ner_tags: O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength O B-Wavelength I-Wavelength I-Wavelength O O O O B-CelestialObject I-CelestialObject O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation
tokens: 4 Power distributions for phase fractions in different H I phases at v LSR = 0 km s −1 . Top left : WNM; top right : LNM; bottom left : CNM. Black lines show all-sky data, red lines are for | b | > 20°. Spectral indices are derived at 10 l 100 as indicated by the vertical lines. Bottom right : uncertainties from the Gaussian decomposition (black) and ringing caused by apodization (red). Fig. 5 Velocity distribution of average H I phase fractions for CNM, LNM, and WNM using unpublished data from Kalberla Haud (2018) . Next we consider the power spectra derived from the Gaussian components of different H I phases. Figures 8 and 9 show still local minima for the CNM spectral indices, however the spectral indices for the other phases are now mostly anti-correlated; the WNM has a particularly smooth distribution. Spectral indices derived from power spectra of the total observed H I also show smooth changes. For high latitudes ( Fig. 9 , red) we find a steepening in anti-correlation to the WNM, but with local minima that are affected by the CNM and LNM. In the all-sky case ( Fig. 8 , black) we observe a smooth trend, but influences from the CNM and LNM are weak. Velocity dependences for the spectral indices have been observed before ( Kalberla Kerp 2016 ; Kalberla et al. 2017 ). Recently, Choudhuri Roy (2019) have presented data that show a steepening of the spectral indices at velocities that are considered to be representative for the CNM. Spectral indices for 13 CO (2–1) and 12 CO (3–2) channel maps in the Perseus cloud were observed by Sun et al. (2006) with a steepening of the indices that can be described asan average structure of the index spectrum similar to the line profile. Numerical studies of the condensation of WNM into CNM structures caused by turbulence and thermal instabilities were conducted by Saury et al. (2014) . They found that turbulence plays a key role in the structure of the cold medium; it can induce the formation of CNM when the WNM is pressurized and put it in a thermally unstable state. They found evidence for subsonic turbulence with a shallow power index γ ~ −2.4. Recent high resolution simulations by Wareing et al. (2019) have shown that the thermal instability dynamically can form sheets and filaments on typical scales of 0.1–0.3 pc, explaining that as the structure grows in the simulation, the density power spectrum rapidly rises and steepens. Wareing et al. (2019 ; Fig. 10) derive γ ~ −3, but the steepening is most prominent on scales below 1 pc. Fig. 6 All-sky velocity dependences of spectral indices for H I phase fractions. The thin lines represent the scatter for one-sigma uncertainties. Fig. 7 High latitude velocity dependences of spectral indices for H I phase fractions. The thin lines represent the scatter for one-sigma uncertainties. The preferred width of the filaments in the range 0.1–0.3 pc is consistent with unresolved cold small-scale structures observed by Clark et al. (2014) and Kalberla et al.