Abstract
Context. A possible correlation between CO luminosity (L′<inf>CO</inf>) 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, hence were inconclusive. Aims. We aim to prove or disprove the L′<inf>CO</inf>-FWHM correlation. Methods. We compiled a large sample of sub-mm galaxies at z > 2 from the literature and investigated 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 a weak but significant correlation exists between L′<inf>CO</inf> and FWHM. We also discuss a feasibility to measure the cosmological distance using the correlation.