CO luminosity - line width correlation of sub-millimeter galaxies and a
  possible cosmological application
  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.
