is the turnover mass, $\gamma_{M_*}$ control the slope of the relation at low mass, $\mu_{M_*}$ is the coefficient. $\Sigma_{\rm TO}$, $\gamma_{\Sigma_*}$ and $\mu_{\Sigma_*}$ are the same as Equation \[eq:sigma-z-fit\]. We apply the Equation \[eq:fmr-fit\] to fit our radial bin sample, and list the best-fitted results in Table \[table2\]. As shown in Table \[table2\], the residuals between observed metallicity and $M_*$ – $\Sigma_*$ – $Z$ relation for all spaxels show smaller scatter than that of the $\Sigma_*$ – $Z$ relation as expected.

![image](plot_fmr_fit_n2o2.pdf){width="60.00000%"}

[@lrr@]{} $p$ & $\Sigma_*$ – $Z$ & $M_*$ – $Z$\
Pearson & 0.746 & 0.668\
Spearman & 0.798 & 0.684\
Kendall & 0.579 & 0.441\

[@lrrlrr@]{} ${\rm log}(M_*/M_\odot)$ & & $[7.8, 11.0]$ & & & $[9.5, 11.0]$\
Parameters & $\Sigma_*$ – $Z$ & $M_*$ – $\Sigma_*$ – $Z$ & & $\Sigma_*$ – $Z$ & $M_*$ – $\Sigma_*$ – $Z$\
$\rm 12+log(O/H)_o$ & 9.267 $\pm$ 0.018 & 9.320 $\pm$ 0.027 & & 9.267 $\pm$ 0.018 & 9.333 $\pm$ 0.032\
$\mu_{M_*}$ & – & 0.406 $\pm$ 0.107 & & – & 0.824 $\pm$ 0.467\
${\rm log}(M_{\rm TO})$ & – & 9.385 $\pm$ 0.140 & & – & 9.016 $\pm$ 0.314\
$\gamma_{M_*}$ & – & 1.062 $\pm$ 0.130 & & – 