the N2O2 index. The blue points connected by black lines represent the median values with different $M_*$ (or $\Sigma_*$) bins at a fixed $\Sigma_*$ (or $M_*$) bin. The arrows in each panel point to the direction of increasing $M_*$ or $\Sigma_*$. The contour lines represent the distribution for $85\%$ of all the spaxels, each contour enclose the $17\%$, consecutively. The red dashed line in the $\Sigma_*$ – $Z$ plot is the best-fit $\Sigma_*$ – $Z$ relation (see details in Section \[subsec:relation-z-mass-surface\]).

As can be seen in this figure, the metallicity increases together with $\Sigma_*$ at a certain stellar mass, and also increases with $M_*$ at a fixed surface mass density. In star-forming galaxies, the inner regions, where the surface mass density tends to be higher, are typically more metal-rich than the outskirt. This is in agreement with the previous findings that star-forming galaxies usually have negative metallicity gradients [e.g. @Zaritsky1994; @Barrera-Ballesteros2016a; @Lin2017; @Lian2018].

On the other hand, for two regions with the same $\Sigma_*$ but residing in different galaxies with different $M_*$, the one in the more massive galaxy appears be more metal-rich than the other, mainly for these galaxies in the low-mass region (${\rm log}(M_*/M_\odot) \leq 10.0$), presumably indicative 