Constraining galactic baryon cycle using the galaxy stellar-to-halo mass relations

Galaxies display several well-behaved scaling relations between their properties, such as the star formation rate-stellar mass relation (the main sequence) and the stellar mass-halo mass relation (SHMR). In principle, these scaling relations could imply different star formation histories (SFHs) of galaxies and different constraints on galaxy formation physics. In this paper, we derive the SFHs of galaxies by assuming that they always follow the SHMRs at different redshifts and use an empirical model to constrain key processes in their baryon cycle. It is found that, besides cold accretion due to halo growth, outflow of gas produced by stellar feedback has to be recycled to sustain the derived SFHs of galaxies. The recycled fraction is strongly affected by the baryon fraction in accreted low-mass haloes and the mass loading factor which quantifies the ratio between the galactic outflow rate and star formation rate. Our fiducial model predicts that around $20-60\%$ of outflow is recycled in $\sim0.5-4Gyrs$, while simulations predict a slightly higher recycle fraction and a lower recycle time. We argue that strong constraints on the baryon cycle process can be obtained from future observation of the circum-galactic medium (CGM) of galaxies, such as the gas cooling rate of CGM. We also find that the implied SFHs from the SHMRs indicate that galaxies stay on the main sequences only for part of their lifetimes. Our model reproduces the evolution of the mass-metallicity relation as well.