each galaxy). We note that at low star formation rates and stellar masses, there is a non-zero velocity dispersion due to the sound speed ($c_s$) of the gas ($c_s\lsim $10kms$^{-1}$ for the Milky Way at the solar circle) which we have neglected since this is below both the resolution limit of our observations and the minimum velocity dispersion caused the stellar disks in these systems.

We can improve these constraints further assuming that star formation in each galaxy behaves in a similar way. We reiterate that this model assumes the star formation is occurring in a marginally Toomre stable disk, where the star formation follows the Kennicutt-Schmidt Law. Over a range $A$=10$^{-5}$–10$^{-2}$(M$_{\odot}$yr$^{-1}$kpc$^{-2}$) and $n$=0.8–2.5 we construct a likelihood distribution for all nine galaxies and then convolve these to provide a composite likelihood distribution, and show this in Fig. \[fig:KS\]. Although the values of $n$ and $A$ are clearly degenerate, the best-fit solutions have $n$=1.34$\pm$0.15 and $A$=3.4$_{-1.6}^{+2.5}$$\times$10$^{-4}$M$_{\odot}$yr$^{-1}$kpc$^{-2}$ Our derived values for the absolute star-formation efficiency, $A$, and power-law index, $n$ are within the 1-$\sigma$ of the values derived for local galaxies [e.g. @KS98; @Leroy08].

Using the $^{12}$CO to trace the cold molecular gas, @Genzel10 showed that gas and star-formation surface densities 