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Asif Iqbal

Publications and source records attributed to Asif Iqbal.

At least 19 recordsLinked to original sources

PASCHEN-1D: A one-dimensional fluid plasma solver with multi-mechanism surface emission and flexible external circuit coupling

We present PASCHEN-1D (Plasma Advanced Solver with Coupled High-fidelity Emission and external Network), a one-dimensional time-dependent fluid plasma solver developed for self-consistent simulation of gas discharges and plasma breakdown with coupled electrode surface emission and flexible external circuit networks. The code solves drift-diffusion continuity equations for electrons and ions together with Poisson's equation. It is dynamically coupled to lumped RLC circuits, which self-consistently treat plasma transport, plasma-surface interaction, dielectric effects, and circuit response within a single framework. The electrode emission module includes ion-induced secondary electron emission, Fowler-Nordheim and Murphy-Good field emission, Richardson-Dushman thermionic emission, and photoemission based on a general, exact quantum mechanical emission theory. A finite-volume formulation with Kurganov-Tadmor fluxes, explicit diffusion, and fourth-order Runge-Kutta time integration is employed to ensure stable transient (sometimes ultrafast) evolution across breakdown and glow regimes. The solver is validated against multiple benchmark cases, including nanosecond pulsed dielectric-barrier discharges, DC breakdown and glow transitions, and Paschen curve construction for argon and nitrogen, with results consistent with published studies. With high-fidelity emission physics and a flexible circuit-coupling framework, PASCHEN-1D provides a versatile and efficient tool for modeling breakdown and transient discharge phenomena.

physics.plasm-ph

Probing the baryonic--dark matter connection in galaxy clusters using X-rays with gated recurrent unit neural networks

Accurate cluster mass measurements are crucial for cosmology, yet conventional hydrostatic equilibrium (HSE) methods can suffer from systematic biases, particularly in dynamically disturbed systems. We present a gated recurrent unit (GRU) based deep learning framework for predicting three-dimensional mass profiles of galaxy clusters from spherically averaged intra-cluster medium (ICM) radial profiles. By treating ICM profiles as sequential data, the GRU captures radial dependencies and naturally handles profiles with different radial samplings. We train and validate the model using high-resolution hydrodynamical simulations from The Three Hundred Project, achieving unbiased mass predictions with a typical 1$σ$ scatter of $\sim$5% over most of the cluster region, significantly improving upon HSE estimates. The model provides radius-dependent uncertainty estimates and remains robust against variations in data quality and cluster morphology. When trained jointly on independent simulation suites (GIZMO-SIMBA and GADGET-X), it successfully generalises across both simulations. Feature importance analysis shows that enclosed gas mass is the dominant predictor, with pressure and temperature providing additional information on the radial mass distribution. We further apply the GRU model to X-ray observations of the REXCESS and X-COP cluster samples from XMM-Newton and compare the inferred mass profiles with HSE estimates. The HSE masses are systematically lower than the GRU predictions for the higher-mass X-COP sample, while the REXCESS sample shows mass differences that are close to zero on average. This work provides a data-driven framework for cluster mass inference that bridges simulations and observations and can be extended to multi-wavelength datasets, including Sunyaev-Zel'dovich and optical observations.

astro-ph.CO

X-ray and Radio Analysis of Abell 1644: Constraints on Cluster Dynamics

We present the first band-2 (120--250\,MHz) uGMRT (upgraded Giant Metrewave Radio Telescope) observations of the bimodal galaxy cluster Abell\,1644 (\(z = 0.0471\)), complemented by Chandra X-ray data. While weak lensing measurements reveal a third substructure in Abell 1644, our radio analysis reveals only two compact sources coinciding with the respective brightest cluster galaxies (BCGs) of the northern (A1644N1) and southern (A1644S) substructures, seen in the X-ray observations. Radio analysis yields compact active galactic nuclei (AGN) powered sources with radio power $P_{A1644S} = 1.1\times 10^{23} W/Hz$ and $P_{A1644N} = 7.3\times 10^{23} W/Hz$ at 200MHz. We find no evidence of non-thermal diffuse radio emission, such as halos or relics, within the sensitivity of our band-2 image. We measured the flux density of each radio source and performed spectral analysis. A1644N1 exhibits a synchrotron power law spectrum while A1644S shows spectral turnover suggestive of synchrotron self-absorption. Our X-ray analysis confirms the presence of a cold front east of the A1644S subcluster core. The temperature map further reveals a previously unreported asymmetry, with a hot intracluster medium (ICM) region to the east of A1644S and cooler gas to the west, likely representing residual signatures of earlier merger activity. Together, these features indicate that Abell 1644 preserves clear imprints of its merger history through long-lived sloshing motions, while the absence of diffuse radio emission suggests that the past merger was relatively minor not injecting enough turbulence for large scale reacceleration or the cluster is approaching a late stage of ICM relaxation.

