Probing interstellar turbulence in spiral galaxies using HI power
  spectrum analysis
  We estimate the \HI intensity fluctuation power spectrum for a sample of 18
spiral galaxies chosen from THINGS. Our analysis spans a large range of
length-scales from $\sim 300 {\rm pc}$ to $\sim 16 {\rm kpc}$ across the entire
galaxy sample. We find that the power spectrum of each galaxy can be well
fitted by a power law $P_{\rm HI}(U) = A U^{\alpha}$, with an index $\alpha$
that varies from galaxy to galaxy. For some of the galaxies the scale-invariant
power-law power spectrum extends to length-scales that are comparable to the
size of the galaxy's disk. The distribution of $\alpha$ is strongly peaked with
50% of the values in the range $\alpha=-1.9$ to 1.5, and a mean and standard
deviation of -1.3 and 0.5 respectively. We find no significant correlation
between $\alpha$ and the star formation rate, dynamical mass, \HI mass or
velocity dispersion of the galaxies.
  Several earlier studies that have measured the power spectrum within our
Galaxy on length-scales that are considerably smaller than $500 {\rm pc}$ have
found a power-law power spectrum with $\alpha$ in the range $\approx -2.8$ to
-2.5. We propose a picture where we interpret the values in the range $\approx
-2.8$ to -2.5 as arising from three dimensional (3D) turbulence in the
Interstellar Medium (ISM) on length-scales smaller than the galaxy's
scale-height, and we interpret the values in the range $\approx -1.9$ to -1.5
measured in this paper as arising from two-dimensional ISM turbulence in the
plane of the galaxy's disk. It however still remains a difficulty to explain
the small galaxy to galaxy variations in the values of $\alpha$ measured here.
