Search

Disentangling the stellar population in the central galaxy from the intrahalo light can help us shed light on the formation history of the host halo, as the properties of the stellar components are expected to retain traces of its formation history. Many approaches are adopted, depending on different physical assumptions (e.g. the light profile, chemical composition, and kinematical differences) and on whether the full six-dimensional phase-space information is known (much like in simulations) or whether one analyses projected quantities (i.e. observations). This paper paves the way for a new approach to bridge the gap between observational and simulation methods. We propose the use of projected kinematical information from stars in simulations in combination with deep learning to create a robust method for identifying intrahalo light in observational data to enhance understanding and consistency in studying the process of galaxy formation. Using a U-Net, we developed a methodology for predicting these contributions from a sample of mock images from hydrodynamical simulations to train, validate and test the network. Reinforced training (Attention U-Net) was used to improve the first results, as the innermost central regions of the mock images consistently overestimate the stellar intrahalo contribution. Our work shows that adequate training over a representative sample of mock images can lead to good predictions of the intrahalo light distribution. The model is mildly dependent on the training size and its predictions are less accurate when applied to mock images from different simulations. However, the main features (spatial scales and gradients of the stellar fractions) are recovered for all tests. While the method presented here should be considered as a proof of concept, future work is required to enable the application of the proposed model to observational data., Comment: Accepted for publication in A&A. Abstract reduced for ArXiv. 12 pages, 11 figures

We present cosmological constraints from the abundance of galaxy clusters selected via the thermal Sunyaev-Zel'dovich (SZ) effect in South Pole Telescope (SPT) data with a simultaneous mass calibration using weak gravitational lensing data from the Dark Energy Survey (DES) and the Hubble Space Telescope (HST). The cluster sample is constructed from the combined SPT-SZ, SPTpol ECS, and SPTpol 500d surveys, and comprises 1,005 confirmed clusters in the redshift range $0.25-1.78$ over a total sky area of 5,200 deg$^2$. We use DES Year 3 weak-lensing data for 688 clusters with redshifts $z<0.95$ and HST weak-lensing data for 39 clusters with $0.6

Refractory metals exhibit high strength at high temperature, but often lack ductility. Multiprinciple element alloys such as high entropy alloys offer the potential to improve ductility while maintaining strength, but we don't know $a-priori$ what compositions will be suitable. A number of measures have been proposed to predict the ductility of metals, notably the Pugh ratio, the Rice-Thomson D-parameter, among others. Here we examine direct $ab-initio$ simulation of deformation under tensile strain, and we apply this to a variety of Nb- and Mo-based binary alloys and to several quaternary alloy systems. Our results exhibit peak stresses for elastic deformation, beyond which defects such as lattice slip, stacking faults, transformation, and twinning, relieve the stress. The peak stress grows strongly with increasing valence electron count. Correlations are examined among several physical properties, including the above-mentioned ductility parameters., Comment: 22 pages, 13 figures, accepted for publication in Physical Review Materials

We present a catalog of 689 galaxy cluster candidates detected at significance $\xi>4$ via their thermal Sunyaev-Zel'dovich (SZ) effect signature in 95 and 150 GHz data from the 500-square-degree SPTpol survey. We use optical and infrared data from the Dark Energy Camera and the Wide-field Infrared Survey Explorer (WISE) and \spitzer \ satellites, to confirm 544 of these candidates as clusters with $\sim94\%$ purity. The sample has an approximately redshift-independent mass threshold at redshift $z>0.25$ and spans $1.5 \times 10^{14} < M_{500c} < 9.1 \times 10^{14}$ $M_\odot/h_{70}$ \ and $0.031$. We use external radio data from the Sydney University Molonglo Sky Survey (SUMSS) to estimate contamination to the SZ signal from synchrotron sources. The contamination reduces the recovered $\xi$ by a median value of 0.032, or $\sim0.8\%$ of the $\xi=4$ threshold value, and $\sim7\%$ of candidates have a predicted contamination greater than $\Delta \xi = 1$. With the exception of a small number of systems $(<1\%)$, an analysis of clusters detected in single-frequency 95 and 150 GHz data shows no significant contamination of the SZ signal by emission from dusty or synchrotron sources. This cluster sample will be a key component in upcoming astrophysical and cosmological analyses of clusters. The SPTpol millimeter-wave maps and associated data products used to produce this sample are available at https://pole.uchicago.edu/public/data/sptpol_500d_clusters/index.html, and the NASA LAMBDA website. An interactive sky server with the SPTpol maps and Dark Energy Survey data release 2 images is also available at NCSA https://skyviewer.ncsa.illinois.edu., Comment: Matches version accepted by OJA. 19 pages + references, 14 figures, cluster candidate table provided in Appendix. Data products available at https://pole.uchicago.edu/public/data/sptpol_500d_clusters/index.html and an interactive sky server at https://skyviewer.ncsa.illinois.edu

