Interstellar thermal pressures can be measured using C I absorption lines that probe the pressure-sensitive populations of the fine-structure levels of its ground state. In a survey of C I absorption toward Galactic hot stars, Jenkins & Tripp (2011) found evidence of small amounts ($sim 0.05%$) of gas at high pressures ($p/k gg 10^4{rm cm^{-3}K}$) mixed with a more general presence of lower pressure material exhibiting a log normal distribution that spanned the range $10^3 lesssim p/k lesssim 10^4{rm cm^{-3}K}$. In this paper, we study Milky Way C I lines in the spectra of extragalactic sources instead of Galactic stars and thus measure the pressures without being influenced by regions where stellar mass loss and H II region expansions could create localized pressure elevations. We find that the distribution of low pressures in the current sample favors slightly higher pressures than the earlier survey, and the fraction of gaseous material at extremely high pressures is about the same as that found earlier. Thus we conclude that the earlier survey was not appreciably influenced by the stellar environments, and the small amounts of high pressure gas indeed exist within the general interstellar medium.
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