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The Star Formation-Gas Density Relation in Four Galactic GMCs: Effects of Stellar Feedback

We present maps of 4 galactic giant molecular clouds (GMCs) in the J=2-1 emission of both CO and $^{13}$CO. We use an LTE analysis to derive maps of the CO excitation temperature and column density and the distribution of total molecular gas column density, $Σ_{gas}$. The depletion of CO by freeze-out onto cold dust grains is accounted for by an approximation to the results of Lewis et al. (2021) which were derived from far-IR observations with {\it Herschel}. The surface density of young stellar objects (YSOs) is obtained from published catalogs. The mean YSO surface density exhibits a power-law dependence on $Σ_{gas}$, with exponents in the range 0.9 to 1.9. Gas column density probability distribution functions (PDFs) show power-law tails extending to high column densities. The distributions of sonic Mach number, $M_S$ are sharply peaked at $M_S \sim 5 - 8$ for 3 GMCs; a fourth has a broad distribution up to $M_S =30$, possibly a result of feedback effects from multiple OB stars. An analysis following the methodology of Pokhrel et al. (2021) finds that our sample of GMCs shows power-law relations that are somewhat shallower than found by Pokhrel et al. (2021) for the star formation rate vs. $<Σ_{gas}>$ and vs. $<Σ_{gas}>/t_{ff}$ in a different sample of clouds. We discuss possible differences in the two samples of star-forming clouds and the effects of stellar feedback on the relation between gas density and star formation rate.