  We analyze the shapes of the HI velocity profiles of The HI Nearby Galaxy
Survey (THINGS) to study the phase structure of the neutral interstellar medium
(ISM) and its relation to global galaxy properties. We use a method analogous
to the stacking method sometimes used in high redshift HI observations to
construct high signal-to-noise (S/N) profiles. We call these high S/N profiles
super profiles. We analyze and discuss possible systematics that may change the
observed shapes of the super profiles. After quantifying these effects and
selecting a sub-sample of unaffected galaxies, we find that the super profiles
are best described by a narrow and a broad Gaussian component, which are
evidence of the presence of the Cold Neutral Medium (CNM) and the Warm Neutral
Medium (WNM). The velocity dispersion of the narrow component range from ~3.4
to ~8.6 km/s with an average of 6.5+/-1.5 km/s, whereas that of the broad
component range from ~10.1 to ~24.3 km/s with an average of 16.8+/-4.3 km/s. We
find that the super profile parameters correlate with star formation indicators
such as metallicity, FUV-NUV colors and H_alpha luminosities. The flux ratio
between the narrow and broad components tends to be highest for high
metallicity, high star formation rate (SFR) galaxies. We show that the narrow
component identified in the super profiles is associated with the presence of
star formation, and possibly with molecular hydrogen.
