An Empirical Representation of a Physical Model for the ISM [C ii], CO, and [C i] Emission at Redshift 1 ? z ? 9

Sub-millimeter emission lines produced by the interstellar medium (ISM) are strong tracers of star formation and some main targets line intensity mapping (LIM) surveys. In this work we present an empirical multi-line model that simultaneously covers mean, scatter, correlations [CII], CO J=1-0 to J=5-4, [CI] in redshift range $1\leq z\leq9$. We assume galaxy ISM luminosity versus halo mass relations can be described double power laws with redshift-dependent log normal scatter. The parameters then derived fitting state art semi-analytic simulation results have successfully reproduced multiple sub-millimeter observations at $0\leq z\lesssim6$. cross check statistics predicted our model, finding $z\geq1$ reproduces simulated intensities fractional error less than about 10%. difference is 25% for spectra. Grounded on physically-motivated self-consistent simulations, computationally efficient will helpful forecasting upcoming LIM