astro-ph.GA

Deriving accurate galaxy cluster masses using X-ray thermodynamic profiles and graph neural networks

Precise determination of galaxy cluster masses is crucial for establishing reliable mass-observable scaling relations in cluster cosmology. We employ graph neural networks (GNNs) to estimate galaxy cluster masses from radially sampled profiles of the intra-cluster medium (ICM) inferred from X-ray observations. GNNs naturally handle inputs of variable length and resolution by representing each ICM profile as a graph, enabling accurate and flexible modeling across diverse observational conditions. We trained and tested GNN model using state-of-the-art hydrodynamical simulations of galaxy clusters from The Three Hundred Project. The mass estimates using our method exhibit no systematic bias compared to the true cluster masses in the simulations. Additionally, we achieve a scatter in recovered mass versus true mass of about 6%, which is a factor of six smaller than obtained from a standard hydrostatic equilibrium approach. Our algorithm is robust to both data quality and cluster morphology and it is capable of incorporating model uncertainties alongside observational uncertainties. Finally, we apply our technique to XMM-Newton observed galaxy cluster samples and compare the GNN derived mass estimates with those obtained with $Y_{\rm SZ}$-M$_{500}$ scaling relations. Our results provide strong evidence, at 5$σ$ level, for a mass-dependent bias in SZ derived masses, with higher mass clusters exhibiting a greater degree of deviation. Furthermore, we find the median bias to be $(1-b)=0.85_{-0.14}^{+0.34}$, albeit with significant dispersion due to its mass dependence. This work takes a significant step towards establishing unbiased observable mass scaling relations by integrating X-ray, SZ and optical datasets using deep learning techniques, thereby enhancing the role of galaxy clusters in precision cosmology.

astro-ph.CO

A Supervised Machine Learning Framework for Multipactor Breakdown Prediction in High-Power Radio Frequency Devices and Accelerator Components: A Case Study in Planar Geometry

Multipactor is a nonlinear electron avalanche phenomenon that can severely impair the performance of high-power radio frequency (RF) devices and accelerator systems. Accurate prediction of multipactor susceptibility across different materials and operational regimes remains a critical yet computationally intensive challenge in accelerator component design and RF engineering. This study presents the first application of supervised machine learning (ML) for predicting multipactor susceptibility in two-surface planar geometries. A simulation-derived dataset spanning six distinct secondary electron yield (SEY) material profiles is used to train regression models - including Random Forest (RF), Extra Trees (ET), Extreme Gradient Boosting (XGBoost), and funnel-structured Multilayer Perceptrons (MLPs) - to predict the time-averaged electron growth rate, $δ_{avg}$. Performance is evaluated using Intersection over Union (IoU), Structural Similarity Index (SSIM), and Pearson correlation coefficient. Tree-based models consistently outperform MLPs in generalizing across disjoint material domains. MLPs trained using a scalarized objective function that combines IoU and SSIM during Bayesian hyperparameter optimization with 5-fold cross-validation outperform those trained with single-objective loss functions. Principal Component Analysis reveals that performance degradation for certain materials stems from disjoint feature-space distributions, underscoring the need for broader dataset coverage. This study demonstrates both the promise and limitations of ML-based multipactor prediction and lays the groundwork for accelerated, data-driven modeling in advanced RF and accelerator system design.

physics.acc-ph

Privacy-Preserving Collaborative Split Learning Framework for Smart Grid Load Forecasting

