Cas A is a Galactic supernova remnant whose supernova explosion is observed to be of Type IIb from spectroscopy of its light echo. Having its SN type known, observational constraints on the mass-loss history of Cas As progenitor can provide crucial information on the final fate of massive stars. In this paper, we study X-ray characteristics of the shocked ambient gas in Cas A using the 1 Ms observation carried out with the Chandra X-Ray Observatory and try to constrain the mass-loss history of the progenitor star. We identify thermal emission from the shocked ambient gas along the outer boundary of the remnant. Comparison of measured radial variations of spectroscopic parameters of the shocked ambient gas to the self-similar solutions of Chevalier show that Cas A is expanding into a circumstellar wind rather than into a uniform medium. We estimate a wind density nH ~ 0.9 $pm$ 0.3 cm$^{-3}$ at the current outer radius of the remnant (~3 pc), which we interpret as a dense slow wind from a red supergiant (RSG) star. Our results suggest that the progenitor star of Cas A had an initial mass around 16 Msun, and its mass before the explosion was about 5 Msun, with uncertainties of several tens of percent. Furthermore, the results suggest that, among the mass lost from the progenitor star (~11 Msun), a significant amount (more than 6 Msun) could have been via its RSG wind.
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