  The stellar mass-to-light ratio gradient in SDSS $r-$band $\nabla (M_*/L_r)$
of a galaxy depends on its mass assembly history, which is imprinted in its
morphology and gradients of age, metallicity, and stellar initial mass function
(IMF). Taking a MaNGA sample of 2051 galaxies with stellar masses ranging from
$10^9$ to $10^{12}M_\odot$ released in SDSS DR15, we focus on face-on galaxies,
without merger and bar signatures, and investigate the dependence of the 2D
$\nabla (M_*/L_r)$ on other galaxy properties, including $M_*/L_r$-colour
relationships by assuming a fixed Salpeter IMF as the mass normalization
reference. The median gradient is $\nabla M_*/L_r\sim -0.1$ (i.e., the
$M_*/L_r$ is larger at the centre) for massive galaxies, becomes flat around
$M_*\sim 10^{10} M_{\odot}$ and change sign to $\nabla M_*/L_r\sim 0.1$ at the
lowest masses. The $M_*/L_r$ inside a half light radius increases with
increasing galaxy stellar mass; in each mass bin, early-type galaxies have the
highest value, while pure-disk late-type galaxies have the smallest.
Correlation analyses suggest that the mass-weighted stellar age is the dominant
parameter influencing the $M_*/L_r$ profile, since a luminosity-weighted age is
easily affected by star formation when the specific star formation rate (sSFR)
inside the half light radius is higher than $10^{-3} {\rm Gyr}^{-1}$. With
increased sSFR gradient, one can obtain a steeper negative $\nabla (M_*/L_r)$.
The scatter in the slopes of $M_*/L$-colour relations increases with increasing
sSFR, for example, the slope for post-starburst galaxies can be flattened to
$0.45$ from the global value $0.87$ in the $M_*/L$ vs. $g-r$ diagram. Hence
converting galaxy colours to $M_*/L$ should be done carefully, especially for
those galaxies with young luminosity-weighted stellar ages, which can have
quite different star formation histories.

Astrophysics of Galaxies