The universality of the empirical laws combined with the evidence for star formation in shells, spiral arms, pillars, and other pressurized structures suggests that the primary ingredient for star formation is cold gas and not a particular geometry. Cold gas means colder than thermal equilibrium commonly gives for atomic gas in the background galactic radiation field. Cold gas for star formation implies shielding from starlight and the presence of molecules for rotational cooling, which can operate down to a few degrees above the microwave background. Once the gas is shielded from starlight and turns molecular, background pressure and turbulent motion will compress it to a high density in small regions. Then gravity becomes important and the thermal Jeans mass drops to be comparable to the region mass. Star formation usually follows.
Shell, ring, or pillar-like triggering and spiral waves might be more important as a net positive contributor to star formation in regions where the molecular fraction is moderately low on average, i.e., at the boundary between highly molecular inner disks of galaxies and highly atomic outer disks. In the inner disks, the gas pretty much stays molecular everywhere because of the high pressure from its weight in the disk, and because of the high opacity. Starlight ionizes and photodissociates molecules at the cloud edges (Heiner et al. 2011) and between the clouds. Cold gas is present in most clouds, so additional pressures from young stars or spiral waves will not make the gas much colder or more molecular. In the far-outer regions, however, it is rather difficult to turn atomic gas into molecular gas because the average pressure and opacity are very low. Then superbubbles might not trigger new star formation, but only make diffuse atomic shells which have little cold gas. Between these two zones, or perhaps in dwarf irregular galaxies where the same intermediate conditions apply, triggering by the pressures of young stars might make more of a difference in the total star formation rate.
An observational test of this prediction would be to measure the radial variation of the ratio of the normalized star formation efficiency in compressed and non-compressed regions. The normalized efficiency is the star formation rate per unit gas mass per unit dynamical rate. An example would be the ratio of the efficiency in the spiral arms to the interarm regions. If this ratio increases with radius, then spiral arm triggering is doing more to enhance star formation in the outer parts of galaxies, where the gas is mostly atomic, than in the inner parts, where the gas is mostly molecular. Alternatively, one could plot this ratio versus the average molecular fraction instead of the radius.
The overriding importance of cold gas for star formation was originally recognized by Kenneth Essex Edgeworth in 1946 – long before the modern star formation era. (For a biography of Edgeworth, see Hollis 1996.) At that time, most stars, like the Earth and the whole universe, were thought to be about 3 Gyr old, star formation was not considered to happen in the present day, except possibly for the most massive stars (which were known to burn their fuel quickly), and the stability of galactic disks was not yet understood. Edgeworth and others were thinking about star formation mostly in the context of the beginning of the universe. He noted from a thermal Jeans analysis that star formation by gravitational instability in a galaxy disk, using an equation like eq. 1, requires a temperature of ~ 2.8K, which he considered "very improbable." He also said that angular momentum from galactic rotation was too large for the solar system to form, and suggested that stars might form instead by successive condensations to overcome the angular momentum problem. This led him to "expect to find that the majority of the stars were members of star clusters" which is "not in agreement with observation." Finally, he suggested that the rotating gas disk of a galaxy, at ~ 1000 K, breaks up into azimuthal filaments, which then break up into stars following the removal of heat. He went on to suggest that the residual material around each star makes planets.
These ideas are all essentially correct by modern standards – even though Edgeworth did not believe or observe them at the time. Edgeworth understood that star formation requires very cold gas, it most likely occurs in massive aggregates, and it should be patterned as beads on a string for the galactic scale. These ideas were too far ahead of their time to have much influence. Star formation as we know it was discovered several years later when Ambartsumian (1949) showed that local OB associations are expanding away from a common center. This limited their age to 10 Myr.