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The Scale Height of NGC 1058 Measured from its HI Power Spectrum

We have measured the HI power spectrum of the nearly face-on spiral galaxy NGC 1058 from radio-interferometric observations using a visibility based estimator. The power spectrum is well fitted by two different power laws $P(U)=AU^α$, one with $α=- 2.5\pm 0.6$ at small length-scales $(600 {\rm pc} {\rm to} 1.5 {\rm kpc})$ and another with $α=- 1.0\pm 0.2$ at large length-scales $(1.5 {\rm kpc} {\rm to} 10.0 {\rm kpc})$. We interpret this change in the slope of the power spectrum as a transition from 3D turbulence at small length-scales to 2D turbulence in the plane of the galaxy's disk at large length-scales. We use the observed break in the power spectrum to estimate the galaxy's scale-height, which we find to be $ 490 \pm 90 $ pc.