MASS PROFILES OF GALAXY CLUSTER CORES: IMPLICATIONS FOR STRUCTURE FORMATION AND SELF-INTERACTING DARK MATTER

ABSTRACTWe present a spectroscopic deprojection analysis of a sample of ten relaxed galaxy clusters. We usean empirical F-test derived from a set of Markov Chain Monte Carlo simulations to determine if thecore plasma in each cluster could contain multiple phases. We derive non-parametric baryon densityand temperature profiles, and use these to construct total gravitating mass profiles. We compare theseprofiles with the standard halo parameterizations. We find central density slopes roughly consistentwith the predictions of ΛCDM: −1 . dlog(ρ)/dlog(r) . −2. We constrain the core size of each clusterand, using the results of cosmological simulations as a calibrator, place an upper limit of ∼ 0.1 cm 2 g −1 = 0.2 b(GeV/c 2 ) (99% confidence) on the dark matter particle self-interaction cross section.Subject headings: X-rays : galaxies: clusters — cosmology : dark matter 1. INTRODUCTION The ΛCDM theory of cosmological structure forma-tion – a cold dark matter (CDM) universe evolving un-der gravitation with a cosmological constant (Λ) – hasbeen very successful in characterizing large scale struc-ture on scales greater than ∼ 0.1 Mpc (Mohr et al. 2000;Lahav et al. 2001; Spergel et al. 2003; Percival et al.2003). However, ΛCDM makes three predictions whichappear to conflict with observations. The first of thesediscrepancies is the “satellite problem” – the MilkyWay contains at least an order of magnitude fewersatellites than simulations predict for a dark matterhalo of its size (Kauffman, White, & Guideroni 1993;Moore et al. 1999a; Klypin et al. 1999). The second isthe “disk problem,” – disk galaxies produced in simu-lations contain too little mass and angular momentum(Navarro & Steinmetz 2000). The third is the “coreproblem” – galaxy-sized dark matter halos produced insimulations tend to have significantly steeper logarithmicdensity gradients in their cores than do observed struc-tures.The density profile of a dark matter halo formedthrough the hierarchical assembly of smaller structuresis usually parameterized as a pair of power laws with atransition scale radius r