Accurate load forecasting is crucial for energy management, infrastructure planning, and demand-supply balancing. Smart meter data availability has led to the demand for sensor-based load forecasting. Conventional ML allows training a single global model using data from multiple smart meters requiring data transfer to a central server, raising concerns for network requirements, privacy, and security. We propose a split learning-based framework for load forecasting to alleviate this issue. We split a deep neural network model into two parts, one for each Grid Station (GS) responsible for an entire neighbourhood's smart meters and the other for the Service Provider (SP). Instead of sharing their data, client smart meters use their respective GSs' model split for forward pass and only share their activations with the GS. Under this framework, each GS is responsible for training a personalized model split for their respective neighbourhoods, whereas the SP can train a single global or personalized model for each GS. Experiments show that the proposed models match or exceed a centrally trained model's performance and generalize well. Privacy is analyzed by assessing information leakage between data and shared activations of the GS model split. Additionally, differential privacy enhances local data privacy while examining its impact on performance. A transformer model is used as our base learner.

cs.LG

HIV/AIDS Suppression in North America: Intervention Plans and Cost-Effectiveness of UNAIDS 90-90-90 and 95-95-95 Targets

This study utilizes mathematical models to assess progress toward achieving the UNAIDS 90-90-90 and 95-95-95 targets aimed at managing and eradicating HIV/AIDS. It contrasts stochastic and deterministic models, focusing on their utility in optimizing public health strategies. Stochastic models account for real-world unpredictability, offering more realistic insights compared to deterministic approaches. The 95-95-95 targets aim for 95\% of people living with HIV to know their status, 95\% of those diagnosed to receive antiretroviral therapy (ART), and 95\% of those on ART to achieve viral suppression. These benchmarks are critical for reducing transmission and improving health outcomes. This analysis establishes the basic reproduction number ($R_0$) to guide interventions and examines the stability of disease-free and endemic equilibria, providing a foundation for applying optimal control strategies to minimize HIV prevalence effectively and cost-efficiently. Moreover, the data for this study was sourced from the official UNAIDS website, focusing on North America. An innovative feature of this study is the application of the Stochastic method, which enhances model accuracy and operational efficiency in simulating HIV transmission under various interventions. This research offers actionable insights for policymakers and contributes to global efforts to achieve the 95-95-95 targets by 2030, advancing the fight against HIV/AIDS.

q-bio.OT

CHEX-MATE: CLUster Multi-Probes in Three Dimensions (CLUMP-3D), I. Gas Analysis Method using X-ray and Sunyaev-Zel'dovich Effect Data

Galaxy clusters are the products of structure formation through myriad physical processes that affect their growth and evolution throughout cosmic history. As a result, the matter distribution within galaxy clusters, or their shape, is influenced by cosmology and astrophysical processes, in particular the accretion of new material due to gravity. We introduce an analysis method to investigate the 3D triaxial shapes of galaxy clusters from the Cluster HEritage project with XMM-Newton -- Mass Assembly and Thermodynamics at the Endpoint of structure formation (CHEX-MATE). In this work, the first paper of a CHEX-MATE triaxial analysis series, we focus on utilizing X-ray data from XMM and Sunyaev-Zel'dovich (SZ) effect maps from Planck and ACT to obtain a three dimensional triaxial description of the intracluster medium (ICM) gas. We present the forward modeling formalism of our technique, which projects a triaxial ellipsoidal model for the gas density and pressure to compare directly with the observed two dimensional distributions in X-rays and the SZ effect. A Markov chain Monte Carlo is used to estimate the posterior distributions of the model parameters. Using mock X-ray and SZ observations of a smooth model, we demonstrate that the method can reliably recover the true parameter values. In addition, we apply the analysis to reconstruct the gas shape from the observed data of one CHEX-MATE galaxy cluster, Abell 1689, to illustrate the technique. The inferred parameters are in agreement with previous analyses for that cluster, and our results indicate that the geometrical properties, including the axial ratios of the ICM distribution, are constrained to within a few percent. With much better precision than previous studies, we thus further establish that Abell 1689 is significantly elongated along the line of sight, resulting in its exceptional gravitational lensing properties.

