stellar mass – metallicity relation and stellar mass – metallicity – SFR relation have been investigated for decades [e.g. @Tremonti2004; @Mannucci2010a; @Ylgao2017]. Previous works suppress the scatter in MZR by introducing the global SFR, finding that at a certain stellar mass, the metallicity scales up remarkably when the stellar mass increases, and scales down slightly when the SFR increases. However, the scatter in the $\Sigma_*$ – $Z$ relation remains significant (about 0.08 dex for the O3N2 estimator) in @Barrera-Ballesteros2016a. In this work, we take the global stellar mass into consideration, because the metallicity also show strong dependence on $M_*$, as can be seen in Figure \[fig:plot\_lmass\_sur\_zoh\].

We modify the MZR relation suggested by [@Moustakas2011] to the following formalism: $$\label{eq:sigma-z-fit}
    {\rm 12+log(O/H)} = {\rm 12+log(O/H)_o} - {\mu_{\Sigma_*}} {\rm log}[1 + (\frac{\Sigma_{\rm TO}}{\Sigma_*})^{\gamma_{\Sigma_*}}],$$ where $\rm 12 + log(O/H)_o$ is the asymptotic metallicity at high stellar mass surface densities, $\Sigma_{\rm TO}$ is the turnover mass surface density, $\gamma_{\Sigma_*}$ controls the slope of the relation at low mass surface densities, and $\mu_{\Sigma_*}$ is a multiplying coefficient. We apply the Equation \[eq:sigma-z-fit\] to fit our radial bin sample (Section \[subsec:metallicity-correlation\]), and list the best-fit results in Table \[table2\]. The locus of the best-fit $\Sigma_*$ – 