Constraint on the inflow/outflow rates in star-forming galaxies at z~1.4
  from molecular gas observations
  We constrain the rate of gas inflow into and outflow from a main-sequence
star-forming galaxy at z~1.4 by fitting a simple analytic model for the
chemical evolution in a galaxy to the observational data of the stellar mass,
metallicity, and molecular gas mass fraction. The molecular gas mass is derived
from CO observations with a metallicity-dependent CO-to-H2 conversion factor,
and the gas metallicity is derived from the H{\alpha} and [NII]{\lambda} 6584
emission line ratio. Using a stacking analysis of CO integrated intensity maps
and the emission lines of H{\alpha} and [NII], the relation between stellar
mass, metallicity, and gas mass fraction is derived. We constrain the inflow
and outflow rates with least-chi-square fitting of a simple analytic chemical
evolution model to the observational data. The best-fit inflow and outflow
rates are ~1.7 and ~0.4 in units of star-formation rate, respectively. The
inflow rate is roughly comparable to the sum of the star-formation rate and
outflow rate, which supports the equilibrium model for galaxy evolution; i.e.,
all inflow gas is consumed by star formation and outflow.
