We construct empirical models of star-forming galaxy evolution assuming that individual galaxies evolve along well-known scaling relations between stellar mass, gas mass and star formation rate following a simple description of chemical evolution. We test these models by a comparison with observations and with detailed Magneticum high resolution hydrodynamic cosmological simulations. Galaxy star formation rates, stellar masses, gas masses, ages, interstellar medium and stellar metallicities are compared. It is found that these simple lookback models capture many of the crucial aspects of galaxy evolution reasonably well. Their key assumption of a redshift dependent power law relationship between galaxy interstellar medium gas mass and stellar mass is in agreement with the outcome of the complex Magneticum simulations. Star formation rates decline towards lower redshift not because galaxies are running out of gas, but because the fraction of the cold ISM gas, which is capable of producing stars, becomes significantly smaller. Gas accretion rates in both model approaches are of the same order of magnitude. Metallicity in the Magneticum simulations increases with the ratio of stellar mass to gas mass as predicted by the lookback models. The mass metallicity relationships agree and the star formation rate dependence of these relationships is also reproduced. We conclude that these simple models provide a powerful tool for constraining and interpreting more complex models based on cosmological simulations and for population synthesis studies analyzing integrated spectra of stellar populations.
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