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tokens: the photometry in all bands has been convolved to match the WFC3/ F 160 W resolution (Guo et al. 2013 ), any influence caused by different PSF sizes of HST filters has been eliminated. All galaxies receive the same statistical weight in a stack. The maximum radial extent to measure colour gradients is set to two times the SMA, where reliable photometry is still available. 4.2 Colour gradients uncorrected for beam smearing and stacked by radius scaled to SMA This subsection shows raw stacked colour gradients without any beam-smearing correction. First, we scale the radial colour profiles of each individual galaxy by its SMA (effective radius along the galaxy major axis), by interpolating between the apertures as described in Section 2 . Then these scaled colour profiles are stacked together to produce the average profiles as shown in Fig. 3 . Figure 3. UVI colour gradients for star-forming galaxies in mass–redshift bins, as indicated at the top and right margins. The radial colour profiles are scaled by effective radius before stacking, without correction for PSF smearing. For each panel, the stacked radial trajectories in U − V and V − I are plotted as the black curves. Dashed lines denote the Calzetti reddening vector. Mean integrated A V and the number of sample galaxies are indicated at upper left in each panel, and the typical standard deviation of the mean of stacked gradients is shown at lower right. The gradient trajectories follow the reddening vector, which indicates that most of the gradients are caused by dust variations and that sSFR is nearly constant with radius. The grid of panels in Fig. 3 shows the shapes of the stacked colour trajectories in UVI space as a function of mass and redshift. Each panel is a UVI diagram, and the black lines are the paths taken by the colours in going from the innermost radius (upper right) to the outermost radius (lower left). The three symbols indicate local colours at 0.2 SMA (star), 1 SMA (open circle) and 2 SMA (dot). The direction of dust reddening by the Calzetti law is shown as the dashed lines. The main feature of this figure is that gradient trajectories approximately follow the reddening vector, which indicates that most of the gradients are caused by dust variations and that sSFR is nearly constant with radius. This conclusion is unchanged under beam-smearing correction and stacking by radius rather than scaled radius, as shown in the next section. 4.3 Colour gradients stacked based on angular distance and beam-smearing correction Next, we turn to another stacking method of colour profiles and then evaluate and correct the beam-smearing effects caused by the PSF. To start with, galaxy colour profiles are stacked together based on the angular distance in arcsec to their centres, instead of the normalization used in Section 4.2 . The resultant colour gradients are shown as red curves in Fig. 4 . This stacking method ensures that the stacked profiles have a well-defined angular