Collisional interaction limits between dark matters 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 σxp. With a relative collisional velocity V−dependent power-law form of σxp = σ0(V/10 km s−1)a where a ≤ 0, our inferred upper limit is σ0/mx ∼ 2 × 10−25 cm GeV−1 withmx 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 nongravitational heating source of intracluster medium (ICM) in inner core regions of ‘cooling flow’ galaxy clusters.