  We investigate radial gradients in the recent star formation history (SFH)
using 1917 galaxies with $0.01<z<0.14$ and integral-field spectroscopy from the
ongoing MaNGA survey. For each galaxy, we obtain two-dimensional maps and
radial profiles for three spectroscopically-measured parameters that are
sensitive to the recent SFH: D$_n$(4000) (the 4000\AA\ break), EW(H$\delta_A$)
(equivalent width of the H$\delta$ absorption line), and EW(H$\alpha$)
(equivalent width of the H$\alpha$ emission line). We find the majority of the
spaxels in these galaxies are consistent with models with continuously
declining star formation rate, indicating that starbursts occur rarely in local
galaxies. We classify the galaxies into three classes: fully star-forming (SF),
partly quenched (PQ) and totally quenched (TQ), according to the fraction of
quenched area within 1.5 times the effective radius, $f_Q(1.5R_e)$. We find
that galaxies less massive than $10^{10}$M$_{\odot}$ present at most weak
radial gradients in all the diagnostic parameters. In contrast, galaxies with
stellar mass above $10^{10}$M$_{\odot}$ present significant gradients in all
the three diagnostic parameters if classified as SF or PQ, but show weak
gradients in D$_n$(4000) and EW(H$\delta_A$) and no gradients in EW(H$\alpha$)
if in the TQ class. This implies the existence of a critical stellar mass, at
$\sim10^{10}$M$_{\odot}$, above which the star formation in a galaxy gets
shutdown from the inside out. Galaxies tend to evolve synchronously from inner
to outer regions before their mass reaches the critical value. We have further
divided the sample at fixed mass by both bulge-to-total luminosity ratio and
morphological type, finding that our conclusions hold regardless of these
factors: it appears that the presence of a central dense object is not a
driving parameter, but rather a byproduct of the star formation cessation
process.
