Comparison of the VIMOS-VLT Deep Survey with the Munich semi-analytical
  model. II. The colour-density relation up to z=1.5
  [Abridged] We perform on galaxy mock catalogues the same colour-density
analysis made by Cucciati et al. (2006) on a 5 Mpc/h scale using the VVDS-Deep
survey, and compare the results from mocks with observed data. We use mocks
with the same flux limits (I=24) as the VVDS (CMOCKS), built using the semi-
analytic model by De Lucia & Blaizot (2007) applied to the Millennium
Simulation. From CMOCKS, we extracted samples of galaxies mimicking the VVDS
observational strategy (OMOCKS). We computed the B-band Luminosity Function LF
and the colour-density relation (CDR) in the mocks. We find that the LF in
mocks roughly agrees with the observed LF, but at z<0.8 the faint-end slope of
the model LF is steeper than the VVDS one. Computing the LF for early and late
type galaxies, we show that mocks have an excess of faint early-type and of
bright late-type galaxies with respect to data. We find that the CDR in OMOCKS
is in excellent agreement with the one in CMOCKS. At z~0.7, the CDR in mocks
agrees with the VVDS one (red galaxies reside mainly in high densities). Yet,
the strength of the CDR in mocks does not vary within 0.2<z<1.5, while the
observed relation flattens with increasing z and possibly inverts at z=1.3. We
argue that the lack of evolution in the CDR in mocks is not due only to
inaccurate prescriptions for satellite galaxies, but that also the treatment of
central galaxies has to be revised. The reversal of the CDR can be explained by
wet mergers between young galaxies, producing a starburst event. This should be
seen on group scales. A residual of this is found in observations at z=1.5 on
larger scales, but not in the mocks, suggesting that the treatment of physical
processes affecting satellites and central galaxies in models should be
revised.
