We have analyzed X-ray spectra from six galaxy clusters which contain cooling flows: A85, A478, A1795, A2142, A2147, & A2199. The X-ray spectra were taken with the HEAO1-A2 Medium and High Energy Detectors and the Einstein Solid State Spectrometer. For each cluster, we simultaneously fit the spectra from these three detectors with models incorporating one or more emission components comprised of either thermal or cooling flow models. Five of the clusters (all but A2142) are better fit by a multi-component model (a cooling flow plus one or two thermal components or a two thermal component model) than by isothermal models. In four of the clusters (A85, A1795, A2147, & A2199), we find evidence for cool gas outside of the canonical cooling flow region. These latter four clusters can be characterized by three temperature components: a temperature inversion in the central region, a hotter region with an emission-weighted temperature which is higher than that of an isothermal model fit to the entire cluster, and a cooler region with an emission-weighted temperature of ~1 keV. The cool component outside the cooling flow region has a large minimum emission measure which we attribute, in part, to diffuse cool gas in the outer cluster atmosphere. If at least some of the cool exterior gas is virialized, this would imply a radially decreasing temperature profile. Together with the density profiles we have found, this leads to a baryon fraction in gas which increases with radius and is larger than that for an isothermal cluster atmosphere. Consequently, if clusters of galaxies trace the mass distribution in the Universe, the gas mass fraction we have calculated for an isothermal gas (which is ~15%) together with the nominal galaxy contribution (~5%) gives a baryon fraction of ~20%. Using the upper limit to the baryon density derived from Big
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