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The observation that these distant ULIRGs appear to be very massive systems means that large amounts of raw material are needed to make one, implying that ULIRGs are likely to be found in regions with large concentrations of baryons. Therefore, in order to understand when, where and why ULIRGs exist, we must turn to galaxy and large-scale structure formation models to see where such large concentrations of baryons are predicted to be found. Modern structure formation models describe the evolution of the total mass distribution (comprising both non-baryonic and baryonic `cold' dark matter) via the evolution of initially Gaussian density fluctuations, which means that the evolution of the total mass distribution should be traced by the formation and evolution of galaxies in some determinable way. Density fluctuations in the dark matter distribution, commonly referred to as `halos', are predicted to undergo successive mergers over time to build halos of steadily increasing mass. Galaxies are predicted to form from the baryonic matter in these halos, driven either by inter- or intra-halo mergers, or passive collapse of baryons to the halo central regions, or some combination of all three mechanisms [Meza et al. 2003, Kobayashi 2004]. This framework of `biased' hierarchical buildup [Cole et al. 2000, Granato et al. 2000, Hatton et al. 2003], coupled with a Lambda cosmology [Spergel et al. 2003], has proven to be remarkably successful in explaining many aspects of galaxy and large-scale structure formation.

Within this framework, the largest concentrations of baryons are expected to be found within the most massive dark matter halos. A basic verification of this idea can be seen in the local Universe, where the most massive elliptical galaxies are almost invariably found within very rich galaxy clusters; which presumably correspond to large overdensities of baryons in the local Universe. The formation history of these very massive galaxies, even before the advent of sub-mm surveys, was controversial. The `naive' expectation from hierarchical theory would be that massive galaxies form relatively late and over a long period of time, representing successive mergers between dark matter halos, building up the required large baryon reservoirs [Baugh et al. 1998], and indeed some massive galaxies do appear to form in this way [van Dokkum et al. 1999, Tamura & Ohta 2003, Bell et al. 2004]. There is however observational evidence that many massive galaxies may form at high redshift and on short timescales, for example from the discovery of evolved systems at high redshift [Dunlop et al. 1996, Martini 2001, Blakeslee et al. 2003], the extremely tight K-band Hubble relation for radio galaxies [De Breuck et al. 2002] implying a very rapid early formation of the most massive galaxies [Rocca-Volmerange et al. 2004], and an inferred early star formation epoch from the colour-magnitude diagram in clusters at z = 0.5 [Ellis et al. 1997], implying that the stars in very massive local galaxies formed within a few Gyr of each other at z > 1.

The SMGs and Spitzer high z ULIRG samples appear to be perfect candidates for the formation events for those local massive ellipticals that appeared to form very early and very fast; they lie at z appeq 2.5 [Simpson et al. 2004, Chapman et al. 2005], which is a high enough redshift to make stars with the ages seen locally, their star formation rates are high enough to make all the stars in a local massive elliptical fast enough to satisfy the observed colour-scaling relationships, and their comoving number density is comparable to that of local gtapprox 3L* ellipticals [Scott et al. 2002, Chapman et al. 2004b]. Serious theoretical difficulties remain however. Early CDM-based galaxy formation models lacked the detailed astrophysics to explain the number of observed SMGs and their star formation rates [Granato et al. 2000, Somerville, Primack & Faber 2001, Guiderdoni et al. 1998]. Later models included improved treatments of starbursts, but still had to include further modifications to explain the observed sub-mm counts. These include a top-heavy initial mass function for the stars formed in bursts, so that the same sub-mm flux can be produced with lower star formation rates [Baugh et al. 2005] 8, modified treatments of virialization and the survival of subhalos to solve the `overmerging' problem in the standard Press-Schechter formalism and make the SFRs high enough [van Kampen et al. 1999, van Kampen et al. 2005], and modifications to gas cooling and supernova feedback [Granato et al. 2004].

