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The evolution of baryonic mass function of galaxies to z=3

We combine the published stellar mass function (SMF) and gas scaling relations to explore the baryonic (stellar plus cold gas) mass function (BMF) of galaxies to redshift $z=3$. We find evidence that at log$(M_{\rm baryon}/M_{\bigodot})>11.3$, the BMF evolves little since $z\sim 2.2$. With the evolution of BMF and SMF, we investigate the baryon net accretion rate ($\dotρ_{\rm baryon}$) and stellar mass growth rate ($\dotρ_{\rm star}$) for the galaxy population of log($M_{\rm star}/M_{\bigodot}$)>10. The ratio between these two quanties, $\dotρ_{\rm baryon}$/$\dotρ_{\rm star}$, decreases from $\dotρ_{\rm baryon}$/$\dotρ_{\rm star}\sim$2 at $z\sim 2.5$ to $\dotρ_{\rm baryon}$/$\dotρ_{\rm star}<$0.5 at $z\sim 0.5$, suggesting that massive galaxies are transforming from the "accretion dominated" phase to the "depletion dominated" phase from high$-z$ to low$-z$. The transition of these two phases occurs at $z\sim1.5$, which is consistent with the onset redshift of the decline of cosmic star formation rate density. This provides evidence to support the idea that the decline of cosmic star formation rate density since $z\sim1.5$ is mainly resulted from the decline of baryon net accretion rate and star formation quenching in galaxies.