:  Light Cone Construction

The lightcones were constructed using the MoMaf code (Blaizot et al. (2005)) with some modifications fully described in section 2.2 of Henriques et al. (2012)

The millennium simulation has side of 500Mpc/h which is considerably smaller than, for example, the commoving distance to z=2. In order to build a lightcone it is then necessary to periodically replicate the simulation box, which can lead to multiple appearances of the same object. Blaizot et al. (2005) suggested applying a set of transformations (rotations, translations and inversions) in order for these duplicates not to fall on a nearly regular lattice. However Kitzbichler & White (2007) showed that, for lightcones of relatively small solid angle, the central line-of-sight can be chosen in such a direction that appearances of multiple images of the same object are minimized. We therefore use this method.

The time between stored snapshots for the Millennium Simulation varies between 100 and 380 Myr. This means that the intrinsic properties of galaxies are not generally available at the time corresponding to their commoving distance. Rather they must be taken from the stored snapshot which is closest to their lightcone position. Hence, galaxies with redshift (zi+zi-1)/2<z<(zi+zi+1)/2 are assigned the physical properties stored at zi. No interpolation in physical properties between snapshots is applied (which has no impact in the statistical properties of galaxies).

On the other hand, the apparent luminosities and colours of galaxies depend strongly on their redshifts through the conversion between rest- and observed-frame photometric bands and through the inverse square dependence of apparent luminosity on distance. The final redshift of the galaxy in the lightcone is not available at the time observed-frame luminosities are computed in the semi-analytic model. However, there will be two extreme redshifts that bracket it. We compute apparent observed-frame luminosities (for fixed intrinsic properties) using these upper and lower limits, and once the galaxy is placed in the lightcone, we interpolate to obtain final observed-frame quantities.