A well calibrated method to describe the environment of galaxies at all redshifts is essential for the study of structure formation. Such a calibration should include well understood correlations with halo mass, and the possibility to identify galaxi
es which dominate their potential well (centrals), and their satellites. Focusing on z = 1 and 2 we propose a method of environmental calibration which can be applied to the next generation of low to medium resolution spectroscopic surveys. Using an up-to-date semi-analytic model of galaxy formation, we measure the local density of galaxies in fixed apertures on different scales. There is a clear correlation of density with halo mass for satellite galaxies, while a significant population of low mass centrals is found at high densities in the neighbourhood of massive haloes. In this case the density simply traces the mass of the most massive halo within the aperture. To identify central and satellite galaxies, we apply an observationally motivated stellar mass rank method which is both highly pure and complete, especially in the more massive haloes where such a division is most meaningful. Finally we examine a test case for the recovery of environmental trends: the passive fraction of galaxies and its dependence on stellar and halo mass for centrals and satellites. With careful calibration, observationally defined quantities do a good job of recovering known trends in the model. This result stands even with reduced redshift accuracy, provided the sample is deep enough to preserve a wide dynamic range of density.
Galaxies grow primarily via accretion-driven star formation in discs and merger-driven growth of bulges. These processes are implicit in semi-analytical models of galaxy formation, with bulge growth in particular relating directly to the hierarchical
build-up of halos and their galaxies. In this paper, we consider several implementations of two semi-analytical models. Focusing on implementations in which bulges are formed during mergers only, we examine the fractions of elliptical galaxies and both passive and star-forming disk galaxies as functions of stellar and halo mass, for central and satellite systems. This is compared to an observational cross-matched SDSS+RC3 z ~ 0 sample of galaxies with accurate visual morphological classifications and M_{stellar} > 10^10.5 M_{sol}. The models qualitatively reproduce the observed increase of elliptical fraction with stellar mass, and with halo mass for central galaxies, supporting the idea that observed ellipticals form during major mergers. However, the overall elliptical fraction produced by the models is much too high compared with the z ~ 0 data. Since the passive -- i.e. non-star-forming -- fractions are approximately reproduced, and since the fraction which are star-forming disc galaxies is also reproduced, the problem is that the models overproduce ellipticals at the expense of passive S0 and spiral galaxies. Bulge-growth implementations (tuned to reproduce simulations) which allow the survival of residual discs in major mergers still destroy too much of the disc. Increasing the lifetime of satellites, or allowing significant disc regrowth around merger remnants, merely increases the fraction of star-forming disc galaxies. Instead, it seems necessary to reduce the mass ratios of merging galaxies, so that most mergers produce modest bulge growth in disc-galaxy remnants instead of ellipticals. [Abridged]
