SNIa realisation re-normalisation parameter, κ_Ia defined in Eq. (20), as a function of the galaxy-wide SFR, . Three different models are tested, and the corresponding best-fit SFT–galaxy-mass relations are shown in Figs. 4, 7, and B.1 for the fiducial model (dotted line), error function model (solid line), and power-law function model (dashed line), respectively. The error function model, formulated in Eq. (21), best reproduces the observed ETGs.