  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.
