Our Milky Way, like other galaxies, assembled over cosmic time from rarefied, gaseous material into immense, regular systems of hydrogen-burning stars. The processes responsible for this star formation were complex and operated over most of cosmic history - and they are not yet fully understood. A predictive theory of star formation is essential to an understanding galaxy formation and evolution, and an important step in that direction is discerning an empirical relation that connects the rate of star formation to the physical properties of the interstellar gas. For over half a century, astronomers have thought that the rate of star formation depends on the gas density, such that the number of stars formed per year varies roughly as gas density to some power, with the scaling usually taken to be approximately as the density squared.
The original conjecture relating star formation to gas density was made for galaxies as a whole. CfA astronomers Charlie Lada and Jan Frobrich and their colleagues examined star formation in four giant molecular clouds in our galaxy to test the extent to which this behavior accurately characterizes physical processes within individual clouds. They were motivated in part by the curious fact that on the one hand star formation rates (numbers of stars per year) do seem to follow this kind of scaling law, yet on the other hand the total numbers of new stars present do not seem to correlate with gas density. The scientists used infrared data from the Spitzer Space Telescope and ground-based, near infrared surveys to perform statistical analyses, comparing star formation over small spatial scales against the gas and dust density as tracked by the amounts of visual obscuration.
The astronomers report that the original relationship is correct as far as it goes (although the scaling often deviates from an exactly square law). The issue is that the total numbers of stars produced depend as well on the volumes of dense gas, and the sizes of these regions can vary widely depending on the detailed evolution of each molecular cloud. Clouds with many high-density regions naturally produce more stars, although in each region the rate depends on the local density. The scientists note that in the study of galaxies as a whole the various kinds of molecular clouds they contain are lumped together, blurring the local physical differences that account for the curious discrepancies noted.
"Schmidt's Conjecture and Star Formation in Molecular Clouds," Charles J. Lada, Marco Lombardi, Carlos Roman-Zuniga, Jan Forbrich, and Joao F. Alves, ApJ 778, 133, 2013