Turbulent power distribution in the local interstellar medium
  Context: The interstellar medium (ISM) on all scales is full of structures
that can be used as tracers of processes that feed turbulence. Aims: We used HI
survey data to derive global properties of the angular power distribution of
the local ISM. Methods: HI4PI observations on an nside = 1024 HEALPix grid and
Gaussian components representing three phases, the cold, warm, and unstable
lukewarm neutral medium (CNM, WNM, and LNM), were used for velocities
$|v_{\mathrm{LSR}}| \leq 25$ \kms. For high latitudes $|b| > 20\deg$ we
generated apodized maps. After beam deconvolution we fitted angular power
spectra. Results: Power spectra for observed column densities are exceptionally
well defined and straight in log-log presentation with 3D power law indices
$\gamma \geq -3$ for the local gas. For intermediate velocity clouds (IVCs) we
derive $\gamma = -2.6$ and for high velocity clouds (HVCs) $\gamma = -2.0$.
Single-phase power distributions for the CNM, LNM, and WNM are highly
correlated and shallow with $ \gamma \sim -2.5$ for multipoles $l \leq 100$.
Excess power from cold filamentary structures is observed at larger multipoles.
The steepest single-channel power spectra for the CNM are found at velocities
with large CNM and low WNM phase fractions. Conclusions: The phase space
distribution in the local ISM is configured by phase transitions and needs to
be described with three distinct different phases, being highly correlated but
having distributions with different properties. Phase transitions cause locally
hierarchical structures in phase space. The CNM is structured on small scales
and is restricted in position-velocity space. The LNM as an interface to the
WNM envelops the CNM. It extends to larger scales than the CNM and covers a
wider range of velocities. Correlations between the phases are self-similar in
velocity.
