Scale lengths in disk surface brightness as probes of dust extinction in three spiral galaxies: M51, NGC 3631, and NGC 4321

We have measured the radial brightness distributions in the disks of three nearby face-on spiral galaxies, M51, NGC 3631, and NGC 4321 (M100), in the photometric bands B through I, with the addition of the K band for M51 only. The measurements were made by averaging azimuthally, in three modes, the two-dimensional surface brightness over the disks in photometric images of the objects in each band: (1) over each disk as a whole, (2) over the spiral arms alone, and (3) over the interarm zones alone. From these profiles, scale lengths were derived for comparison with schematic exponential disk models that incorporate interstellar dust. These models include both absorption and scattering in their treatment of radiative transfer. The model fits show that the arms exhibit greater optical depth in dust than the interarm zones. The average fraction of emitted stellar light in V that is extinguished by dust within 3 scale lengths of the center of each galaxy does not rise above 20% in any of them. We show that this conclusion is also valid for models with similar overall quantities of dust but in which this is concentrated in lanes. These can also account for the observed scale lengths and their variations.