astro-ph.CO

A Novel DDPM-based Ensemble Approach for Energy Theft Detection in Smart Grids

Energy theft, characterized by manipulating energy consumption readings to reduce payments, poses a dual threat-causing financial losses for grid operators and undermining the performance of smart grids. Effective Energy Theft Detection (ETD) methods become crucial in mitigating these risks by identifying such fraudulent activities in their early stages. However, the majority of current ETD methods rely on supervised learning, which is hindered by the difficulty of labelling data and the risk of overfitting known attacks. To address these challenges, several unsupervised ETD methods have been proposed, focusing on learning the normal patterns from honest users, specifically the reconstruction of input. However, our investigation reveals a limitation in current unsupervised ETD methods, as they can only detect anomalous behaviours in users exhibiting regular patterns. Users with high-variance behaviours pose a challenge to these methods. In response, this paper introduces a Denoising Diffusion Probabilistic Model (DDPM)-based ETD approach. This innovative approach demonstrates impressive ETD performance on high-variance smart grid data by incorporating additional attributes correlated with energy consumption. The proposed methods improve the average ETD performance on high-variance smart grid data from below 0.5 to over 0.9 w.r.t. AUC. On the other hand, our experimental findings indicate that while the state-of-the-art ETD methods based on reconstruction error can identify ETD attacks for the majority of users, they prove ineffective in detecting attacks for certain users. To address this, we propose a novel ensemble approach that considers both reconstruction error and forecasting error, enhancing the robustness of the ETD methodology. The proposed ensemble method improves the average ETD performance on the stealthiest attacks from nearly 0 to 0.5 w.r.t. 5%-TPR.

cs.LG

Heating of the intracluster medium by buoyant bubbles and sound waves

Active galactic nuclei (AGN) powered by the central Super-Massive Black Holes (SMBHs) play a major role in modifying the thermal properties of the intracluster medium (ICM). In this work, we implement two AGN heating models: (i) by buoyant cavities rising through stratified ICM (effervescent model) and, (ii) by viscous and conductive dissipation of sound waves (acoustic model). Our aim is to determine whether these heating models are consistent with ICM observables and if one is preferred over the other. We assume an initial entropy profile of ICM that is expected from the purely gravitational infall of the gas in the potential of the dark matter halo. We then incorporate heating, radiative cooling, and thermal conduction to study the evolution of ICM over the age of the clusters. Our results are: (i) Both the heating processes can produce comparable thermal profiles of the ICM with some tuning of relevant parameters. (ii) Thermal conduction is crucially important, even at the level of 10\% of the Spitzer values, in transferring the injected energy beyond the central regions, and without which the temperature/entropy profiles are unrealistically high. (iii) The required injected AGN power scales with cluster mass as $M_{\rm vir}^{1.5}$ for both models. (iv) The required AGN luminosity is comparable with the observed radio jet power, reinforcing the idea that AGNs are the dominant heating source in clusters. (v) Finally, we estimate that the fraction of the total AGN luminosity available as the AGN mechanical luminosity at $0.02r_{500}$ is less than 0.05\%.

astro-ph.CO

Exploring diffuse radio emission in galaxy clusters and groups with the uGMRT and the SKA

Diffuse radio emission has been detected in a considerable number of galaxy clusters and groups, revealing the presence of pervasive cosmic magnetic fields, and of relativistic particles in the large-scale structure (LSS) of the Universe. Since cluster radio emission is faint and steep spectrum, its observations are largely limited by the instrument sensitivity and frequency of observation, leading to a dearth of information, more so for lower-mass systems. The unprecedented sensitivity of recently commissioned low-frequency radio telescope arrays, aided by the development of advanced calibration and imaging techniques, have helped in achieving unparalleled image quality. At the same time, the development of sophisticated numerical simulations and the availability of supercomputing facilities have paved the way for high-resolution numerical modeling of radio emission, and the structure of the cosmic magnetic fields in LSS, leading to predictions matching the capabilities of observational facilities. In view of these rapidly-evolving scenerio in modeling and observations, in this review, we summarise the role of the new telescope arrays and the development of advanced imaging techniques and discuss the detections of various kinds of cluster radio sources. In particular, we discuss observations of the cosmic web in the form of supercluster filaments, studies of emission in poor clusters and groups of galaxies, and of ultra-steep spectrum sources. We also review the current theoretical understanding of various diffuse cluster radio sources and the associated magnetic field and polarization. As the statistics of detections improve along with our theoretical understanding, we update the source classification schemes based on their intrinsic properties. We conclude by summarising the role of the upgraded GMRT and our expectations from the upcoming Square Kilometre Array (SKA) observatories.

