The Star Formation Laws of Eddington-Limited Star-Forming Disks

Two important avenues into understanding the formation and evolution of galaxies are the Kennicutt-Schmidt (KS) and Elmegreen-Silk (ES) laws. These relations connect the surface densities of gas and star formation (\sigmagas\ and \sigmastar, respectively) in a galaxy. To elucidate the KS and ES laws for disks where \sigmagas >~ 10^4 Msun pc-2}, we compute 132 Eddington-limited star-forming disk models with radii spanning tens to hundreds of parsecs. The theoretically expected slopes (approx. 1 for the KS law and approx. 0.5 for the ES relation) are relatively robust to spatial averaging over the disks. However, the star formation laws exhibit a strong dependence on opacity that separates the models by the dust-to-gas ratio that may lead to the appearance of a erroneously large slope. The total infrared luminosity (L_TIR) and multiple carbon monoxide (CO) line intensities were computed for each model. While L_TIR can yield an estimate of the average \sigmastar\ that is correct to within a factor of 2, the velocity-integrated CO line intensity is a poor proxy for the average \sigmagas\ for these warm and dense disks, making the CO conversion factor (\alpha_CO) all but useless. Thus, observationally derived KS and ES laws at these values of \sigmagas\ that uses any transition of CO will provide a poor measurement of the underlying star formation relation. Studies of the star formation laws of Eddington-limited disks will require a high-J transition of a high density molecular tracer, as well as a sample of galaxies with known metallicity estimates.