$Z$ relation is shown with red dashed lines in Figure \[fig:plot\_lmass\_sur\_zoh\]. The mean value ($\mu$) and the standard deviation (scatter, $\sigma$) of the residuals when the predicted metallicity from the $\Sigma_*$ – $Z$ relation is subtracted from the observed values derived from N2O2 index are also listed in Table \[table2\]. $\mu_{\rm bin }$ and $\sigma_{\rm bin }$ represent the mean value and the scatter of the residuals for the radial bin sample, while $\mu_{\rm all}$ and $\sigma_{\rm all}$ are the mean value and the scatter of the residuals for all spaxels, respectively.

Since the local metallicities also strongly correlate with $M_*$ (see the upper panels in Figure \[fig:plot\_lmass\_sur\_zoh\], and $p$ values for $M_*$ – $Z$ in Table \[table1\]), we deduce that the remarkable scatter in the $\Sigma_*$ – $Z$ relation may be largely contributed by the variation of the stellar mass. Introducing this ingredient, we extend the $\Sigma_*$ – $Z$ relation (Equation \[eq:sigma-z-fit\]) to the following format: $$\label{eq:fmr-fit}
    \begin{split}
    {\rm 12+log(O/H)} = {\rm 12+log(O/H)_o} - \mu_{M_*} {\rm log}[1 + (\frac{M_{\rm TO}}{M_*})^{\gamma_{M_*}}]  \\
    - \mu_{\Sigma_*} {\rm log}[1 + (\frac{\Sigma_{\rm TO}}{\Sigma_*})^{\gamma_{\Sigma_*}}], 
    \end{split}$$ where $\rm 12 + log(O/H)_o$ is the asymptotic metallicity at high mass and high stellar mass surface density, $M_{\rm TO}$ 