4. RESULTS FROM NUMERICAL SIMULATIONS

4.1. General results from semi-analytical models of galaxy formation

SAMs have been remarkably successful in constructing mock catalogs of galaxies at different epochs and are used in motivating and in interpreting the large surveys of galaxies.

For example, they reproduce very well the z = 0 stellar mass function and correlation function (see Fig. 13).

Figure 13. Illustrations of predictions of SAMs at z = 0. Upper left: Stellar mass functions (Guo et al. 2011): symbols are from SDSS (Li & White 2009), while curves are from a SAM run on both wide and low-resolution Millennium Simulation and on the higher but smaller MS-II simulation. Upper right: Galaxy correlation functions (Guo et al. 2011). Bottom left: Evolution of the cosmic SFR (Guo et al. 2011). Bottom right: Very low end of the galaxy luminosity function (Koposov et al. 2009).

However, attempts to solve the problems of high redshift galaxies have so far been woefully inadequate. For example, they cannot reproduce the rapid decrease in the cosmic SFR since z = 1 (see Fig. 14). 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 excessive amounts of dust in order to hide most of the AGNs seen in deep X-ray surveys (Fanidakis et al. 2011). An early indication that SAMs were entering uncertain territory can be seen in the early predictions of the cosmic star formation history: as numerical resolution was increased, the predicted SFR increased without limit (Springel & Hernquist 2003). This makes one begin to doubt the predictive power of SAMs.

Figure 14. Evolution of stellar mass functions predicted by Guo et al. (2011). Open triangles and red circles represent observations by Pérez-González et al. (2008) and Marchesini et al. (2009), respectively. Black and green curves represent the predicted stellar mass functions of galaxies, respectively before and after convolving the stellar masses by 0.25 dex measurement errors.

Clearly, baryon physics is far more complicated than assumed in the early SAMs of the 1990s. In fact, we still lack an adequate explanation for the evolution of the stellar mass function. 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. 2011). However the price is that the lower redshift galaxy count predictions no longer fit the models.

4.2. Feedback and dwarfs

Dwarf spheroidal galaxies are dark matter laboratories, dominated by dark matter. However the numbers defy interpretation. Feedback is readily adjusted to reduce the numbers of low mass dwarfs (Koposov et al. 2009), but the most massive dwarfs predicted by CDM simulations are not observed (Boylan-Kolchin et al. 2012). This may be a function of the neglect of baryons in the Aquarius simulations: inclusion of baryons reduces the central densities of massive dwarfs (Zolotov et al. 2012). Unorthodox feedback (AGN) may also be a solution (Boylan-Kolchin et al. 2011). Moreover, most low-mass dwarfs have cores rather than the cusps predicted by CDM-only simulations. Baryonic feedback may reconcile data on dwarf core profiles with simulations that include star formation and gas cooling (Oh et al. 2011, Governato et al. 2012), who find that SN-driven outflows help flatten dark matter central density cusps. As mentioned earlier, enhanced early star formation and SN production creates strong tensions with the need for strong late low mass galaxy evolution. SN feedback at later epochs may turn cusps into cores by sloshing of more recently accreted gas clouds (Mashchenko et al. 2006), more recently addressed in Pontzen & Governato (2012), who consider bulk gas motions and require short intense bursts of star formation. There may be evidence for such phenomena in dwarf galaxies (Weisz et al. 2012).

Multiphase simulations (Powell et al. 2011) confirm the effectiveness of SN-driven winds, but find that they do not lead to baryon ejection. In a multi-phase medium with more realistic filamentary accretion, outflows are only typically 10% of the gas accretion rate. It is not clear whether SN feedback may still provide enough momentum to yield an acceptable fit to the low mass end of the galaxy luminosity function for the classical dwarfs. Ram pressure stripping (Gunn & Gott 1972, Mayer et al. 2007) remains an alternative or complimentary mechanism, and morphological transformation of disks into dwarf spheroidals may be accomplished by repeated rapid encounters, i.e. "harassment" (Moore et al. 1998) or gravitationally-induced resonances (D'Onghia et al. 2009).

