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Taken as a whole, the observations of local Luminous Infrared Galaxies suggest that, at lower luminosities at least, they are dominated by starburst emission. The continuity of the LHCN vs LFIR relation [Gao & Solomon 2004] provides circumstantial evidence that most, if not all, Luminous IR Galaxies are starburst powered. Their sample, however, as well as many others quoted above, suffers from the low space density of ULIRGs, with only 6 classical ULIRGs (Lir > 1012 Lodot) and only two with Lir > 1012.2 Lodot). The LRSN discovered in compact ULIRGs would seem to indicate starburst dominance in these systems, however we do not understand enough about these LRSN to establish a star-formation rate or a starburst bolometric luminosity, leaving open the possibility of significant if not dominant AGN power even in the best studied source Arp 220. ULIRGs are generally under-luminous in the X-rays compared to classical AGN, requiring sensitive, high energy, observations to detect them. Evidence for very high X-ray obscuring columns is mounting, which could explain the low observed flux levels, and estimates of the importance of the X-ray-detected, obscuration-corrected AGN power to ULIRG energetics range from minor to dominant. Spectroscopy from the optical through mid-infrared suggests that the incidence of AGN and their strength relative to the ubiquitous starbursts increases with FIR Luminosity and that AGN may dominate for Lir > 1012.5 Lodot, but there are very few such ULIRGs in most local samples. Mid-infrared high excitation diagnostic lines are a very promising line of investigation, however very deep silicate and ice absorptions are also detected in some ULIRGs, so even these mid-IR diagnostics may severely under-estimate AGN energetic contributions due to extinction.

And so the debate continues, and the very fact that it continues two decades after IRAS highlights that most ULIRGs almost certainly contain both a starburst and a monster, and that the key question really concerns the connection between the two, be it evolutionary (one evolves into the other), causal (one triggers the other somehow) or coincidental (another influence triggers both). We cannot address the wealth of literature on this topic here, involving as it does evolutionary schemes of all kinds and their implications, and extensive comparative AGN and starburst population studies and demographics, and so we outline here only a few key points. One popular scenario is an evolutionary sequence in which major gas rich galaxy mergers first result in a massive cool starburst-dominated ULIRG, followed by a warm ULIRG as a QSO turns on inside the dust cocoon and heats the surrounding dust, and then finally the QSO emerges in an optically bright phase when it blows away the surrounding dust cocoon, and the resulting stellar system resembles a spheroid ([Sanders et al. 1988a; Kormendy and Sanders 1992; Joseph 1999; Fabian 1999; Lipari et al. 2003]). Another important scenario is unification-by-orientation of AGN, in which a broad-line (type I) active nucleus is highly obscured by a dusty molecular torus (or other non-symmetrical geometry) when viewed off-axis, so that an optically bright QSO viewed off-axis would appear as a ULIRG. Both of these scenarios predict close relationships between starbursts and AGN.

The evolutionary scenarios have recently received a boost from a sequence of papers reporting high resolution hydrodynamic simulations of gas rich major mergers ([Di Matteo et al., 2005; Springel et al., 2005; Hopkins et al., 2005a, b, c, d]), motivated by linking the growth of spheroid masses and supermassive black hole (SMBH) masses in order to explain the the observed correlations between SMBH mass and bulge mass (Magorrian et al. 1998) or velocity dispersion ([Ferrarese and Merritt 2000, Gebhardt et al. 2000]) of local spheroids. Accretion rates are predicted to be highest at late merger stages, when the SMBH grows exponentially, followed by the most luminous optically-visible QSO phase when the active QSO essentially explosively drives out all remaining material in the system ([Hopkins et al. 2005a]). The period of high obscuration during the high accretion rate phase would correspond to an obscured QSO, ie an AGN-powered ULIRG. Starburst events occur earlier in the lifetime of the merger when gas is still plentiful, and a starburst-ULIRG phase could occur when the gas is centrally concentrated into a dense compact region at relatively late stages.

[Hopkins et al. 2005e] have made approximate predictions of ULIRG space densities based on these simulations, estimating at z = 0.15, 3 × 10-7 and 9 × 10-8 Mpc-3 at infrared luminosities of 1.6 and 2.5 × 1012 Lodot, respectively, which is in good agreement with the 1Jy survey of [Kim and Sanders 1998]. Hopkins et al. also predict a decrease by a factor of 1.5 to the lower redshift, z = 0.04, which also agrees well with the Kim and Sanders work, and an increase to z ~ 1-3 of Phi(L > 1011 Lodot) of 1-3 × 10-5 Mpc-3, which they compare to the sub-mm number counts of [Barger et al. 2005]. [Chapman et al. 2005] have derived the first estimate of ULIRG luminosity functions in this redshift range, though sensitive only to systems above about 1012.3 Lodot. They find space densities > 6 × 10-6 Mpc-3 in their luminosity range, which could be significantly higher than the Hopkins et al. predictions, depending on the unmeasured break of the IR ULIRG luminosity function at these redshifts. Deep Spitzer surveys should help extend the ULIRG luminosity function to lower luminosities in this redshift range.

