Star formation seems to be too complex to be simply gravity-induced. Merging and AGN triggering are culprits for playing possible roles. What seems to be progressively clear is that there are two distinct modes of star formation. One mode occurs without any intervention from active galactic nuclei and is characteristic of disk galaxies such as the MWG, on a time-scale of order at least several galactic rotation times. Another mode is more intense, occurring on a relatively rapid time-scale, and involves the intervention of AGN, at least for quenching and possibly for enhancement or even triggering.
The most important aspect of star formation is the role of the raw material, cold gas. There are two modes of gas accretion, which may be classified as cold flows/minor mergers and major mergers/cooling flows The cold flows occur in filamentary streams that follow the cosmic web of large-scale structure, and include minor mergers via the dwarf galaxies that similarly trace the web (Dekel et al. 2009). Theory suggests that at low redshift, gas accretion by cold streams is important, and that the cold streams are invariably clumpy and essentially indistinguishable from minor mergers of gas-rich dwarfs. Major galaxy mergers account for the observed morphological distortions that are more common at high z (Toomre & Toomre 1972) and generally lead to cloud agglomeration, angular momentum loss and cooling flows that feed star formation (Bournaud et al. 2010).
Observationally, one finds that cold flows are rarely observed. This is because of the small covering factor of the filaments (Stewart et al. 2010, Faucher-Giguere and Keres 2010). Indirect evidence in favour of cold accretion comes from studies of star formation in dwarfs. The best example may be the Carina dwarf where three distinct episodes of star formation are found (Tolstoy, Hill and Tosi 2009). However at high redshift, major mergers between galaxies are common. Indeed ULIRGs are invariably undergoing major gas-rich mergers and dominate the cosmic star formation rate history at z 2, whereas normal star-forming galaxies predominate at low redshift (z 2) (Le Borgne et al. 2009). This certainly favours the idea of massive spheroid formation by major mergers.
A recent compilation (Gonzalez et al. 2010) of the specific star formation rate (SSR, or star formation rate per unit stellar mass) to z ~ 7 in the GOODS field suggests that the star formation time-scale (or 1/SSR) goes from the MWG value of ~ 10 Gyr at low redshift to ~ 0.5 Gyr at z 2. This results provides the primary argument for two distinct feedback-regulated modes of star formation: at low redshift via supernovae and without AGN, and at high redshift with, most plausibly, quenching and possibly triggering by AGN playing a central role. One would expect a transition between these two modes as the AGN duty cycle becomes shorter beyond z ~ 1. A related triggering mechanism appeals to enhanced merging at high z (Khochfar and Silk 2011). Alternatively, it has been argued that intensified halo cold gas accretion at early epochs may account for all but the most the extreme star formation rates at high z, although this may require an implausibly high SFE (Dekel et al. 2009).
If the disk formation mode is indeed distinct from the spheroid formation mode, then SMBH might be expected to show some reflection of alternative growth histories. So-called pseudobulges form from secular instability of disks and contain smaller SMBH than do the more massive bulges that may have formed via major gas-rich mergers. It is interesting that SMBH in pseudobulges lie low on the Magorrian relation (Kormendy & Tremaine 2010), as do SMBH in disks relative to those in ellipticals (Graham et al. 2011). These results are for the local universe. Recent data on z ~ 6 quasars suggest that the most massive black holes also lie high on the black hole/dynamical mass relation (Wang et al. 2010). Much work still needs to be done to see whether allowance for two modes of star formation can help resolve some of the outstanding problems in galaxy formation (Fig. 2). In addition to the many uncertainties in star formation theory (and I have not addressed one of the key issues, that of the IMF), there remains the nature of black hole growth. Whether the black holes grow by gas accretion, in which case feedback may play a role in angular momentum transfer (Antonuccio-Delogu and Silk 2010), or by mergers, or by an appropriate combination, remains unresolved.
Figure 2. The rationale for two modes of star formation
4.1. Galaxies downsize
Our understanding of galaxy formation is driven by observations. A good example of this is the phenomenon of downsizing. This was not anticipated by theorists. Prior to 2000 or so, it was accepted that hierarchical galaxy formation predicted that small galaxies form prior to massive galaxies. Moreover the dynamical or collapse time of a newly condensed protogalaxy increases with epoch and hence mass. Hence star formation time should likewise increase with mass, if star formation time tracks free-fall time.
The first indications that this was in error came from the recognition that  / [Fe] metallicity ratios were systematically enhanced for the more massive early-type galaxies, indicative of a shorter star formation time. In effect, we have a cosmic clock: incorporation into stars of debris from SNII ( 108 yr) versus SNI ( 109 yr) provides a means of dating the duration of star formation. This result was soon followed by infrared observations that showed that stellar mass assembly favoured more massive systems at earlier epochs. Even metallicity, via the [O / Fe] ratio, has been found to demonstrate downsizing.
Clearly, baryon physics is far more complicated than assumed in the early models of the 1990s. In fact we stlll lack an adequate explanation. Attempts to patch up the problem at low redshift, to avoid an excess of massive galaxies, exacerbate the inadequacy of the predicted numbers of massive galaxies at high redshift (Fontanot et al. 2009). One attempt to correct the problem at large redshift incorporates for the first time thermally pulsing AGB (or carbon) stars in the models, and the extra NIR luminosity reduces the inferred galaxy masses (Henriques et al. 2010). However the price is that the lower redshift galaxy count predictions no longer fit the models. A clue as to the nature of a possible solution may come from the fact that quasars also reveal luminosity downsizing. This translates into downsizing of central supermassive black hole mass. One might be able to connect the two phenomena if feedback from AGN were initially positive and also a strongly nonlinear function of SMBH mass.
4.2. Semi-analytical models of galaxy formation
Given current computational constraints, it is impossible to achieve the sub-parsec or finer resolution needed to adequately model star formation in a cosmological simulation. Theorists have invented a swindle, wherein the complex processes of srar formation are hidden inside a black box called "sub-grid physics" that can be tagged onto to a large-scale simulation. This results in semi-analytical models of galaxy formation (SAMs) which have been remarkably successful in constructing mock catalogues of galaxies at different epochs and are used in motivating and in interpreting the large surveys of galaxies.
However attempts to solve the problems of high redshift galaxies have so far been woefully inadequate. For example, the early SAM feedback models used AGN quenching, and required excessive dust in early types in the nearby universe (Bower et al. 2006). Refinements to high redshift attempted to account simultaneously for galaxy and AGN accounts, and only succeeded by requiring inordinate amounts of dust in order to hide most of the AGNs seen in deep x-ray surveys (Fanidakis et al. 2011). A frank assessment of the state-of-the-art in SAMs (Benson 2010) found that there were some 70 free parameters that need to be adjusted in the newest SAM. An early indication that SAMs were entering uncertain territory can be seen in the early predictions of the cosmic star formation history (Springel & Hernquist 2003). This showed that as numerical resolution was increased, the predicted star formation rate increased without limit. This makes one begin to doubt the predictive power of SAMs.