Observational Evidence of Dynamic Star Formation Rate in Milky Way Giant
  Molecular Clouds
  Star formation on galactic scales is known to be a slow process, but whether
it is slow on smaller scales is uncertain. We cross-correlate 5469 giant
molecular clouds (GMCs) from a new all-sky catalog with 256 star forming
complexes (SFCs) to build a sample of 191 SFC-GMC complexes---collections of
multiple clouds each matched to 191 SFCs. The total mass in stars harbored by
these clouds is inferred from WMAP free-free fluxes. We measure the GMC mass,
the virial parameter, the star formation efficiency $\epsilon$ and the star
formation rate per free-fall time $\epsilon_{\rm ff}$. Both $\epsilon$ and
$\epsilon_{\rm ff}$ range over 3--4 orders of magnitude. We find that 68.3% of
the clouds fall within $\sigma_{\log\epsilon}=0.79\pm0.22\,{\rm dex}$ and
$\sigma_{\log\epsilon_{\rm ff}}=0.91\pm0.22\,{\rm dex}$ about the median.
Compared to these observed scatters, a simple model with a time independent
$\epsilon_{\rm ff}$ that depends on the host GMC properties predicts
$\sigma_{\log\epsilon_{\rm ff}}=$0.12-0.24. Allowing for a time-variable
$\epsilon_{\rm ff}$, we can recover the large dispersion in the rate of star
formation. This strongly suggests that star formation in the Milky Way is a
dynamic process on GMC scales. We also show that the surface star formation
rate profile of the Milky Way correlates well with the molecular gas surface
density profile.
