We study the star formation (SF) law in 12 Galactic molecular clouds with ongoing high-mass star formation (HMSF) activity, as traced by the presence of a bright IRAS source and other HMSF tracers. We define the molecular cloud (MC) associated to each IRAS source using 13CO line emission, and count the young stellar objects (YSOs) within these clouds using GLIMPSE and MIPSGAL 24 micron Spitzer databases.The masses for high luminosity YSOs (Lbol>10~Lsun) are determined individually using Pre Main Sequence evolutionary tracks and the evolutionary stages of the sources, whereas a mean mass of 0.5 Msun was adopted to determine the masses in the low luminosity YSO population. The star formation rate surface density (sigsfr) corresponding to a gas surface density (siggas) in each MC is obtained by counting the number of the YSOs within successive contours of 13CO line emission. We find a break in the relation between sigsfr and siggas, with the relation being power-law (sigsfr ~ siggas^N) with the index N varying between 1.4 and 3.6 above the break. The siggas at the break is between 150-360 Msun/pc^2 for the sample clouds, which compares well with the threshold gas density found in recent studies of Galactic star-forming regions. Our clouds treated as a whole lie between the Kennicutt (1998) relation and the linear relation for Galactic and extra-galactic dense star-forming regions. We find a tendency for the high-mass YSOs to be found preferentially in dense regions at densities higher than 1200 Msun/pc^2 (~0.25 g/cm^2).
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