Context. A possible correlation between CO luminosity (L_CO ) and its line width (FWHM) has been suggested and denied in the literature. Such claims were often based on a small, or heterogeneous sample of galaxies, and thus inconclusive. Aims. We aim to prove or dis-prove the L_CO -FWHM correlation. Methods. We compile a large sample of submm galaxies at z>2 from the literature, and investigate the L_CO-FWHM relation. Results. After carefully evaluating the selection effects and uncertainties such as inclination and magnification via gravitational lensing, we show that there exist a weak but significant correlation between L_CO and FWHM. We also discuss a feasibility to measure the cosmological distance using the correlation.
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