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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 itsmorphology 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 $M_*/L_r$-colourrelationships by assuming a fixed Salpeter IMF as the mass normalizationreference. 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 thelowest masses. The $M_*/L_r$ inside a half light radius increases withincreasing galaxy stellar mass; in each mass bin, early-type galaxies have thehighest value, while pure-disk late-type galaxies have the smallest.Correlation analyses suggest that the mass-weighted stellar age is the dominantparameter influencing the $M_*/L_r$ profile, since a luminosity-weighted age iseasily affected by star formation when the specific star formation rate (sSFR)inside the half light radius is higher than $10^{-3} {\rm Gyr}^{-1}$. Withincreased sSFR gradient, one can obtain a steeper negative $\nabla (M_*/L_r)$.The scatter in the slopes of $M_*/L$-colour relations increases with increasingsSFR, 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. Henceconverting galaxy colours to $M_*/L$ should be done carefully, especially forthose galaxies with young luminosity-weighted stellar ages, which can havequite different star formation histories.

SDSS-IV MaNGA: Stellar M/L gradients and the M/L-colour relation in galaxies