We present the first results of hydrodynamical simulations that follow the formation of galaxies to the present day in nearly spherical regions of radius \sim 20 h ^ { -1 } { Mpc } drawn from the Millennium Simulation ( Springel et al . ) .
The regions have mean overdensities that deviate by ( -2 , -1 , 0 , +1 , +2 ) \sigma from the cosmic mean , where \sigma is the rms mass fluctuation on a scale of \sim 20 h ^ { -1 } { Mpc } at z = 1.5 .
The simulations have mass resolution of up to \sim 10 ^ { 6 } h ^ { -1 } { M } _ { \odot } , cover the entire range of large-scale cosmological environments , including rare objects such as massive clusters and sparse voids , and allow extrapolation of statistics to the ( 500 h ^ { -1 } { Mpc } ) ^ { 3 } Millennium Simulation volume as a whole .
They include gas cooling , photoheating from an imposed ionising background , supernova feedback and galactic winds , but no AGN .
In this paper we focus on the star formation properties of the model .
We find that the specific star formation rate density at z \lesssim 10 varies systematically from region to region by up to an order of magnitude , but the global value , averaged over all volumes , closely reproduces observational data .
Massive , compact galaxies , similar to those observed in the GOODS fields ( Wiklind et al .
) , form in the overdense regions as early as z = 6 , but do not appear in the underdense regions until z \sim 3 .
These environmental variations are not caused by a dependence of the star formation properties on environment , but rather by a strong variation of the halo mass function from one environment to another , with more massive haloes forming preferentially in the denser regions .
At all epochs , stars form most efficiently in haloes of circular velocity v _ { c } \sim 250 { km } { s } ^ { -1 } .
However , the star-formation history exhibits a form of “ downsizing ” ( even in the absence of AGN feedback ) : the stars comprising massive galaxies at z = 0 have mostly formed by z = 1 - 2 , whilst those comprising smaller galaxies typically form at later times .
However , additional feedback is required to limit star formation in massive galaxies at late times .