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,
Σ(FIR), is proportional linearly to the H2 surface mass density,
Σ(H2), for the two samples; Σ(FIR) ∝Σ(H2)1.01±0.06 with a correlation coefficient of 0.96. It is
often considered that Σ(FIR) provides a good measure of the star
formation rate per unit area, Σ(SFR). It is also known that molecular
gas is dominated in circumnuclear regions in the luminous starburst mergers;
i.e., Σ(gas) ≃Σ(H2). Therefore, the above relationship
suggests a star formation law; Σ(SFR) ∝Σ(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