Collisional interaction limits between dark matters and baryons in `cooling flow' clusters

Abstract

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 ${\sigma }_{\mathrm{xp}}$. With a relative collisional velocity $V-$dependent power-law form of ${\sigma }_{\mathrm{xp}}={\sigma }_0(V/10^3\mathrm{km}{\mathrm{s}}^{-1}{)}^a$ where $a\le 0$, our inferred upper limit is $σ_0/m_{\rm x}\lsim 2\times10^{-25} {\rm cm}^2 {\rm GeV}^{-1}$ with $m_{\mathrm{x}}$ 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 nongravitational heating source of intracluster medium (ICM) in inner core regions of `cooling flow' galaxy clusters.

8 pages, 2 figures, MNRAS accepted

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