The Euclid photometric survey of galaxy clusters stands as a powerful cosmological tool, with the capacity to significantly propel our understanding of the Universe. Despite being sub-dominant to dark matter and dark energy, the baryonic component in our Universe holds substantial influence over the structure and mass of galaxy clusters. This paper presents a novel model to precisely quantify the impact of baryons on galaxy cluster virial halo masses, using the baryon fraction within a cluster as proxy for their effect. Constructed on the premise of quasi-adiabaticity, the model includes two parameters calibrated using non-radiative cosmological hydrodynamical simulations and a single large-scale simulation from the Magneticum set, which includes the physical processes driving galaxy formation. As a main result of our analysis, we demonstrate that this model delivers a remarkable one percent relative accuracy in determining the virial dark matter-only equivalent mass of galaxy clusters, starting from the corresponding total cluster mass and baryon fraction measured in hydrodynamical simulations. Furthermore, we demonstrate that this result is robust against changes in cosmological parameters and against varying the numerical implementation of the sub-resolution physical processes included in the simulations. Our work substantiates previous claims about the impact of baryons on cluster cosmology studies. In particular, we show how neglecting these effects would lead to biased cosmological constraints for a Euclid-like cluster abundance analysis. Importantly, we demonstrate that uncertainties associated with our model, arising from baryonic corrections to cluster masses, are sub-dominant when compared to the precision with which mass-observable relations will be calibrated using Euclid, as well as our current understanding of the baryon fraction within galaxy clusters., Comment: 18 pages, 10 figures, 4 tables, 1 appendix, abstract abridged for arXiv submission; v2 matches published version

We present a Bayesian population modeling method to analyze the abundance of galaxy clusters identified by the South Pole Telescope (SPT) with a simultaneous mass calibration using weak gravitational lensing data from the Dark Energy Survey (DES) and the Hubble Space Telescope (HST). We discuss and validate the modeling choices with a particular focus on a robust, weak-lensing-based mass calibration using DES data. For the DES Year 3 data, we report a systematic uncertainty in weak-lensing mass calibration that increases from 1% at $z=0.25$ to 10% at $z=0.95$, to which we add 2% in quadrature to account for uncertainties in the impact of baryonic effects. We implement an analysis pipeline that joins the cluster abundance likelihood with a multi-observable likelihood for the Sunyaev-Zel'dovich effect, optical richness, and weak-lensing measurements for each individual cluster. We validate that our analysis pipeline can recover unbiased cosmological constraints by analyzing mocks that closely resemble the cluster sample extracted from the SPT-SZ, SPTpol ECS, and SPTpol 500d surveys and the DES Year 3 and HST-39 weak-lensing datasets. This work represents a crucial prerequisite for the subsequent cosmological analysis of the real dataset., Comment: Accepted for publication in Phys. Rev. D. arXiv v2 corresponds to published article