These ULIRG-QSO evolutionary sequences are appealing and seem likely to be correct for at least a fraction of the ULIRG population. Many predictions remain to be verified, however, and alternative scenarios are also popular. A key test is the host morphology of ULIRGs and optically-bright QSOs. As we have described in Section 3, not all ULIRGs are found at late stages of a merger, although most are indeed found to be associated with the merger process. [Farrah et al. 2001] have proposed an alternative merger-evolution scheme in which the stage at which a ULIRG occurs depends chiefly on the morphological type of the two interacting systems. Deep HST imaging of QSO hosts is now revealing that significant numbers also appear to inhabit disturbed systems [Lim & Ho 1999, Percival et al. 2001, Sánchez et al. 2004], supporting an evolutionary connection between starbursts and QSOs, although some QSOs appear to occur in spiral hosts with very little evidence of recent disturbance. This latter result has been taken to indicate that they could not have been triggered by a recent major merger, however recent simulations have demonstrated that major gas-rich mergers can result in disk systems under certain circumstances [Springel & Hernquist 2005, Robertson et al. 2005]

[Genzel et al. 2001] and [Tacconi et al. 2002] observed NIR structural properties and stellar dynamics of 18 z<0.18 ULIRGs, showing that ULIRG hosts lie on the fundamental plane of elliptical galaxies and thus are very likely to evolve into ellipticals, but that they have significantly lower mass hosts than a luminosity-matched sample of radio-loud and radio-quiet QSOs from [Dunlop et al. 2003]. A difficulty with this approach is that both starbursts and QSOs are expected to have rapidly varying luminosity during the merger sequence, so it is not clear that samples should be luminosity matched to compare their host masses. These authors also reviewed the cluster environment of local ULIRGs, QSOs (from the study of McLure & Dunlop 2002) and ellipticals, finding that while the ellipticals and quasars are found in all environments, none of the 117 ULIRGs that were investigated are located in an environment richer than a small group, which provides some statistical evidence that at least those quasars found locally in rich environments may not have evolved via a ULIRG phase.

[Haas et al. 2003] searched for a red transition population between obscured and unobscured QSO populations amongst Palomar-Green (PG) QSOs. Optically-selected QSOs as a class have a very high incidence rate of luminous FIR and submm emission, consistent with most of them qualifying as ULIRGs by IR luminosity level ([Haas et al., 2003, Polletta et al., 2000, Hatziminaoglou et al., 2005]). Haas et al. suggested a sequence of near-, mid- and far-infrared SEDs for their PG QSO sample which could plausibly represent the transition from a young dust-obscured QSO through the stages of re-distribution of the dust and settling of the dust into a torus, and which is less well explained by simple orientation effects alone. Late evolution-stage systems may be expected to have low fuel supplies, perhaps as seen some moderate redshift HLIRGs with low CO masses and Lir / Mgas ratios or which lack cool dust components (eg. [Yun & Scoville 1998, Verma et al., 2002]). Another suggested young QSO transitory class are the broad absorption line (BAL) QSOs, especially those with strong FeII and weak [OIII] emission, which are preferentially found to be infrared luminous and which could therefore be young dusty QSOs ([Voit et al., 1993, Lipari, 1994, Egami et al., 1996; Canalizo & Stockton 2001, Lipari et al., 2003]). FeLoBAL QSOs could alternatively be older QSOs viewed preferentially along the radial surface of the torus ([Elvis 2000]).

Another class of potentially young broad-line QSOs are the red 2MASS QSOs, selected to have J-K > 2 and expected to be significantly dust-obscured ([Cutri et al. 2002]). These objects tend to be type-1 AGN with moderate luminosities and z < 0.8, the relatively low luminosities and redshifts being due to a selection bias due to the near-infrared k-correction. [Leipski et al. 2005] extended this red 2MASS QSO search using ISO 6.7 µm data, and found a surface density of 1.5 times that of SDSS QSOs to the same optical magnitude depths, and also that the 2MASS-ISO QSOs are significantly redder than SDSS QSOs, and that SDSS QSO colour selection criteria would have missed about 1/3 of these red QSOs.

Most detailed imaging and morphological studies so far have focused on relatively low redshift systems. At higher redshifts we might expect different triggering mechanisms under different environmental circumstances, which we discuss further in Section 5.

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