SN feedback enables present day disk galaxy properties to be reproduced, including the Tully- Fisher relation and sizes, except for massive disks. More energetic feedback, from an AGN phase, is envisaged as a possible solution (McCarthy et al. 2012). Many galaxies, including early types, have extended star formation histories. Minor mergers provide an adequate gas supply to account for these (Kaviraj et al. 2009). However, hydrodynamical studies of the baryonic evolution and SFR in low mass galaxies disagree about whether or not one can reproduce their observed properties, including dark matter cores and baryon fraction. Outflows may reproduce the observed cores (Governato et al. 2012) if the SFE is high at early epochs, but such models fail to result in the strong evolution observed at low redshift (Weinmann et al. 2012).

Tidal disruption also plays a role in disrupting satellites whose orbits intersect the disk or bulge. Dramatic discoveries due to deep imaging of nearby galaxies with very small, wide field of view, telescopes confirm the ubiquity of tidal tails that trace dwarf disruption in the remote past (Martínez-Delgado et al. 2010). Simulations provide a convincing demonstration that we are seeing tidal disruption in action (Cooper et al. 2010). An independent confirmation of disruption in action comes from studies of the tidal tails around the outermost MW globular star clusters such as Pal 13. Gaps in the tails (Grillmair 2009) indicate the presence of dark satellites. Numerical simulations (Yoon et al. 2011) find that high M/L satellites of mass ~ 10⁷ M are required, again a prediction of the CDM model.

At z = 0, it is possible that SN feedback at intermediate and low masses combines with entropy feedback from photoionization at low masses to conspire to give a linear baryonic Tully-Fisher relation (BTFR), as observed (see Fig. 15). This is an important issue as the normalization, slope and linearity of the BTFR have been used as evidence for MOdified Newtonian Dynamics (MOND, Milgrom 1983) and against CDM. Indeed, McGaugh (2011) has pointed out that the observations of baryonic mass (stars plus cold gas) as a function of the velocity of the flat part of the rotation curve is very well matched by the MOND prediction (with no free parameters). He argues that considerable fine-tuning is required to bring the naïve CDM (slope 3) prediction with no feedback to match the data. Our best-fit model matches the data equally well (with three free parameters), but the entropy feedback (photoionization) implies that the relation should curve at low masses, except if one considers galaxies in which the bulk of the stars formed before the reionization epoch (z > 6). Dutton (2012) also matched the BTFR data with a SAM. Moreover, two of the lowest mass galaxies in the McGaugh (2012) sample have rotation velocities corrected for asymmetric drift (see Begum & Chengalur 2004), after which the rotation curve of these galaxies is roughly linear with radius, and therefore depends on the last data point obtained with radio-observations, contradicting the flat part of the rotation curve sought by McGaugh (2012).

Figure 15. Baryonic Tully-Fisher relation (Mamon & Silk, in prep.). Symbols are from HI measurements, where the velocity is the flat part of the rotation curve (green, from McGaugh 2012) or from line-widths (black, Gurovich et al. 2010; magenta, Hall et al. 2011). The grey line is the naïve CDM (slope 3) prediction with no feedback, while the brown dashed line is the (slope 4) prediction from MOND. Note that the inclination of Ho II is uncertain (Gentile et al. 2012).

Intermediate-mass dwarfs are present at high redshift and have a steep luminosity function (Bradley et al. 2012, see Fig. 16). They may contribute significantly to the reionization of the Universe.

Figure 16. Left: Galaxy luminosity function at z = 8 (Bradley et al. 2012). Middle and right: evolution of the galaxy luminosity function (Bouwens et al. 2012) and of its faint-end slope (Bradley et al. 2012).

4.3. Gas accretion versus mergers

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 AGN and is characteristic of disk galaxies such as the MW, 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 former provide supplies of cold gas along filaments, the latter a source of hot gas which may cool and feed star formation.

