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We present probability distribution functions (PDFs) of the surface densitiesof ionized and neutral gas in the nearby spiral galaxies M31 and M51, as wellas of dust emission and extinction Av in M31. The PDFs are close to lognormaland those for HI and Av in M31 are nearly identical. However, the PDFs for H2are wider than the HI PDFs and the M51 PDFs have larger dispersions than thosefor M31. We use a simple model to determine how the PDFs are changed byvariations in the line-of-sight (LOS) pathlength L through the gas, telescoperesolution and the volume filling factor of the gas, f_v. In each of thesecases the dispersion sigma of the lognormal PDF depends on the variable with anegative power law. We also derive PDFs of mean LOS volume densities of gascomponents in M31 and M51. Combining these with the volume density PDFs fordifferent components of the ISM in the Milky Way (MW), we find that sigmadecreases with increasing length L with an exponent of -0.76 +/- 0.06, which issteeper than expected. We show that the difference is due to variations in f_v.As f_v is similar in M31, M51 and the MW, the density structure in the gas inthese galaxies must be similar. Finally, we demonstrate that an increase in f_vwith increasing distance to the Galactic plane explains the decrease in sigmawith latitude of the PDFs of emission measure and FUV emission observed for theMW.

Probability distribution functions of gas in M31 and M51