Some observations such as those presented in Walker et al. show that the observed entropy profiles of the intra-cluster medium (ICM) deviate from the power-law prediction of adiabatic simulations. This implies that non-gravitational processes, which are absent in the simulations, may be important in the evolution of the ICM, and by quantifying the deviation, we may be able to estimate the feedback energy in the ICM and use it as a probe of the non-gravitational processes. To address this issue we calculate the ICM entropy profiles in a sample of 47 galaxy clusters and groups, which have been observed out to at least $sim r_{500}$ with Chandra, XMM-Newton and/or Suzaku, by constructing a physical model to incorporate the effects of both gravity and non-gravitational processes to fit the observed gas temperature and surface brightness profiles via Bayesian statistics. After carefully evaluating the effects of systematic errors, we find that the gas entropy profiles derived with best-fit results of our model are consistent with the simulation-predicted power-law profile near the virial radius, while the flattened profiles reported previously can be explained by introducing the gas clumping effect, the existence of which is confirmed in 19 luminous targets in our sample. We calculate the total feedback energy per particle and find that it decreases from $sim 10$ keV at the center to about zero at $sim 0.35$$r_{200}$ and is consistent with zero outside $sim 0.35$$r_{200}$, implying the upper limit of the feedback efficiency $sim 0.02$ for the super-massive black holes hosted in the brightest cluster galaxies.
Download