The clustering of galaxy clusters is a powerful cosmological tool, which can help to break degeneracies between parameters when combined with other cosmological observables. We aim to demonstrate its potential in constraining cosmological parameters and scaling relations when combined with cluster counts and weak lensing mass information, using as a case study the redMaPPer cluster catalog derived from the Sloan Digital Sky Survey (SDSS). We extend the analysis of number counts and weak lensing signal performed by Costanzi et al. 2019a, with the addition of the real-space 2-point correlation function. We derive cosmological and scaling relation posteriors for all the possible combinations of the three observables to assess their constraining power, parameter degeneracies, and possible internal tensions. We find no evidence for tensions between the three data set analyzed. We demonstrate that the inclusion of the cluster clustering statistic can greatly enhance the constraining power of the sample thanks to its capability of breaking the $\Omega_{\rm m} - \sigma_8$ degeneracy characteristic of cluster abundance studies. In particular, for a flat $\Lambda$CDM model with massive neutrinos, we obtain $\Omega_{\rm m}=0.28 \pm 0.03$ and $\sigma_8 = 0.82 \pm 0.05$, a 33% and 50% improvement compared to the posteriors derived combining cluster abundance and weak lensing analyses. Our results are consistent with cosmological posteriors from other cluster surveys, as well as with Planck CMB results and DES-Y3 galaxy clustering and weak-lensing analysis., Comment: 15 pages, 10 figures

We present an extension to a Sunyaev-Zel'dovich Effect (SZE) selected cluster catalog based on observations from the South Pole Telescope (SPT); this catalog extends to lower signal-to-noise than the previous SPT-SZ catalog and therefore includes lower mass clusters. Optically derived redshifts, centers, richnesses and morphological parameters together with catalog contamination and completeness statistics are extracted using the multi-component matched filter algorithm (MCMF) applied to the S/N>4 SPT-SZ candidate list and the Dark Energy Survey (DES) photometric galaxy catalog. The main catalog contains 811 sources above S/N=4, has 91% purity and is 95% complete with respect to the original SZE selection. It contains 50% more total clusters and twice as many clusters above z=0.8 in comparison to the original SPT-SZ sample. The MCMF algorithm allows us to define subsamples of the desired purity with traceable impact on catalog completeness. As an example, we provide two subsamples with S/N>4.25 and S/N>4.5 for which the sample contamination and cleaning-induced incompleteness are both as low as the expected Poisson noise for samples of their size. The subsample with S/N>4.5 has 98% purity and 96% completeness, and will be included in a combined SPT cluster and DES weak-lensing cosmological analysis. We measure the number of false detections in the SPT-SZ candidate list as function of S/N, finding that it follows that expected from assuming Gaussian noise, but with a lower amplitude compared to previous estimates from simulations., Comment: 16 pages, 17 figures, submitted to MNRAS

Galaxy clusters are the most massive gravitationally bound structures in the Universe, comprising thousands of galaxies and pervaded by a diffuse, hot ``intracluster medium'' (ICM) that dominates the baryonic content of these systems. The formation and evolution of the ICM across cosmic time is thought to be driven by the continuous accretion of matter from the large-scale filamentary surroundings and dramatic merger events with other clusters or groups. Until now, however, direct observations of the intracluster gas have been limited only to mature clusters in the latter three-quarters of the history of the Universe, and we have been lacking a direct view of the hot, thermalized cluster atmosphere at the epoch when the first massive clusters formed. Here we report the detection (about $6\sigma$) of the thermal Sunyaev-Zeldovich (SZ) effect in the direction of a protocluster. In fact, the SZ signal reveals the ICM thermal energy in a way that is insensitive to cosmological dimming, making it ideal for tracing the thermal history of cosmic structures. This result indicates the presence of a nascent ICM within the Spiderweb protocluster at redshift $z=2.156$, around 10 billion years ago. The amplitude and morphology of the detected signal show that the SZ effect from the protocluster is lower than expected from dynamical considerations and comparable with that of lower-redshift group-scale systems, consistent with expectations for a dynamically active progenitor of a local galaxy cluster., Comment: 18 pages (main text + methods), 10 figures, 2 tables; published online in Nature on March 29th, 2023

