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.