Measuring Turbulence in the Interstellar Medium by Comparing N(H I; Lyα) and N(H I; 21 cm)

We present a study of the small-scale structure of the interstellar medium (ISM) in the Milky Way. We used HST STIS data to measure N(H I) in a pencil beam toward 59 active galactic nuclei and compared the results with the values seen at 9'-36' resolution in the same directions using radio telescopes (Green Bank Telescope, Green Bank 140-ft, and LAB survey). The distribution of ratios N(Ly Delta *a)/N(H I) has an average of 1 and a dispersion of about 10%. Our analysis also revealed that spectra from the Leiden-Argentina-Bonn (LAB) all-sky H I survey need to be corrected, taking out a broad Gaussian component (peak brightness temperature 0.048 K, FWHM 167 km s--1, and central velocity --22 km s--1). The column density ratios have a distribution showing similarities to simple descriptions of hierarchical structure in the neutral ISM as well as to a more sophisticated three-dimensional magnetohydrodynamic simulation. From the comparison with such models, we find that the sonic Mach number of the local ISM should lie between 0.6 and 0.9. However, none of the models yet matches the observed distribution in all details, but with many more sightlines (as will be provided by the Cosmic Origins Spectrograph) our approach can be used to constrain the properties of interstellar turbulence.