Relationship between molecular gas depletion timescale and the specific star formation rate for HRS galaxies (black symbols), COLD GASS galaxies (grey symbols), and high-redshift objects, from Tacconi et al. (2008) (yellow filled dots), Daddi et al. (2009a,b) (blue filled dots), Genzel et al. (2010) (red crosses), Combes et al. (2013) (green open squares), and Tacconi et al. (2013) (cyan open triangles). The molecular gas content of all high-z galaxies regardless of whether they are star-forming or starburst galaxies, has been determined using a starburst conversion factor X_CO = 0.64 × 10²⁰ cm^-2 (K km s^-1)^-1 In the left panel the H₂ gas mass of HRS and COLD GASS galaxies is measured using a constant X_CO conversion factor, and in the right panel the luminosity-dependent X_CO factor of Boselli et al. (2002). Both the local (HRS and COLD GASS) and the high-z samples include only detected late-type galaxies. The big blue circles indicate the mean values of τ_H2 in different bins of SSFR determined from the HRS sample. The black dotted line shows the best fit determined for HRS galaxies, the coloured lines the best fits for the COLD GASS sample. The red vertical arrow indicate the systematic shift that all high-redshift galaxies would have if the molecular gas mass is determined assuming a Galactic conversion factor.