In this work we develop a new method to turn a state-of-the-art hydrodynamical cosmological simulation of galaxy formation ( HYD ) into a simple semi-analytic model ( SAM ) .
This is achieved by summarizing the efficiencies of accretion , cooling , star formation , and feedback given by the HYD , as functions of the halo mass and redshift .
The SAM then uses these functions to evolve galaxies within merger-trees that are extracted from the same HYD .
Surprisingly , by turning the HYD into a SAM , we conserve the mass of individual galaxies , with deviations at the level of 0.1 dex , on an object-by-object basis , with no significant systematics .
This is true for all redshifts , and for the mass of stars and gas components , although the agreement reaches 0.2 dex for satellite galaxies at low redshift .
We show that the same level of accuracy is obtained even in case the SAM uses only one phase of gas within each galaxy .
Moreover , we demonstrate that the formation history of one massive galaxy provides sufficient information for the SAM to reproduce the population of galaxies within the entire cosmological box .
The reasons for the small scatter between the HYD and SAM galaxies are : a ) The efficiencies are matched as functions of the halo mass and redshift , meaning that the evolution within merger-trees agrees on average .
b ) For a given galaxy , efficiencies fluctuate around the mean value on time scales of 0.2-2 Gyr .
c ) The various mass components of galaxies are obtained by integrating the efficiencies over time , averaging out these fluctuations .
We compare the efficiencies found here to standard SAM recipes and find that they often deviate significantly .
For example , here the HYD shows smooth accretion that is less effective for low mass haloes , and is always composed of hot or dilute gas ; cooling is less effective at high redshift ; and star formation changes only mildly with cosmic time .
The method developed here can be applied in general to any HYD , and can thus serve as a common language for both HYDs and SAMs .