Abstract
We study the gas inflow rate ($\zeta_inflow$) and outflow rate
($\zeta_outflow$) evolution of local Milky Way-mass star-forming galaxies
(SFGs) since $z=1.3$. The stellar mass growth history of Milky Way-mass
progenitor SFGs is inferred from the evolution of the star formation rate
(SFR)$-$stellar mass ($M_\ast$) relation, and the gas mass ($M_gas$) is
derived using the recently established gas scaling relations. With the
$M_\ast+M_gas$ growth curve, the net inflow rate $\kappa$ is quantified
at each cosmic epoch. At $z1.3$, $\kappa$ is comparable with the SFR,
whereas it rapidly decreases to $0.15\times$SFR at $z=0$. We then
constrain the average outflow rate $\zeta_outflow$ of progenitor galaxies
by modeling the evolution of their gas-phase metallicity. The best-fit
$\zeta_outflow$ is found to be $(0.5-0.8)\times$SFR. Combining $\kappa$
and $\zeta_outflow$, we finally investigate the evolution of $\zeta_\rm
inflow$ since $z=1.3$. We find that $\zeta_inflow$ rapidly decreases by
$\sim$80\% from $z=1.3$ to $z=0.5$. At $z<0.5$, $\zeta_inflow$
continuously decreases but with a much lower decreasing rate. Implications of
these findings on galaxy evolution are discussed.
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