τ_SF as a function of M_dyn. The colour bar indicates the goodness of the fit, p(g_conv, τ_SF) (Eq. (17)), for our fiducial SNIa model. For a given mass and SFT, τ_SF, any star-to-gas-mass fraction, g_conv, is allowed. The most likely SFT for a given galaxy mass is indicated by the yellow ridge line. The black dotted curve (Eq. (18)) is a power-law fit of the yellow ridge line. The red dashed curve and the red dash-dotted curve (Eq. (19)) represent the SFT constrained by SPS studies by de La Rosa et al. (2011) and McDermid et al. (2015), respectively. As is introduced in Sect. 1, The SFT suggested by chemical evolution studies assuming the invariant canonical gwIMF performed by Pipino & Matteucci (2004) and Thomas et al. (2005) are shown by the blue triangles and blue dotted curve, respectively. The lower and upper yellow dotted curves correspond, respectively, to polynomial regressions of the yellow ridge lines in Figs. 5 and 7 of Yan et al. (2019a), derived using invariant canonical gwIMF. The mass ranges of the coloured curves are limited by the mass ranges of the galaxy data sets they are based on.