Constraints on the dark matter-baryon interaction cross section from galaxy cluster thermodynamics

Dark matter (DM) models with a non-zero DM-baryon interaction cross section imply energy transfer between DM and baryons. We present a new method of constraining the DM-baryon interaction cross section and DM particle mass for velocity-independent interactions using the thermodynamics of galaxy clusters. If the baryonic gas in these clusters is in thermodynamic equilibrium and DM cools baryons, this cooling rate is limited by the net heating rate of other mechanisms in the cluster. We use the REFLEX clusters from the Meta-Catalogue of X-ray detected Clusters of Galaxies (MCXC) with mass estimates from the Atacama Cosmology Telescope (ACT) catalog of Sunyaev-Zel'dovich (SZ) selected galaxy clusters. This yields 95% upper bounds on the DM-proton interaction cross section for velocity-independent interactions of $\sigma_0\leq9.3\times10^{-28} \mathrm{~cm^2}$ for DM masses, $m_\chi = 10^{-4} - 10^{-1}$ GeV. These constraints are within an order of magnitude of the best constraints derived in this mass range, and serve as a complementary, independent constraint. We also apply this model to the fractional interacting DM scenario, where only 10% and 1% of the DM is interacting. Unlike other methods, this constraint scales linearly with this fraction. This yields 95% upper bounds of $\sigma_0\leq1.1\times10^{-26} \mathrm{~cm^2}$ and $\sigma_0\leq8.2\times10^{-26} \mathrm{~cm^2}$, which are the strongest existing constraints for this scenario. This paper serves as a proof of concept. Upcoming SZ measurements will provide temperature profiles for galaxy clusters. Combining these measurements with more complex thermodynamic models could lead to more robust constraints.