  We constrain the spatial gradient of star formation history within galaxies
using the colour gradients in NUV-u and u-i for a local spatially-resolved
galaxy sample. By splitting each galaxy into an inner and an outer part, we
find that most galaxies show negative gradients in these two colours. We first
rule out dust extinction gradient and metallicity gradient as the dominant
source for the colour gradient. Then using stellar population models, we
explore variations in star formation history to explain the colour gradients.
As shown by our earlier work, a two-phase SFH consisting of an early secular
evolution (growth) phase and a subsequent rapid evolution (quenching) phase is
necessary to explain the observed colour distributions among galaxies. We
explore two different inside-out growth models and two different inside-out
quenching models by varying parameters of the SFH between inner and outer
regions of galaxies. Two of the models can explain the observed range of colour
gradients in NUV-u and u-i colours. We further distinguish them using an
additional constraint provided by the u-i colour gradient distribution, under
the assumption of constant galaxy formation rate and a common SFH followed by
most galaxies. We find the best model is an inside-out growth model in which
the inner region has a shorter e-folding time scale in the growth phase than
the outer region. More spatially resolved ultraviolet (UV) observations are
needed to improve the significance of the result.