Fundamentally, there are two testable basic predictions of these hierarchical models for high-redshift ULIRGs. Firstly, these ULIRGs should reside within rich environments, that is to say we should see clustering of other galaxies around the ULIRGs on length scales of < 5Mpc, representing galaxy overdensities resulting from the local overdensity of baryons. Testing this observationally is, however, difficult. At z < 1 there have been numerous successful measurements of galaxy overdensities around AGN using deep optical/near-IR imaging to find evolved systems [Wold et al. 2001, Wold et al. 2003], but at the mean redshift of high-redshift ULIRGs it is certainly not clear whether their local environments have built up overdensities of evolved galaxies, even if they are overdense in baryons. Secondly, we should observe the high-redshift ULIRGs themselves to cluster together strongly on the sky, or in other words clustering of just the high-redshift ULIRGs on length scales gtapprox 25 Mpc. This prediction is a consequence of the assumed form of the evolution of density fluctuations with redshift; rare fluctuations in the underlying mass distribution are predicted to cluster together on the sky, with the strength of clustering depending on the degree of rarity [Bardeen et al. 1986]. Very massive halos (those with masses gtapprox 1014 Modot), which are universally predicted to be extremely rare at high redshift, are therefore predicted to cluster together very strongly (e.g. [Moscardini et al. 1998, Kauffmann et al. 1999, Mo & White 2002]). This clustering should be traced by very massive galaxies, as only the most massive halos contain sufficient baryon reservoirs to form these galaxies. This also means that the clustering strength of massive galaxies should translate straightforwardly to measure of halo mass [Percival et al. 2003]. Strong clustering among high-redshift ULIRGs is also predicted if, as some suspect, they are part of a population uniting QSOs and spheroids [Magliocchetti et al. 2001]. Measuring this form of clustering observationally is however also difficult, requiring either gtapprox 50 sources with spectroscopic redshifts so that `associations' in redshift space between different sources can be searched for, or a minimum of several hundred sources with a reasonably well constrained redshift distribution, and found over a large enough area of sky such that the length scales of interest can be examined.

Despite these difficulties, numerous studies of both the environments of high-redshift ULIRGs, and their clustering, have taken place, and while these studies are not (yet) conclusive, they do generally lend support to the idea that high-redshift ULIRGs form within massive dark matter halos. Considering environment studies first; near-IR imaging studies of the environmental richness of ULIRGs over 0.5 < z < 1.5 [Farrah et al. 2004b] have shown that these systems reside in richer environments than their local counterparts on average, and that some reside in moderate rich clusters even at z gtapprox 1, though it is not clear whether this represents a genuine increase in environmental richness for ULIRGs, or whether this just reflects the global increase in `bias' over 0 < z < 1. At lower redshifts, LIRGs and ULIRGs have also been found in clusters [Duc et al. 2004, Lemonon et al. 1998, Kleinmann et al. 1988]. Turning to higher redshifts, then several authors have noted overdensities of sub-mm sources around high-redshift systems that are thought to reside within mass overdensities, including z ~ 4 radio galaxies [Stevens et al. 2003, De Breuck et al. 2004] (several of these sub-mm sources are also detected in the X-ray, suggesting the presence of obscured AGN [Smail et al. 2003] and seen as z ~ 3 Lyman Break galaxies [Chapman et al. 2001, Geach et al. 2005].

Turning to high-z ULIRG clustering; early efforts to measure angular clustering on the sky came up against the limitations of available instrumentation; at the time of writing there exists no sub-mm array instrument that can map large enough areas of the sky to the required depths (though SCUBA2, APEX and Herschel, are coming soon). No clear picture has therefore emerged; some sub-mm surveys have uncovered tentative hints of clustering on scales of a few arcminutes [Scoville et al. 2000], whereas others show no signs of clustering whatsoever [Borys et al. 2003]. An intriguing result from these wide field surveys is that the high-redshift ULIRGs appear to trace moderately bright X-ray survey sources on the sky, even though the direct overlap between the two populations is minimal [Almaini et al. 2003]. This could suggest that the high-redshift sub-mm and X-ray populations are tracing the same, overdense dark matter halos. More recent efforts to measure SMG clustering using spectroscopic redshifts have met with greater success, resulting in a reliable detection of clustering for the first time [Blain et al. 2004a]. The strength of the clustering, while significant, is not particularly strong, at r0 = 6.9 ± 2.2 (comoving). This clustering strength is consistent with high-redshift ULIRGs residing in ~ 1013 Modot halos which will eventually become the cores of rich clusters in the local Universe, but the relatively high redshift of the sources in this sample, coupled with the significant error on their clustering and the unknown growth modes of dark matter overdensities (see e.g. [Matarrese et al. 1997, Moscardini et al. 1998]) leaves other possible interpretations open. More precise measurements of both high-redshift ULIRGs, and other ULIRGs at lower (and higher) redshifts are needed to resolve this issue. The new Spitzer ULIRG surveys, sampling much larger volumes and linear dimensions than current submm/mm surveys, can be expected open up this field of enquiry dramatically.

8 an interesting conundrum from this model is that while the sub-mm counts are predicted to be dominated by bursts, these bursts would be responsible for making only a small fraction of the stellar mass in evolved ellipticals in the local Universe if their IMFs are top heavy. Back.

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