Graph neural networks that model 3D data, such as point clouds or atoms, are typically desired to be $SO(3)$ equivariant, i.e., equivariant to 3D rotations. Unfortunately equivariant convolutions, which are a fundamental operation for equivariant networks, increase significantly in computational complexity as higher-order tensors are used. In this paper, we address this issue by reducing the $SO(3)$ convolutions or tensor products to mathematically equivalent convolutions in $SO(2)$ . This is accomplished by aligning the node embeddings' primary axis with the edge vectors, which sparsifies the tensor product and reduces the computational complexity from $O(L^6)$ to $O(L^3)$, where $L$ is the degree of the representation. We demonstrate the potential implications of this improvement by proposing the Equivariant Spherical Channel Network (eSCN), a graph neural network utilizing our novel approach to equivariant convolutions, which achieves state-of-the-art results on the large-scale OC-20 and OC-22 datasets., Comment: 19 pages, 10 figures

We investigate structural properties of massive galaxy populations in the central regions of five very massive galaxy clusters at z~1.4-1.7 from the South Pole Telescope Sunyaev Zel'dovich effect survey. We probe the connection between galaxy structure and broad stellar population properties, at stellar masses log(M/Msun)>10.85. We find that quiescent and star-forming cluster galaxy populations are largely dominated by bulge- and disk-dominated sources, respectively, with relative contributions consistent with those of field counterparts. At the same time, the enhanced quiescent galaxy fraction observed in these clusters with respect to the coeval field is reflected in a significant morphology-density relation, with bulge-dominated galaxies clearly dominating the massive galaxy population in these clusters already at z~1.5. At face value, these observations show no significant environmental signatures in the correlation between broad structural and stellar population properties. In particular, the Sersic index and axis ratio distribution of massive, quiescent sources are consistent with field counterparts, in spite of the enhanced quiescent galaxy fraction in clusters. This consistency suggests a tight connection between quenching and structural evolution towards a bulge-dominated morphology, at least in the probed cluster regions and galaxy stellar mass range, irrespective of environment-related processes affecting star formation in cluster galaxies. We also probe the stellar mass vs. size relation of cluster galaxies, and find that star-forming and quiescent sources populate the mass-size plane in a manner largely similar to their field counterparts, with no evidence of a significant size difference for any probed sub-population. In particular, both quiescent and bulge-dominated cluster galaxies have average sizes at fixed stellar mass consistent with their counterparts in the field., Comment: 17 pages, 10 figures, A&A in press

Aims. We validate a semi-analytical model for the covariance of real-space 2-point correlation function of galaxy clusters. Methods. Using 1000 PINOCCHIO light cones mimicking the expected Euclid sample of galaxy clusters, we calibrate a simple model to accurately describe the clustering covariance. Then, we use such a model to quantify the likelihood analysis response to variations of the covariance, and investigate the impact of a cosmology-dependent matrix at the level of statistics expected for the Euclid survey of galaxy clusters. Results. We find that a Gaussian model with Poissonian shot-noise does not correctly predict the covariance of the 2-point correlation function of galaxy clusters. By introducing few additional parameters fitted from simulations, the proposed model reproduces the numerical covariance with 10 per cent accuracy, with differences of about 5 per cent on the figure of merit of the cosmological parameters $\Omega_{\rm m}$ and $\sigma_8$. Also, we find that the cosmology-dependence of the covariance adds valuable information that is not contained in the mean value, significantly improving the constraining power of cluster clustering. Finally, we find that the cosmological figure of merit can be further improved by taking mass binning into account. Our results have significant implications for the derivation of cosmological constraints from the 2-point clustering statistics of the Euclid survey of galaxy clusters., Comment: 18 pages, 14 figures

