Environmental dependences for star formation triggered by expanding shell collapse

Criteria for gravitational collapse of expanding shells in rotating, shearing galaxy discs were determined using three-dimensional numerical simulations in the thin shell approximation. The simulations were run over a grid of seven independent variables, and the resultant probabilities for triggering and unstable masses were determined as functions of eight dimensionless parameters. When the ratio of the midplane gas density to the midplane total density is small, an expanding shell reaches the disc scaleheight and vents to the halo before it collapses. When the Toomre instability parameter Q, or a similar shear parameter, Q(A), is large, Coriolis forces and shear stall or reverse the collapse before the shell accumulates enough mass to be unstable. With large values of c(sh)(5)/(GL), for rms velocity dispersion c(sh) in the swept-up matter and shell-driving luminosity L, the pressure in the accumulated gas is too large to allow collapse during the expansion time. Considering similar to5000 models covering a wide range of parameter space, the common properties of shell collapse as a mechanism for triggered star formation are: (1) the time-scale is similar to4(c(sh)/2piGrho[GL](0.2))(0.5) for ambient midplane density rho, (2) the total fragment mass is similar to2 x 10(7) M-circle dot, of which only a small fraction is likely to be molecular, (3) the triggering radius is similar to2 times the scaleheight, and the triggering probability is similar to0.5 for large OB associations. Star formation triggered by shell collapse should be most common in gas-rich galaxies, such as young galaxies or those with late Hubble types.