2017MNRAS.472..713I

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 Sunyaev-Zel'dovich and ROSAT X-ray observations, spanning a large radial range from 0.2r₅₀₀ up to r₂₀₀. 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 r₅₀₀ and r₂₀₀ by 10-20 per cent. When clumpiness is not considered it leads to an underestimation of ΔK ≃ 300 keV cm² at r₅₀₀ and ΔK ≃ 1100 keV cm² at r₂₀₀. On the other hand, neglecting non-thermal pressure results in an overestimation of ΔK ≃ 100 keV cm² at r₅₀₀ and underestimation of ΔK ≃ 450 keV cm² at r₂₀₀. For the estimated feedback energy, we find that ignoring clumping leads to an underestimation of energy per particle ΔE ≃ 1 keV at r₅₀₀ and ΔE ≃ 1.5 keV at r₂₀₀. Similarly, neglect of the non-thermal pressure results in an overestimation of ΔE ≃ 0.5 keV at r₅₀₀ and underestimation of ΔE ≃ 0.25 keV at r₂₀₀. We find entropy floor of ΔK ≃ 300 keV cm² is ruled out at ≃3σ throughout the entire radial range and ΔE ≃ 1 keV at more than 3σ beyond r₅₀₀, strongly constraining intracluster medium pre-heating scenarios. We also demonstrate robustness of results w.r.t. sample selection, X-ray analysis procedures, entropy modelling, etc.