Collisional interaction limits between dark matter particles and baryons in ‘cooling flow’ clusters

Presuming weak collisional interactions to exchange the kinetic energy between dark matter and baryonic matter in a galaxy cluster, we re-examine the effectiveness of this process in several 'cooling flow' galaxy clusters using available X-ray observations and infer an upper limit on the heavy dark matter particle (DMP)-proton cross-section σ xp . With a relative collisional velocity V-dependent power-law form of σ xp = σ 0 (V/10 3 kms -1 ) where a ≤ 0, our inferred upper limit is σ 0 /m x ≤ 2 x 10 -25 cm 2 GeV -1 with m x being the DMP mass. Based on a simple stability analysis of the thermal energy balance equation, we argue that the mechanism of DMP-baryon collisional interactions is unlikely to be a stable non-gravitational heating source of intracluster medium (ICM) in inner core regions of 'cooling flow' galaxy clusters.