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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.