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We discuss physical conditions in Galactic neutral hydrogen based on deep,high velocity resolution interferometric HI 21 cm absorption spectroscopytowards 33 compact extra-galactic radio sources. The HI 21 cm optical depthspectra have root-mean-square noise values \lesssim 10^{-3} per 1 km/s velocitychannel, i.e., sufficiently sensitive to detect HI 21 cm absorption by the warmneutral medium (WNM). Comparing these spectra with HI 21 cm emission spectrafrom the Leiden-Argentine-Bonn (LAB) survey, we show that some of theabsorption detected on most sightlines must arise in gas with temperatureshigher than that in the stable cold neutral medium (CNM). A multi-Gaussiandecomposition of 30 of the HI 21 cm absorption spectra yielded very fewcomponents with line widths in the temperature range of stable WNM, with nosuch WNM components detected for sixteen of the thirty sightlines. We find thatsome of the detected HI 21 cm absorption along thirteen of these sightlinesmust arise in gas with spin temperatures larger than the CNM range. For thesesightlines, we use very conservative estimates of the CNM spin temperature andthe non-thermal broadening to derive strict upper limits to the gas columndensities in the CNM and WNM phases. Comparing these upper limits to the totalHI column density, we find that typically at least 28% of the gas must havetemperatures in the thermally unstable range (200-5000 K). Our observationshence robustly indicate that a significant fraction of the gas in the Galacticinterstellar medium has temperatures outside the ranges expected for thermallystable gas in two-phase models.

The temperature of the diffuse HI in the Milky Way II: Gaussian decomposition of the HI 21 cm absorption spectra