We present the X-ray imaging and spectral analysis of the diffuse emission around the Spiderweb galaxy at z=2.16 and of its nuclear emission, based on a deep (700 ks) Chandra observation. We characterize the nuclear emission and computed the contamination in the surrounding regions due to the wings of the instrument PSF. Then, we quantified the extended emission within 12". We find that the Spiderweb galaxy hosts a mildly absorbed quasar, with modest yet significant variability on a timescale of ~1 year. We find that the emission in the jet regions is well described by a power law with Gamma~2-2.5, and it is consistent with IC upscattering of the CMB photons by the relativistic electrons. We also find a roughly symmetric, diffuse emission within a radius of ~100 kpc. This emission is consistent with thermal bremsstrahlung from a hot ICM with a temperature of kT=2.0_{-0.4}^{+0.7} keV, and a metallicity of Z<1.6Z_sun. The average electron density within 100 kpc is n_e=(1.51+-0.24+-0.14)E-2 cm^{-3}, corresponding to an upper limit for the total ICM mass of <=(1.76+-0.30+-0.17)E+12 M_sun (where error bars are 1 sigma statistical and systematic, respectively). If we apply hydrostatic equilibrium to the ICM, we measure a total gravitational mass M(<100 kpc)=(1.5^{+0.5}_{-0.3})E+13 M_sun and, extrapolating at larger radii, we estimate a total mass M_{500}=(3.2^{+1.1}_{-0.6})E+13 M_sun within a radius of r_{500}=(220+-30) kpc. We conclude that the Spiderweb protocluster shows significant diffuse emission within a radius of 12 arcsec, whose major contribution is provided by IC scattering associated with the radio jets. Outside the jet regions, we also identified thermal emission within a radius of ~100 kpc, revealing the presence of hot, diffuse baryons that may represent the embryonic virialized halo of the forming cluster., Comment: 19 pages, 16 figures, accepted in Astronomy & Astrophysics

Euclid's photometric galaxy cluster survey has the potential to be a very competitive cosmological probe. The main cosmological probe with observations of clusters is their number count, within which the halo mass function (HMF) is a key theoretical quantity. We present a new calibration of the analytic HMF, at the level of accuracy and precision required for the uncertainty in this quantity to be subdominant with respect to other sources of uncertainty in recovering cosmological parameters from Euclid cluster counts. Our model is calibrated against a suite of N-body simulations using a Bayesian approach taking into account systematic errors arising from numerical effects in the simulation. First, we test the convergence of HMF predictions from different N-body codes, by using initial conditions generated with different orders of Lagrangian Perturbation theory, and adopting different simulation box sizes and mass resolution. Then, we quantify the effect of using different halo-finder algorithms, and how the resulting differences propagate to the cosmological constraints. In order to trace the violation of universality in the HMF, we also analyse simulations based on initial conditions characterised by scale-free power spectra with different spectral indexes, assuming both Einstein--de Sitter and standard $\Lambda$CDM expansion histories. Based on these results, we construct a fitting function for the HMF that we demonstrate to be sub-percent accurate in reproducing results from 9 different variants of the $\Lambda$CDM model including massive neutrinos cosmologies. The calibration systematic uncertainty is largely sub-dominant with respect to the expected precision of future mass-observation relations; with the only notable exception of the effect due to the halo finder, that could lead to biased cosmological inference., Comment: 25 pages, 21 figures, 5 tables, 3 appendixes; v2 matches published version

The environments where galaxies reside crucially shape their star formation histories. We investigate a large sample of 1626 cluster galaxies located within 105 galaxy clusters spanning a large range in redshift ($0.26 < z < 1.13)$. The galaxy clusters are massive (M$_{500} \gtrsim 2\times10^{14}$M$_{\odot}$), and are uniformly selected from the SPT and ACT Sunyaev-Zel'dovich (SZ) surveys. With spectra in-hand for thousands of cluster members, we use galaxies' position in projected phase space as a proxy for their in-fall times, which provides a more robust measurement of environment than quantities such as projected cluster-centric radius. We find clear evidence for a gradual age increase of the galaxy's mean stellar populations ($\sim$ 0.71 $\pm$ 0.4 Gyr based on a 4000 $\r{A}$ break, $\rm D_{\rm n}4000$) with the time spent in the cluster environment. This environmental quenching effect is found regardless of galaxy luminosity (faint or bright) and redshift (low-$z$ or high-$z$), although the exact stellar age of galaxies depends on both parameters at fixed environmental effects. Such a systematic increase of $\rm D_{\rm n}4000$ with in-fall proxy would suggest that galaxies that were accreted into hosts earlier were quenched earlier, due to longer exposure to environmental effects such as ram pressure stripping and starvation. Compared to the typical dynamical time scales of $1-3$ Gyr of cluster galaxies, the relatively small age increase ($\sim$ 0.71 $\pm$ 0.4 Gyr) found in our sample galaxies seems to suggest that a slow environmental process such as starvation is the dominant quenching pathway. Our results provide new insights into environmental quenching effects spanning a large range in cosmic time ($\sim 5.2$ Gyr, $z=0.26$--1.13) and demonstrate the power of using a kinematically-derived in-fall time proxy., Comment: 22 pages, 9 figures, 3 tables. Accepted for publication by ApJ

