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The Luminosity Function of OB Associations in the Galaxy

OB associations ionize the interstellar medium, producing both localized H II regions and diffuse ionized gas. The supernovae resulting from these associations pressurize and stir the interstellar medium. Using Smith, Biermann, & Mezger's compilation of radio H II regions in the Galaxy, and Kennicutt, Edgar, & Hodge's optical study of H II regions in nearby galaxies, we show that the luminosity distribution of giant OB associations in the Galaxy can be fit by a truncated power law of the form 𝒩a(>S)=𝒩au[(Su/S)-1], where S is the ionizing photon luminosity, 𝒩a(>S) is the number of associations with a luminosity of at least S, and Su is the upper limit to the distribution. The coefficient 𝒩au is the number of the most luminous associations, with a luminosity between 0.5Su and Su. For the Galaxy, 𝒩au=6.1; the fact that the number of the most luminous associations is significantly larger than unity indicates that there is a physical limit to the maximum size of H II regions in the Galaxy. To extend the luminosity distribution to small H II regions, we assume that the birthrate of associations, a(>𝒩*), is also a truncated power law, a(>𝒩*)∝[(𝒩*u/𝒩*)-1], where 𝒩* is the number of stars in the association. For large associations, the ionizing luminosity is proportional to the number of stars, S∝𝒩*; for smaller associations, we use both an analytic and a Monte Carlo approach to find the resulting luminosity distribution 𝒩a(>S). H II regions are generally centrally concentrated, with only the dense central regions being bright enough to appear in radio catalogs. Anantharamaiah postulated that radio H II regions have extended envelopes in order to account for diffuse radio recombination line emission in the Galaxy. Some of these envelopes are visible as the ionized “worms” discussed by Heiles and coworkers. We estimate that on the average the envelopes of radio H II regions absorb about twice as many ionizing photons as the radio H II regions themselves. Allowing for the ionizing radiation that is absorbed by dust (about 25% of the total), we find that the maximum ionizing photon luminosity of a Galactic OB association is Su ≃ 4.9 × 1051 photons s-1, corresponding to an Hα luminosity of about 5 × 1039 ergs s-1. The total ionizing luminosity of this distribution of OB associations can account for the thermal radio emission and the N II far-infrared emission of the Galaxy. The number of massive stars in the associations is consistent with estimates of the rate of massive star supernovae in the Galaxy. Associations produce several generations of stars over their lifetimes, and the largest associations are predicted to produce about 7000 supernova progenitors. Fitting the surface density of associations to an exponential of the form d𝒩a(𝒩*)/dA∝ exp (-R/HR) with a scale length HR = 3.5 kpc gives a number of OB associations in the solar neighborhood that is consistent with observation. The H II envelopes contribute to pulsar dispersion measures and can account for the increased dispersion measure observed in the inner Galaxy.