Schmidt's conjecture and star formation in molecular clouds
We investigate Schmidt's conjecture (i.e., that the star formation rate (SFR) scales in a power-law fashion with the gas density) for four well-studied local molecular clouds (giant molecular clouds, GMCs). Using the Bayesian methodology, we show that a local Schmidt scaling relation of the form Σ{sub ∗}(A{sub K})=κA{sub K}{sup β} (protostars pc{sup –2}) exists within (but not between) GMCs. Further, we find that the Schmidt scaling law does not by itself provide an adequate description of star formation activity in GMCs. Because the total number of protostars produced by a cloud is given by the product of Σ{sub *}(A {sub K}) and S'(> A {sub K}), the differential surface area distribution function, integrated over the entire cloud, the cloud's structure plays a fundamental role in setting the level of its star formation activity. For clouds with similar functional forms of Σ{sub *}(A {sub K}), observed differences in their total SFRs are primarily due to the differences in S'(> A {sub K}) between the clouds. The coupling of Σ{sub *}(A {sub K}) with the measured S'(> A {sub K}) in these clouds also produces a steep jump in the SFR and protostellar production above A{sub K} ∼ 0.8 mag. Finally, we show that there is no global Schmidt law that relates the SFR and gas mass surface densities between GMCs. Consequently, the observed Kennicutt-Schmidt scaling relation for disk galaxies is likely an artifact of unresolved measurements of GMCs and not a result of any underlying physical law of star formation characterizing the molecular gas.