From a survey of edge-on disks, we find that disk galaxies show a sharp, mass- dependent transition in the structure of their dusty ISM. In more massive, rapidly rotating disks with V-c > 120 km s(-1), we see the well-defined dust lanes traditionally associated with edge-on galaxies. However, in more slowly rotating, lower mass galaxies with V-c < 120 km s(-1), we find no dust lanes. Instead, the distribution of dust in these galaxies has a much larger scale height and thus appears more diffuse. Evidence suggests that the change in scale height is due primarily to changes in the turbulent velocities supporting the gas layer rather than to sharp changes in the gas surface density. A detailed analysis of our sample reveals that the decrease in the dust scale height is associated with the onset of disk instabilities, evaluated for a mixed star+gas disk. Specifically, we find that all of the high-mass galaxies with dust lanes are gravitationally unstable and thus are prone to fragmentation and gravitational collapse along spiral arms. Empirically, our data imply that turbulence has lower characteristic velocities in the presence of disk instabilities, leading to smaller gas scale heights and the appearance of narrow dust lanes. The drop in velocity dispersion may be due either to a switch in the driving mechanism for turbulence from supernovae to gravitational instabilities or to a change in the response of the ISM to supernovae after the ISM has collapsed to a dense layer. We hypothesize that the drop in gas scale height may lead to significant increases in the star formation rate when disk instabilities are present. First, the collapse of the gas layer increases the typical gas density, reducing the star formation timescale. Second, the star formation efficiency increases because of lower turbulent velocities. These two effects can combine to produce a sharp increase in the star formation rate with little change in the gas surface density and may therefore provide an explanation for the Kennicutt surface density threshold for star formation. Our data also suggest that star formation will be systematically less efficient in low-mass disks with V-c < 120 km s(-1), since these galaxies are stable and lie entirely below the Kennicutt surface density threshold. In these stable systems the effective nucleosynthetic yield is reduced because the star formation timescale becomes longer than the gas accretion timescale, suppressing the metallicity. This effect can possibly produce the observed fall-off in metallicity at rotation speeds V-c < 120 km s(-1). Thus, infall provides an equally plausible explanation of the mass- metallicity relation in disks as global outflows driven by supernova winds. The transitions in disk stability, dust structure, and/or star formation efficiency may also be responsible for the observed changes in the slope of the Tully-Fisher relation, in the sharp increase in the thickness of low-mass galaxy disks, and in the onset of bulges in galaxies with V-c greater than or similar to 120 km s(-1). The latter observation lends support to theories in which bulges in late-type galaxies grow through secular evolution in response to disk instabilities. We include in this paper relationships between the surface density and the vertical stellar velocity dispersion as a function of galaxy rotation speed, which may be useful constraints on galaxy formation models.
