We present a spectroscopic deprojection analysis of a sample of ten relaxed galaxy clusters .
We use an empirical F-test derived from a set of Markov Chain Monte Carlo simulations to determine if the core plasma in each cluster could contain multiple phases .
We derive non-parametric baryon density and temperature profiles , and use these to construct total gravitating mass profiles .
We compare these profiles with the standard halo parameterizations .
We find central density slopes roughly consistent with the predictions of \Lambda CDM : -1 \lesssim d \log ( \rho ) / d \log ( r ) \lesssim - 2 .
We constrain the core size of each cluster and , using the results of cosmological simulations as a calibrator , place an upper limit of \sim 0.1 cm ^ { 2 } g ^ { -1 } = 0.2 b ( GeV/c ^ { 2 } ) ^ { -1 } ( 99 % confidence ) on the dark matter particle self-interaction cross section .