As we have seen over the last four lectures, star formation can be initiated by a variety of processes, including spontaneous gravitational instabilities in the combined stellar and gaseous medium, occasional cloud collisions, especially in density-wave shocks, and triggered gravitational instabilities in compressed regions ranging from spiral-arm dust lanes, to Lindblad resonance rings, tidal arcs around interacting galaxies, gaseous shells and rings in galactic disks, and molecular clouds at the edges of HII regions. The role of compression is either to bring some amount of otherwise stable gas together so it can collapse and form stars on its own, or to compress an existing cloud from a stable configuration to an unstable configuration, at which point it, too, forms stars on its own. Always accompanying this gas redistribution or compression is an enhancement in internal energy dissipation. Otherwise, the region would have collapsed into stars on its own. Compression through a shock does this reduction, or compression-enhancement of magnetic diffusion, or even compression to reduce the turbulent dissipation time. Without compression, the region may still collapse on its own, but with a longer time scale.
Because the final step in all of these triggering scenarios is the formation of stars deep in a cloud core, away from any pressure source that may be acting on the cloud surface, the detailed processes of star formation, such as stellar collapse, accretion, disk formation, and so on, should not depend much on triggering. If the source of compression also heats the gas, then perhaps the thermal Jeans mass increases in the compressed region, and this might affect the stellar initial mass function. However, higher driving luminosities and therefore higher cloud temperatures are usually accompanied by higher pressures in a way that the thermal Jeans mass stays about constant (Elmegreen et al. 2008).
The overall affect of triggered star formation on the average star formation rate seems to be small in the main parts of galaxy disks. The empirical laws discussed in Lecture 1 seem not to depend on how the self-gravitating molecular gas is made, as long as it is made quickly between previous molecular cloud disruptions. If the dispersed gas from a previous event of star formation lingers around in a diffuse state for a long time, without forming stars, then it might still turn molecular from self-shielding, thereby contributing to H2, but not contribute in the right proportion to SFR. The empirical Bigiel et al. (2008) law would then fail. We suggested in Lecture 2 that this may be the case for dust clouds in the interarm regions of M51, i.e., that they are marginally stable to have lasted so long from their formation in the previous spiral arm. But the fraction of molecules in a non-gravitating form cannot be large for the correlation between SFR and H2 to work out as well as it does. Frequent gas compression by all of the various pressures in the ISM, combined with the forced loss of internal energy that accompanies this compression, ensures that most of the molecular and atomic debris from one event of star formation soon makes it into another event of star formation. Prevalent triggering thereby acts as a scavenger for inert diffuse clouds, keeping most parts of the ISM in a constant state of collapse or imminent collapse. This is the saturation in star formation that previous lectures have mentioned.
With very low star formation rates, as in dwarf galaxies and the outer parts of disks, a much higher fraction of the gas can be in diffuse form, and then triggering can play a more direct role in the average star formation rate. At a very minimum, it can provide locally high pressures where the thermal stability of the gas allows a cool phase to exist in equilibrium with the radiation field. Without such cool phases, disk instabilities will just make warm and diffuse flocculent spirals in the gas, and there will not be enough dense matter to affect the star formation rate. Put simply, at very low average pressures, cool diffuse clouds seem to require pressure disturbances for their formation from the warm phase. Most commonly, outer spiral arms seem to do this, but stellar pressure sources might be important too. This enablement of cool cloud formation is presumably the first step in the condensation process that leads to star formation.