We present deep broadband radio polarization observations of the Spiderweb radio galaxy (J1140-2629) in a galaxy proto-cluster at $z=2.16$. These yield the most detailed polarimetric maps yet made of a high redshift radio galaxy. The intrinsic polarization angles and Faraday Rotation Measures (RMs) reveal coherent magnetic fields spanning the $\sim60$ kpc length of the jets, while $\sim50$% fractional polarizations indicate these fields are well-ordered. Source-frame absolute RM values of $\sim1,000$ rad/m/m are typical, and values up to $\sim11,100$ rad/m/m are observed. The Faraday-rotating gas cannot be well-mixed with the synchrotron-emitting gas, or stronger-than-observed depolarization would occur. Nevertheless, an observed spatial coincidence between a localized absolute RM enhancement of $\sim1,100$ rad/m/m, a bright knot of Ly$\alpha$ emission, and a deviation of the radio jet provide direct evidence for vigorous jet-gas interaction. We detect a large-scale RM gradient totaling $\sim1,000$s rad/m/m across the width of the jet, suggesting a net clockwise (as viewed from the AGN) toroidal magnetic field component exists at 10s-of-kpc-scales, which we speculate may be associated with the operation of a Poynting-Robertson cosmic battery. We conclude the RMs are mainly generated in a sheath of hot gas around the radio jet, rather than the ambient foreground proto-cluster gas. The estimated magnetic field strength decreases by successive orders-of-magnitude going from the jet hotspots ($\sim90$ $\mu$G) to the jet sheath ($\sim10$ $\mu$G) to the ambient intracluster medium ($\sim1$ $\mu$G). Synthesizing our results, we propose that the Spiderweb radio galaxy is actively magnetizing its surrounding proto-cluster environment, with possible implications for theories of the origin and evolution of cosmic magnetic fields., Comment: 12 pages, 7 figures, 2 tables. Accepted for publication in ApJ

Data analysis in cosmology requires reliable covariance matrices. Covariance matrices derived from numerical simulations often require a very large number of realizations to be accurate. When a theoretical model for the covariance matrix exists, the parameters of the model can often be fit with many fewer simulations. We write a likelihood-based method for performing such a fit. We demonstrate how a model covariance matrix can be tested by examining the appropriate $\chi^2$ distributions from simulations. We show that if model covariance has amplitude freedom, the expectation value of second moment of $\chi^2$ distribution with a wrong covariance matrix will always be larger than one using the true covariance matrix. By combining these steps together, we provide a way of producing reliable covariances without ever requiring running a large number of simulations. We demonstrate our method on two examples. First, we measure the two-point correlation function of halos from a large set of $10000$ mock halo catalogs. We build a model covariance with $2$ free parameters, which we fit using our procedure. The resulting best-fit model covariance obtained from just $100$ simulation realizations proves to be as reliable as the numerical covariance matrix built from the full $10000$ set. We also test our method on a setup where the covariance matrix is large by measuring the halo bispectrum for thousands of triangles for the same set of mocks. We build a block diagonal model covariance with $2$ free parameters as an improvement over the diagonal Gaussian covariance. Our model covariance passes the $\chi^2$ test only partially in this case, signaling that the model is insufficient even using free parameters, but significantly improves over the Gaussian one., Comment: Accepted for publication in JCAP. 24 pages, 8 figures

