Observed CO line widths (normalized by the CO(2−1) line width) as a function of the upper rotational quantum number J_up. Top row: CO line widths computed using the velocity percentile v₈₄ − v₁₆ interval, derived from the analytical expression of the best-fit line profile obtained with the multi-Gaussian fit. Bottom row: line widths obtained via a single Gaussian spectral fit to each CO emission line. Left column: all the sources in our sample; middle and right columns show the ULIRGs with low and high excitation CO SLEDs, respectively (see explanation in Sect. 3.1). The sources are color coded as presented in the upper legend, the mean trend is computed for each plot and shown with black square markers.