astro-ph.CO

Hybrid Nano Communications

In this paper, we propose a hybrid nano communication (HNC) system that integrates three possible modes of nano communications: terahertz communication (TC), molecular communication (MC), and neural communication (NC). The paper provides some insights into how the required four key building blocks, namely, terahertz to molecular (T2M) relay interface, molecular to terahertz (M2T) interface, molecular to neural (M2N) relay, and neural to molecular (N2M) interface can be designed to implement the HNC system. In addition, the capacity analysis for the hybrid channel is provided. Sub-channels' capacities are also calculated. Finally, numerical results are presented to comprehend the data transmission capacity of the proposed HNC system.

cs.IT

Confronting phantom inflation with Planck data

The latest Planck results are in excellent agreement with the theoretical expectations predicted from standard normal inflation based on slow-roll approximation which assumes equation-of-state $ω\geq-1$. In this work, we study the phantom inflation ($ω<-1$) as an alternative cosmological model within the slow-climb approximation using two hybrid inflationary fields. We perform Chain Monte Carlo analysis to determine the posterior distribution and best fit values for the cosmological parameters using Planck data and show that current CMB data does not discriminate between normal and phantom inflation. Interestingly, unlike in normal inflation, $ω$ in phantom induced inflation evolves very slowly away from $-1$ during the inflation. Furthermore, in contrast to the standard normal inflation for which only upper bound on tensor-to-scalar ratio $r$ are possible, we obtain both upper and lower bounds for the two hybrid fields in the phantom scenario. Finally, we discuss prospects of future high precision polarization measurements and show that it may be possible to establish the dominance of one model over the other.

astro-ph.CO

Correlations of the feedback energy and BCG radio luminosity in galaxy clusters

We study the excess entropy and the corresponding non-gravitational feedback energy ($E_{feedback}$) in the intra-cluster medium (ICM) by considering a sample of 38 galaxy clusters using Chandra X-ray and NRAO VLA Sky Survey (NVSS)/Giant Metrewave Radio Telescope (GMRT) radio observations. We find moderate correlation of the feedback energy and brightest cluster galaxy (BCG) radio luminosity ($L_R$) with the various cluster thermal properties. We show conclusively that the active galactic nucleus (AGN) is more effective in transferring feedback energy to the ICM in less massive clusters. We find that within $0.3r_{500}$, the feedback energy correlates with cluster temperature as $E_{feedback}\propto T_{obs}^{0.98\pm0.37}$. Moreover, for radio detected BCG sample we find that BCG radio luminosity at 1.4 GHz scales with gas mass as $L_R\propto m_{g,obs}^{ 1.76\pm0.71}$ and with X-ray luminosity as $L_R\propto L_{X,obs}^{0.94\pm0.35}$. Finally, we discuss the implications of our results with regard to feedback in clusters.

astro-ph.CO

AGN feedback with the Square Kilometer Array (SKA) and implications for cluster physics and cosmology

AGN feedback is regarded as an important non-gravitational process in galaxy clusters, providing useful constraints on large-scale structure formation. It modifies the structure and energetics of the intra-cluster medium (ICM) and hence its understanding is crucially needed in order to use clusters as high precision cosmological probes. In this context, particularly keeping in mind the upcoming high quality radio data expected from radio surveys like SKA with its higher sensitivity, high spatial and spectral resolutions, we review our current understanding of AGN feedback, its cosmological implications and the impact that SKA can have in revolutionizing our understanding of AGN feedback in large-scale structures. Recent developments regarding the AGN outbursts and its possible contribution to excess entropy in the hot atmospheres of groups and clusters, its correlation with the feedback energy in ICM, quenching of cooling flows and the possible connection between cool core clusters and radio mini-halos, are discussed. We describe current major issues regarding modeling of AGN feedback and its impact on the surrounding medium. With regard to the future of AGN feedback studies, we examine the possible breakthroughs that can be expected from SKA observations. In the context of cluster cosmology, for example, we point out the importance of SKA observations for cluster mass calibration by noting that most of $z>1$ clusters discovered by eROSITA X-ray mission can be expected to be followed up through a 1000 hour SKA-1 mid programme. Moreover, approximately $1000$ radio mini halos and $\sim 2500$ radio halos at $z<0.6$ can be potentially detected by SKA1 and SKA2 and used as tracers of galaxy clusters and determination of cluster selection function.

