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The Galactic Distribution of OB Associations in Molecular Clouds

Molecular clouds account for half of the mass of the interstellar medium interior to the solar circle and for all current star formation. Using cloud catalogs of two CO surveys of the first quadrant, we have fitted the mass distribution of molecular clouds to a truncated power law in a similar manner as the luminosity function of OB associations in the companion paper to this work. After extrapolating from the first quadrant to the entire inner Galaxy, we find that the mass of cataloged clouds amounts to only 40% of current estimates of the total Galactic molecular mass. Following Solomon & Rivolo, we have assumed that the remaining molecular gas is in cold clouds, and we normalize the distribution accordingly. The predicted total number of clouds is then shown to be consistent with that observed in the solar neighborhood where cloud catalogs should be more complete. Within the solar circle, the cumulative form of the distribution is 𝒩c(>M)=105[(Mu/M)0.6-1], where 𝒩c is the number of clouds, and Mu = 6 × 106 M☉ is the upper mass limit. The large number of clouds near the upper cutoff to the distribution indicates an underlying physical limit to cloud formation or destruction processes. The slope of the distribution corresponds to d𝒩c/dM∝M−1.6, implying that although numerically most clouds are of low mass, most of the molecular gas is contained within the most massive clouds. The distribution of cloud masses is then compared to the Galactic distribution of OB association luminosities to obtain statistical estimates of the number of massive stars expected in any given cloud. The likelihood of massive star formation in a cloud is determined, and it is found that the median cloud mass that contains at least one O star is ~105 M☉. The average star formation efficiency over the lifetime of an association is about 5% but varies by more than 2 orders of magnitude from cloud to cloud and is predicted to increase with cloud mass. O stars photoevaporate their surrounding molecular gas, and even with low rates of formation, they are the principal agents of cloud destruction. Using an improved estimate of the timescale for photoevaporation and our statistics on the expected numbers of stars per cloud, we find that 106 M☉ giant molecular clouds (GMCs) are expected to survive for about 3 × 107 yr. Smaller clouds are disrupted, rather than photoionized, by photoevaporation. The porosity of H II regions in large GMCs is shown to be of order unity, which is consistent with self-regulation of massive star formation in GMCs. On average, 10% of the mass of a GMC is converted to stars by the time it is destroyed by photoevaporation.