  In order to understand what controls the star formation process in luminous
starburst mergers (e.g., NGC 6240, Arp 220, and so on), we investigate
observational properties of two samples of high-luminosity starburst galaxies
mapped in CO($J$=1--0) independently using both the Owens Valley Radio
Observatory (Scoville et al. 1991) and the IRAM interferometer (Downes &
Solomon 1998). We find that the surface density of far-infrared luminosity,
$\Sigma$(FIR), is proportional linearly to the H$_2$ surface mass density,
$\Sigma$(H$_2$), for the two samples; $\Sigma$(FIR) $\propto
\Sigma$(H$_2$)$^{1.01\pm0.06}$ with a correlation coefficient of 0.96. It is
often considered that $\Sigma$(FIR) provides a good measure of the star
formation rate per unit area, $\Sigma$(SFR). It is also known that molecular
gas is dominated in circumnuclear regions in the luminous starburst mergers;
i.e., $\Sigma$(gas) $\simeq \Sigma$(H$_2$). Therefore, the above relationship
suggests a star formation law; $\Sigma$(SFR) $\propto \Sigma$(gas). We suggest
that this star formation law favors the gravitational instability scenario
rather than the cloud-cloud collision one.
