What Controls the Star Formation in Luminous Starburst Mergers?

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.Comment: 14 pages, 2 figures. The Astrophysical Journal (Letters), in pres