astro-ph.CO

Excess entropy and energy feedback from within cluster cores up to r$_{200}$

We estimate the "non-gravitational" entropy-injection profiles, $ΔK$, and the resultant energy feedback profiles, $ΔE$, of the intracluster medium for 17 clusters using their Planck SZ and ROSAT X-Ray observations, spanning a large radial range from $0.2r_{500}$ up to $r_{200}$. The feedback profiles are estimated by comparing the observed entropy, at fixed gas mass shells, with theoretical entropy profiles predicted from non-radiative hydrodynamic simulations. We include non-thermal pressure and gas clumping in our analysis. The inclusion of non-thermal pressure and clumping results in changing the estimates for $r_{500}$ and $r_{200}$ by 10\%-20\%. When clumpiness is not considered it leads to an under-estimation of $ΔK\approx300$ keV cm$^2$ at $r_{500}$ and $ΔK\approx1100$ keV cm$^2$ at $r_{200}$. On the other hand, neglecting non-thermal pressure results in an over-estimation of $ΔK\approx 100$ keV cm$^2$ at $r_{500}$ and under-estimation of $ΔK\approx450$ keV cm$^2$ at $r_{200}$. For the estimated feedback energy, we find that ignoring clumping leads to an under-estimation of energy per particle $ΔE\approx1$ keV at $r_{500}$ and $ΔE\approx1.5$ keV at $r_{200}$. Similarly, neglect of the non-thermal pressure results in an over-estimation of $ΔE\approx0.5$ keV at $r_{500}$ and under-estimation of $ΔE\approx0.25$ keV at $r_{200}$. We find entropy floor of $ΔK\approx300$ keV cm$^2$ is ruled out at $\approx3σ$ throughout the entire radial range and $ΔE\approx1$ keV at more than 3$σ$ beyond $r_{500}$, strongly constraining ICM pre-heating scenarios. We also demonstrate robustness of results w.r.t sample selection, X-Ray analysis procedures, entropy modeling etc.

astro-ph.CO

Low-$\ell$ power suppression in punctuated inflation

Motivated by Planck confirmation of an anomalously low value of the CMB temperature fluctuations up to multipole $\ell<40$, we in this paper try to explain such feature by investigating case of punctuated inflation scenario. This form of inflation potential is inspired by Minimal Super-symmetric Standard Model (MSSM) wherein suppression of curvature perturbation power at large scales is produced by introducing period of fast-roll phase of the inflation sandwiched between two stages of slow-roll phase. We apply Markov Chain Monte Carlo analysis to determine posterior distribution and the best fit values of the model parameters using recent WMAP9 and Planck data. We show that WMAP9 and Planck results are consistent with each other and that with Planck data we obtain tighter constraints for punctuated inflation parameters. We find that punctuated inflation leads to better fit in CMB data compared to simple power law model. The improvement in the fit to the WMAP9 data is $Δχ^2\sim 3.6$ and for Planck the improvement is $Δχ^2\sim 5.4$. We find that $AIC$ does not discriminate between punctuated inflation and simple power law model for WMAP9 data. However, for Planck data we find that punctuated inflation is moderately preferred over a simple power law model.

astro-ph.CO

Little evidence for entropy and energy excess beyond $r_{500}$ - An end to ICM preheating?

Non-gravitational feedback affects the nature of the intra-cluster medium (ICM). X-ray cooling of the ICM and in situ energy feedback from AGN's and SNe as well as {\it preheating} of the gas at epochs preceding the formation of clusters are proposed mechanisms for such feedback. While cooling and AGN feedbacks are dominant in cluster cores, the signatures of a preheated ICM are expected to be present even at large radii. To estimate the degree of preheating, with minimum confusion from AGN feedback/cooling, we study the excess entropy and non-gravitational energy profiles upto $r_{200}$ for a sample of 17 galaxy clusters using joint data sets of {\it Planck} SZ pressure and {\it ROSAT/PSPC} gas density profiles. The canonical value of preheating entropy floor of $\gtrsim 300$ keV cm$^2$, needed in order to match cluster scalings, is ruled out at $\approx 3σ$. We also show that the feedback energy of 1 keV/particle is ruled out at 5.2$σ$ beyond $r_{500}$. Our analysis takes both non-thermal pressure and clumping into account which can be important in outer regions. Our results based on the direct probe of the ICM in the outermost regions do not support any significant preheating.

astro-ph.CO