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Figure 1 shows a spiral arm segment with large rings of gas and star formation downstream from the arms. These are giant cavities are made by star formation, as discussed above. The solar neighborhood is downstream from the Carina spiral arm and also has a large cavity apparently made by star formation. This is associated with the expanding HI ring discovered by Lindblad et al. (1973) with a hole in the diffuse dust (Lallement et al. 2003). The size of the dust hole is 100 pc by 300 pc, and it extends all the way through the disk. The cavities in Figure 1 are about the same size, and larger than the ISM thickness. Thus they are rings rather than shells. The smaller regions could be three-dimensional shells.

Expanding rings are more unstable than expanding shells because the self-gravitational force vectors that drive gas collection in a one-dimensional section of a ring are all directed toward the growing condensation. According to Elmegreen (1994), the time for significant collapse in an expanding shell is ~ 100(n M)-0.5 Myr for ambient density n in cm-3 and Mach number M, and the time in an expanding ring is 124(n M2)-0.5 Myr. The ring expression contains a stronger dependence on the Mach number, and this give the ring a shorter collapse time.

Generally, the expansion scale equals the shock speed multiplied by the time, and the shock speed is about (P / ρ0)0.5 for driving pressure P and preshock density ρ0. If the relevant time is the collapse time, (Gρcomp)-0.5 for compressed density ρcomp, then the expansion scale is, after rearrangement, (P / ρcomp)0.5(G ρ0)-0.5, which is the velocity dispersion in the compressed region multiplied by the dynamical time in the ambient gas. Details about the compression source drop out.

If the expansion scale is less than the cloud scale, then pillars and bright rims form by the push-back of interclump gas (Elmegreen, Kimura & Tosa 1995, Gritschneder et al. 2009). Star formation is a fast process (squeezing pre-existing clumps), the velocity of triggered stars is small, and causality is difficult to determine, i.e., stars could have formed in the clumps anyway. If the expansion scale is larger than the cloud scale, then shells and rings form by the push-back of all ISM gas (e.g. Dale et al. 2011), triggering is a slow process because new clumps have to form on a timescale of (Gρshell)-0.5, and the velocity of triggered stars can be large, on the order of the shock speed, (P / ρ0)1/2. There is also a clear causality condition because two stellar generations have to be separated by a distance equal to the age times the mean velocity.

A popular cloud formation scenario considers the compression of gas between two "colliding flows" (e.g., Heitsch et al. 2008, Audit & Hennebelle 2010). Shell or ring accumulation forms clouds too, but is different in several ways. Shells and rings have a lateral expansion as they expand radially, and this lateral expansion resists gravitational collapse. Shells and rings also decelerate so that newly formed condensations protrude out the front and have the potential to erode. Shells and rings have a shock on only one side. A shock boundary condition causes a diverging flow at each clump, and this divergence resists collapse. The pressure boundary condition on the other side of the shell or ring squeezes the perturbations and aids collapse. For colliding flows with constant velocity streams, there is a shock on each side and no acceleration of the condensation between them when it is in equilibrium. We observe shells and rings commonly, as shown in the figures and in surveys (e.g., Konyves et al. 2007, Ehlerová & Palous, 2005), but there is no clear evidence yet for cloud formation on GMC-scales by colliding flows (on much larger scales, the collision between two galaxies can have a colliding flow; Herrara et al. 2011). Still, colliding flows are a good model to study molecule formation and fragmentation in a dynamic environment.

Triggering in the ring RCW 79 was studied in detail by Zavagno et al. (2006), who suggested there was a collapsed neutral region containing young stars, 0.1 Myr old, along the periphery of a swept-up region that was 1.7 Myr old. There are several neutral condensations in this shell, somewhat equally spaced around part of the projected edge. Deharveng et al. (2010) studied 102 Milky Way bubbles and suggested that 18 of them have either ultracompact HII regions or methanol masers along their edge, suggesting triggering of massive stars in swept-up gas.

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