Star Formation in Massive Clusters Via the Wilkinson Microwave Anisotropy Probe and the Spitzer Glimpse Survey

We use the Wilkinson Microwave Anisotropy Probe (WMAP) maximum entropy method foreground emission map combined with previously determined distances to giant H II regions to measure the free-free flux at Earth and the free-free luminosity of the Galaxy. We find a total flux f _ν = 54, 211 Jy and a flux from 88 sources of f _ν = 36, 043 Jy. The bulk of the sources are at least marginally resolved, with mean radii ~60 pc, electron density n_e ~ 9 cm^-3, and filling factor φ_H II ≈ 0.005 (over the Galactic gas disk). The total dust-corrected ionizing photon luminosity is Q = 3.2 × 10⁵³ ± 5.1 × 10⁵² photons s^-1, in good agreement with previous estimates. We use GLIMPSE and Midcourse Space Experiment (MSX) 8 μm images to show that the bulk of the free-free luminosity is associated with bubbles having radii r ~ 5-100 pc, with a mean of ~20 pc. These bubbles are leaky, so that ionizing photons emitted inside the bubble escape and excite free-free emission beyond the bubble walls, producing WMAP sources that are larger than the 8 μm bubbles. We suggest that the WMAP sources are the counterparts of the extended low density H II regions described by Mezger. The 18 most luminous WMAP sources emit half the total Galactic ionizing flux. These 18 sources have 4 × 10⁵¹ s^-1 lsim Q lsim 1.6 × 10⁵² s^-1, corresponding to 6 × 10⁴ M _sun lsim M _* lsim 2 × 10⁵ M _sun; half to two thirds of this will be in the central massive star cluster. We convert the measurement of Q to a Galactic star formation rate (SFR) \dot{M}_*=1.3± 0.2 M_⊙ yr^{-1}, where the errors reflect only the error in free-free luminosity. We point out, however, that our inferred \dot{M}_* is highly dependent on the exponent Γ ≈ 1.35 of the high-mass end of the stellar initial mass function. For 1.21 < Γ < 1.5, we find 0.9 M_⊙ yr^{-1}<\dot{M}_*<2.2 M_⊙ yr^{-1}. We also determine a SFR of 0.14 M _sun yr^-1 for the Large Magellanic Cloud and 0.015 M _sun yr^-1 for the Small Magellanic Cloud.