The Star Formation Rate and Gas Surface Density Relation in the Milky
  Way: Implications for Extragalactic Studies
  We investigate the relation between star formation rate (SFR) and gas surface
densities in Galactic star forming regions using a sample of YSOs and massive
clumps. Our YSO sample consists of objects located in 20 molecular clouds from
the Spitzer cores to disks and Gould's Belt surveys. We estimate the gas
surface density (Sigma_gas) from Av maps and YSO SFR surface densities
(Sigma_SFR) from the number of YSOs, assuming a mean mass and lifetime. We also
divide the clouds into contour levels of Av, counting only the youngest Class I
and Flat SED YSOs. For a sample of massive star forming clumps, we derive SFRs
from the infrared luminosity and use HCN gas maps to estimate Sigma_gas. We
find that Galactic clouds lie above the extragalactic relations (e.g.,
Kennicutt-Schmidt Law) by factors up to 17. Cloud regions with high Sigma_gas
lie above extragalactic relations up to a factor of 54 and overlap with massive
clumps. We use 12CO and 13CO gas maps of the Perseus and Ophiuchus clouds to
estimate Sigma_gas and compare to Sigma_gas from Av maps. We find that 13CO,
underestimates the Av-based mass by factors of 4-5. 12CO may underestimate the
total gas mass at Sigma_gas > 200 Msun pc^-2 by > 30%;however, this does not
explain the large discrepancy between Galactic and extragalactic relations. We
find evidence for a threshold of star formation (Sigma_th) at 129+-14 Msun
pc^-2. At Sigma_gas > Sigma_th, the Galactic relation is linear. A possible
reason for the difference between Galactic and extragalactic relations is that
all the CO-emitting gas, including Sigma_gas below Sigma_th, is measured in
extragalactic studies. If the Kennicutt-Schmidt relation (Sigma_SFR
Sigma_gas^1.4) and a linear relation between dense gas and star formation is
assumed, the fraction of dense star forming gas (f_dense) increases as
Sigma_gas^0.4. When Sigma_gas reaches ~300Sigma_th, f_dense is 1. (Abridged)
