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Sub-millimeter emission lines produced by the interstellar medium (ISM) arestrong tracers of star formation and are some of the main targets of lineintensity mapping (LIM) surveys. In this work we present an empiricalmulti-line emission model that simultaneously covers the mean, scatter, andcorrelations of [CII], CO J=1-0 to J=5-4, and [CI] lines in redshift range$1\leq z\leq9$. We assume the galaxy ISM line emission luminosity versus halomass relations can be described by double power laws with redshift-dependentlog normal scatter. The model parameters are then derived by fitting to thestate of the art semi-analytic simulation results that have successfullyreproduced multiple sub-millimeter line observations at $0\leq z\lesssim6$. Wecross check the line emission statistics predicted by the semi-analyticsimulation and our empirical model, finding that at $z\geq1$ our modelreproduces the simulated line intensities with fractional error less than about10%. The fractional difference is less than 25% for the power spectra. Groundedon physically-motivated and self-consistent galaxy simulations, thiscomputationally efficient model will be helpful in forecasting ISM emissionline statistics for upcoming LIM surveys.

An empirical representation of a physical model for the ISM [CII], CO, and [CI] emission at redshift $1\leq z\leq9$