It can certainly be argued that we already have incontrovertible evidence for some form of biased hierarchical galaxy formation, particularly after the discovery of strongly clustered Lyman-break objects at z~3 (Steidel et al. 1998). The prediction of these models is, after all, that we expect stronger galaxy clustering in the most massive haloes (Baugh et al. 1998). These massive systems would then represent the progenitors of cluster galaxies in the local Universe.
However this population cannot directly represent the formation of the most massive present-day galaxies (e.g. ellipticals). Even correcting for the possible effects of dust, the inferred star-formation rates in typical Lyman-break objects are too modest (typically <50M(sun)yr-1, falling an order of magnitude short of the ~1000M(sun)yr-1 required to form the stars in the most massive ellipticals on a timescale of <1Gyr). This leaves a major unanswered question. When were the bulk of the stars in elliptical galaxies formed, and how does this fit in with current theories of biased hierarchical galaxy formation? This is a fundamental issue, since ellipticals represent the most massive galaxies in the local Universe. They also appear to be intimately related to the quasar phenomenon (Kormendy & Richstone 1995, Magorrian et al. 1998, Gebhardt et al. 2000).
For many years the view was held that these galaxies formed the bulk of their stars in a single, explosive burst of star formation at high redshift, after which their stellar populations evolved passively (e.g. Tinsley & Gunn 1976). The discovery of a number of very old elliptical galaxies at high redshift lends weight to this hypothesis (e.g. Dunlop et al. 1996). Furthermore, Ellis et al. (1997) found that the scatter in the colour-magnitude relation of early-type galaxies is very small in clusters at z~0.5, suggesting that the bulk of the star formation occurred at z>3. In the field, however, the situation is more uncertain. Abraham et al. (1999) argue that many early-type field galaxies have experienced a major phase of star formation since z=1. In short, the formation redshift for massive ellipticals is still a major unanswered question.
If most elliptical galaxies formed at very high redshift (z>3), this would be in agreement with the monolithic collapse scenario expected in both the isocurvature CDM (Peebles 1998) or warm dark matter models (Columbi, Dodelson & Widrow 1995; Moore et al. 1999). Both models predict the assembly of elliptical galaxies at z>3 in single collapse events. This is in stark contrast with the hierarchical CDM models of galaxy formation, in which typical elliptical galaxies form from the merging of intermediate-mass disks at lower redshifts (e.g. Kauffmann, Charlot & White 1996; Baugh, Cole & Frenk 1996). In rich clusters the distinction between these models becomes somewhat blurred, since hierarchical galaxy formation predicts a much earlier epoch of star formation and merging activity (Kauffmann & Charlot 1998). For more typical ellipticals, however, we can form a clear and unambiguous test by determining the abundance of passively evolved ellipticals at z>2. The galaxy colours, clustering and links with the SCUBA and X-ray population provide further constraints on formation scenarios (see below) but the basic goal of this proposal is to determine the comoving number density of passively evolved ellipticals from a representative volume in the crucial era at z>2.
As we will see below, to detect at z=3 an elliptical galaxy that has an L* luminosity today and which formed at z>5 requires surveying to a point source equivalent depth of K~23. (The galaxy itself may be brighter, but ellipticals are rather large and of low average surface brightness.) Over a wide parameter range we should then expect to find all the most massive elliptical galaxies (those more luminous than 4L*) in the redshift range z=2-4. In the local universe, such objects have a space density of 1.5X10-5 Mpc-3 (Im, Griffith and Ratnatunga 1996, Kochanek et al. 2001).
Monolithic models. In a pure monolithic scenario, with no merging history at all, the co-moving space density of massive galaxies is the same as today. Assuming a standard cosmology with omegam=0.3 and lambda=0.7, we would expect to find ~100 4L* ellipticals in the range z=2-4 over our survey area of 0.77sq. degs. Down to 2L* we would find ~1000, with ~5000 at L*.
Hierarchical models. In hierarchical models, the abundance of massive ellipticals drops sharply with redshift. For a high density CDM model, the abundance at z=2 drops by a factor ~13 compared to the local abundance, and by a factor ~30 by z=3. For a low density lambda CDM model, the drop is by a factor ~3 at z=2 and a factor ~11 at z=3 (Kauffmann and Charlot 1998). Clearly a definitive test needs to probe to z=3, and to collect a reasonably large sample. With ~1000 2L* objects predicted for the monolithic scenario, lambda CDM predicts ~100, and high density CDM predicts ~30. As well as testing the monolithic idea, one can then also discriminate between the variety of hierarchical models. In addition to pure counts, colours will be crucial, both for distinguishing different types of galaxy, and for constraining the formation epoch (see Section 5.6).
Recent pioneering work by Daddi et al. (2000) has shown the power of wide area K-band surveys, but by reaching K~19.5 they were only able to probe bright elliptical galaxies to z~1.5.
Surveys reaching K~23 do, of course, already exist (cf. the deep surveys with the Keck NIRC camera, Djorgovski et al. 1995), but previous ultradeep imaging has been restricted to very small fields of view (~1-2 arcmin2). With typically ~30 sources per field, the samples are clearly insufficient to conduct meaningful statistics, particularly for rare, very red objects.
Results on the abundance of high-z (z>2) passive ellipticals have therefore been totally inconclusive. Cowie et al. (1994) found little evidence for such an old population to a limit of K=22, but this may be due to aperture correction affects (Dunlop & Gloag, in preparation). Djorgovski et al. (1995) and Bershady, Lowenthal & Koo (1998) find a few faint EROs, but from very small samples of ~ 30 sources they cannot draw firm conclusions. Even in a monolithic scenario one would only expect ~1 elliptical galaxy of 2XL* in such small fields. With a thousand-fold increase in area coverage, the proposed WFCAM survey will allow the UK community to make a significant leap forward in this area.