Sequential star formation in OB associations: The role of molecular cloud turbulence

Abstract

Numerical simulations of shock propagation into a two-dimensional, clumpy, turbulent cloud suggest that the average shock speed, vs, approximately equals the square root of the ratio of the external pressure to the average preshock density, ρ0, and that the average shocked layer density, ρs, approximately equals the product of ρ0 and the square of the velocity ratio, vs/aturb, for postshock rms turbulent speed aturb. A comparison is made between seven theoretical formulations for the shock speed; all differ slightly from each other and from the measured shock speed, but usually not by more than a factor of 1.5. The maximum postshock density is much larger than the average postshock density because of the clumpy postshock structure; the maximum is comparable to ρ0(vs/ath)2 for postshock thermal speed ath. These relations are useful for the interpretation of forced cloud motions and shock speeds in turbulent molecular clouds near H II regions. Preshock clumps form self-consistently by supersonic turbulence compression in the initial preshock gas. As the shock moves into the cloud, these clumps are squeezed and collected into the compressed layer, and they merge into a few massive, clumpy, postshock cores. The cores should produce bright rims in a real H II region because they protrude slightly into the ionized gas. The escape velocity in a typical model postshock core is larger than both the internal core velocity dispersion and the shock speed. Such a core would collapse gravitationally and ultimately form a star cluster. Stars could also form earlier when the preshock turbulent clumps collide with each other inside the postshock layer or when the clumps are squeezed by the high-pressure shock. Thus, there could be an age spread inside the triggered cluster equal to the entire age of the shock, although most of the stars will form when the massive postshock cores collapse. The separation between OB association subgroups should be related to the time for the embedded cluster to grow to such a large mass that the stellar pressures inside the core disperse the gas and halt further star formation.