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We study the gas inflow rate ($\zeta_{\rm inflow}$) and outflow rate($\zeta_{\rm outflow}$) evolution of local Milky Way-mass star-forming galaxies(SFGs) since $z=1.3$. The stellar mass growth history of Milky Way-massprogenitor SFGs is inferred from the evolution of the star formation rate(SFR)$-$stellar mass ($M_{\ast}$) relation, and the gas mass ($M_{\rm gas}$) isderived using the recently established gas scaling relations. With the$M_{\ast}+M_{\rm gas}$ growth curve, the net inflow rate $\kappa$ is quantifiedat each cosmic epoch. At $z\sim 1.3$, $\kappa$ is comparable with the SFR,whereas it rapidly decreases to $\sim 0.15\times$SFR at $z=0$. We thenconstrain the average outflow rate $\zeta_{\rm outflow}$ of progenitor galaxiesby modeling the evolution of their gas-phase metallicity. The best-fit$\zeta_{\rm outflow}$ is found to be $(0.5-0.8)\times$SFR. Combining $\kappa$and $\zeta_{\rm outflow}$, we finally investigate the evolution of $\zeta_{\rminflow}$ since $z=1.3$. We find that $\zeta_{\rm inflow}$ rapidly decreases by$\sim$80\% from $z=1.3$ to $z=0.5$. At $z<0.5$, $\zeta_{\rm inflow}$continuously decreases but with a much lower decreasing rate. Implications ofthese findings on galaxy evolution are discussed.

The inflow and outflow rate evolution of local Milky Way-mass star-forming galaxies since z=1.3