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We report the discovery and characterization of a power law correlationbetween the local surface densities of Spitzer-identified, dusty young stellarobjects and the column density of gas (as traced by near-IR extinction) ineight molecular clouds within 1 kpc and with 100 or more known YSOs. Thiscorrelation, which appears in data smoothed over size scales of ~1 pc, variesin quality from cloud to cloud; those clouds with tight correlations, MonR2 andOphiuchus, are fit with power laws of slope 2.67 and 1.87, respectively. Thespread in the correlation is attributed primarily to local gas disruption bystars that formed there or to the presence of very young sub-regions at theonset of star formation. We explore the ratio of the number of Class II toClass I sources, a proxy for the star formation age of a region, as a functionof gas column density; this analysis reveals a declining Class II to Class Iratio with increasing column density. We show that the observed star-gascorrelation is consistent with a star formation law where the star formationrate per area varies with the gas column density squared. We also propose asimple picture of thermal fragmentation of dense gas in an isothermal,self-gravitating layer as an explanation for the power law. Finally, we brieflycompare the star gas correlation and its implied star formation law with otherrecent proposed of star formation laws at similar and larger size scales fromnearby star forming regions.

A Correlation Between Surface Densities of Young Stellar Objects and Gas in Eight Nearby Molecular Clouds