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We use TNG and EAGLE hydrodynamic simulations to investigate the centralgalaxy - dark matter halo relations that are needed for a halo-based empiricalmodel of star formation in galaxies. Using a linear dimension reductionalgorithm and a model ensemble method, we find that for both star-forming andquenched galaxies, the star formation history (SFH) is tightly related to thehalo mass assembly history (MAH). The quenching of a low-mass galaxy is mainlydue to the infall-ejection process related to a nearby massive halo, while thequenching of a high-mass galaxy is closely related to the formation of amassive progenitor in its host halo. The classification of star-forming andquenched populations based solely on halo properties contains contaminationproduced by sample imbalance and overlapping distributions of the twopopulations. Guided by the results from hydrodynamic simulations, we build anempirical model to predict the SFH of central galaxies based on the MAH oftheir host halos, and we model the star-forming and quenched populationsseparately. Our model is based on the idea of adopting star formation templatesfrom hydrodynamic simulations to reduce model complexity. We use various teststo demonstrate that the model can recover star formation histories ofindividual galaxies, and can statistically reproduce the galaxy bimodaldistribution, stellar mass - halo mass and star formation rate - halo massrelations from low to high redshift, and assembly bias. Our study provides aframework of using hydrodynamic simulations to discover, and to motivate theuse of, key ingredients to model galaxy formation using halo properties.

How to empirically model star formation in dark matter halos: I. Inferences about central galaxies from numerical simulations