart systematic effect control. We discuss the experimental efforts spent in this field, highlighting the key observational difference and the choice that could lead, in the near future, to the detection of the curl component of the CMB polarization, a clear sign of the inflationary expansion.

Several methods are used to evaluate, from observational data, the dynamical state of galaxy clusters. Among them, the morphological analysis of cluster images is well suited for this purpose. We report a new approach to the morphology, which consists in analytically modelling the images with a set of orthogonal functions, the Zernike polynomials (ZPs). We validated the method on mock high-resolution Compton parameter maps of synthetic galaxy clusters from The Three Hundred project. To classify the maps for their morphology we defined a single parameter, C, by combining the contribution of some ZPs in the modelling. We verify that C is linearly correlated with a combination of common morphological parameters and also with a proper 3D dynamicalstate indicator available for the synthetic clusters we used. We also show the early results of the Zernike modelling applied on Compton parameter maps of local clusters (z < 0:1) observed by the Planck satellite. At last, we report the preliminary results of this kind of morphological analysis on mock X-ray maps of The Three Hundred clusters.

We measure the local correlation between radio emission and Compton-y signal across two galaxy clusters, Abell 399 and Abell 401, using maps from the Low-Frequency Array (LOFAR) and the Atacama Cosmology Telescope (ACT) + Planck. These datasets allow us to make the first measurement of this kind at ∼arcminute resolution. We find that the radio brightness scales as Fradio∝y1.5 for Abell 401 and Fradio∝y2.8 for Abell 399. Furthermore, using XMM-Newton data, we derive a sublinear correlation between radio and X-ray brightness for both the clusters ($F_{\mathrm{radio}} \propto F_{\rm X}^{0.7}$). Finally, we correlate the Compton-y and X-ray data, finding that an isothermal model is consistent with the cluster profiles, $y \propto F_{\rm X}^{0.5}$. By adopting an isothermal–β model, we are able, for the first time, to jointly use radio, X-ray, and Compton-y data to estimate the scaling index for the magnetic field profile, B(r)∝ne(r)η in the injection and re-acceleration scenarios. Applying this model, we find that the combined radio and Compton-y signal exhibits a significantly tighter correlation with the X-ray across the clusters than when the datasets are independently correlated. We find η ∼ 0.6 − 0.8. These results are consistent with the upper limit we derive for the scaling index of the magnetic field using rotation measure values for two radio galaxies in Abell 401. We also measure the radio, Compton-y, and X-ray correlations in the filament between the clusters but conclude that deeper data are required for a convincing determination of the correlations in the filament.

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