systematic effect with $M_*$, while the rest scatter (0.07 dex) is caused by other galactic parameters and/or intrinsic scatter (0.04 dex, N2O2) in metallicity calibration. This tight $M_*$ – $\Sigma_*$ – $Z$ relation extends over three orders of magnitude in the global stellar mass, nearly four orders of magnitude in the mass surface density, a factor of 6 in metallicity with N2O2 index.

In the $bottom$ panels of Figure \[fig:fmr\_fit\], we show the same relations but for massive galaxies. We note that the scatter in $\Sigma_*$ – $Z$ relation is 0.068 dex, while reduced slightly to 0.061 dex in $M_*$ – $\Sigma_*$ – $Z$ relation. The much smaller reduction in scatter, less than 0.01 dex, suggests that the local metallicity distribution in massive galaxies probably has no or much weak dependence on their global stellar masses.

Discussion {#sec:discussion}
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Comparison with Previous Studies {#subsec:comparison}
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In this work, we analyze the dependence of metallicity on local stellar mass surface density and global stellar mass in a sample of 1122 SFGs from the MaNGA survey. Figure \[fig:plot\_lmass\_sur\_zoh\] shows that the metallicity increases largely with increasing $M_*$ (or $\Sigma_*$) at a fixed $\Sigma_*$ (or $M_*$) value. Furthermore, we perform PCOR analyses to 