Nowadays, Machine Learning techniques offer fast and efficient solutions for classification problems that would require intensive computational resources via traditional methods. We examine the use of a supervised Random Forest to classify stars in simulated galaxy clusters after subtracting the member galaxies. These dynamically different components are interpreted as the individual properties of the stars in the Brightest Cluster Galaxy (BCG) and IntraCluster Light (ICL). We employ matched stellar catalogues (built from the different dynamical properties of BCG and ICL) of 29 simulated clusters from the DIANOGA set to train and test the classifier. The input features are cluster mass, normalized particle cluster-centric distance, and rest-frame velocity. The model is found to correctly identify most of the stars, while the larger errors are exhibited at the BCG outskirt, where the differences between the physical properties of the two components are less obvious. We investigate the robustness of the classifier to numerical resolution, redshift dependence (up to $z=1$), and included astrophysical models. We claim that our classifier provides consistent results in simulations for $z<1$, at different resolution levels and with significantly different subgrid models. The phase-space structure is examined to assess whether the general properties of the stellar components are recovered: (i) the transition radius between BCG-dominated and ICL-dominated region is identified at $0.04$ \r200; (ii) the BCG outskirt ($> 0.1$ \r200) is significantly affected by uncertainties in the classification process. In conclusion, this work suggests the importance of employing Machine Learning to speed up a computationally expensive classification in simulations., Comment: 19 pages, accepted to MNRAS

Deep Chandra and VLA imaging reveals a clear correlation between X-ray and radio emission on scales $\sim 100$~kpc in the Spiderweb radio galaxy at z=2.16. The X-ray emission associated with the extended radio source is likely dominated by inverse Compton up-scattering of cosmic microwave background photons by the radio emitting relativistic electrons. For regions dominated by high surface brightness emission, such as hot spots and jet knots, the implied magnetic fields are $\sim 50~\mu$G to $70~\mu$G. The non-thermal pressure is these brighter regions is then $\sim 9\times 10^{-10}$ dyne cm$^{-2}$, or three times larger than the non-thermal pressure derived assuming minimum energy conditions, and an order of magnitude larger than the thermal pressure in the ambient cluster medium. Assuming ram pressure confinement implies an average advance speed for the radio source of $\sim 2400$ km s$^{-1}$, and a source age of $\sim 3\times 10^7$ years. Considering the lower surface brightness, diffuse radio emitting regions, we identify an evacuated cavity in the Ly$\alpha$ emission coincident with the tail of the eastern radio lobe. Making reasonable assumptions for the radio spectrum, we find that the relativistic electrons and fields in the lobe are plausibly in pressure equilibrium with the thermal gas, and close to a minimum energy configuration. The radio morphology suggests that the Spiderweb is a high-$z$ example of the rare class of hybrid morphology radio sources (or HyMoRS), which we attribute to interaction with the asymmetric gaseous environment indicated by the Ly$\alpha$ emission., Comment: 8 figures, 25 pages, to appear in the ApJ

(Abridged) We present an analysis of the 700 ks Chandra ACIS-S observation of the field around the Spiderweb Galaxy at z=2.156, focusing on the nuclear activity in the associated large-scale environment. We identify unresolved X-ray sources down to flux limits of 1.3X10^{-16} and 3.9X10^{-16} erg/s/cm^2 in the soft and hard band, respectively. We search for counterparts in the optical, NIR and submm bands to identify X-ray sources belonging to the protocluster. We detect 107 X-ray unresolved sources within 5 arcmin (corresponding to 2.5 Mpc) of J1140-2629, among which 13 have optical counterparts with spectroscopic redshift 2.11~1.84+-0.04. The best-fit intrinsic absorption for 5 protocluster X-ray members is N_H>10^{23} cm^{-2}, while other 6 have upper limits of the order of fewX10^{22} cm^{-2}. Two sources can only be fitted with very flat \Gamma<=1, and are therefore considered Compton-thick candidates. Their 0.5-10 keV rest frame luminosities are larger than 2X10^{43} erg/s, significantly greater than X-ray luminosities expected from star formation activity. The X-ray luminosity function of AGN in the volume associated to the Spiderweb protocluster in the range 10^{43}10.5, corresponding to an enhancement of 6.0^{+9.0}_{-3.0} with respect to the COSMOS field at comparable redshifts and stellar mass range. We conclude that the galaxy population in the Spiderweb Protocluster is characterized by enhanced X-ray nuclear activity triggered by environmental effects on Mpc scales., Comment: Astronomy & Astrophysics. Minor changes in this version. Version accepted in A&A