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