The cold flows occur in filamentary streams that follow the cosmic web of large-scale structure (see Fig. 17), 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, and generally lead to cloud agglomeration, angular momentum loss and cooling flows that feed star formation (Bournaud et al. 2011b).

Figure 17. Mass flux map of a Mv = 1012 M halo at z = 2.5 from a hydrodynamical simulation (Dekel et al. 2009). The circle denotes the virial radius.

Observationally, one finds that cold flows are rarely if at all observed. This is presumably because of the small covering factor of the filaments (Stewart et al. 2011, Faucher-Giguère & Keres 2011). Indirect evidence in favor 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 et al. 2009). However at high redshift, major mergers between galaxies are common. Indeed, Ultra-Luminous Infrared Galaxies (ULIRGs), whose SFRs are huge, are invariably undergoing major, often multiple, gas-rich mergers (Borne et al. 2000) and dominate the cosmic SFR history at z 2, whereas normal star-forming galaxies predominate at low (z 2) redshift (Le Borgne et al. 2009). This certainly favors the idea of massive spheroid formation by major mergers.

Using, their analytical model of galaxy formation on top of a high-resolution cosmological simulation, Cattaneo et al. (2011) show that only in massive galaxies (m_stars > 10¹¹ h^-1 M) do galaxy mergers contribute to the bulk of the stellar mass growth (see also Guo & White 2008, who analyzed a simulation with 11 times worse mass resolution) and these mergers are mainly `dry' (gas-poor). As one goes to lower stellar masses (down to their simulation's effective resolution limit of 10<sup>10.6</sup> h<sup>-1</sup> M) the role of mergers sharply diminishes, suggesting, by extrapolation, that mergers are, in general, unimportant for the mass growth of both these intermediate-mass galaxies and low-mass galaxies, for which the bulk of the growth must be by gas accretion. Nevertheless, among those rare intermediate-mass galaxies built by mergers, the growth in mass is mostly in `wet' (gas-rich) and minor mergers. In particular, the non-dominant cluster galaxies, known to be mostly dwarf ellipticals, are rarely built by mergers.

The sudden dominance of major mergers at high galaxy masses is confirmed by trends with stellar mass of the colors, color gradients and elongations of SDSS galaxies (Tremonti et al. 2004, Bernardi et al. 2010), see also van der Wel et al. 2009, Thomas et al. 2010). At lower masses (and low redshift), minor mergers are required to account for sizes and masses (McLure et al. 2012, López-Sanjuan et al. 2012).

Herschel observations of the Main Sequence of galaxy formation (SFR versus stellar mass) suggests that starbursts, commonly associated with major mergers, are displaced to higher mass and SFR, but only account for 10% of the SFR density at z = 2 (Rodighiero et al. 2011). However, this conclusion depends critically on the ~ 100 Myr timescale assumed for the starbursts. If the starbursts had shorter duration, say 20 Myr, given their effective observation time of ~ 1 Gyr, they would account for as much as 50% of the star formation at z ~ 2. It is difficult to gauge independent estimates of starburst age, but for example the UV continuum flattening observed at high z for luminous star-forming galaxies favors a younger starburst age (González et al. 2011b) as would possible SED corrections for nebular emission.

4.4. Initial stellar mass function

The IMF of stars forming in galaxies is usually treated as universal in galaxy formation modelling. There has been a recent flurry of papers finding evidence for a systematic steepening, from the Chabrier (2003) to Salpeter (1955) IMFs, in massive early type galaxies. From a spectral absorption line analysis, a correlation of IMF steepening with enhanced velocity dispersion, [Mg/Fe] and sodium abundance is reported by Conroy & van Dokkum (2012). A similar result is reported for stacked massive galaxy spectra (Ferreras et al. 2012).

The modeling of the internal kinematics of early-type galaxies using integral field spectroscopy provides evidence for steeper IMFs (regardless of many plausible assumptions on the DM) in increasingly more massive galaxies (Cappellari et al. 2012, see Fig. 18). Lensing plus gas kinematics provides evidence for a Salpeter-like IMF in several massive ellipticals (Dutton et al. 2012b). There may also be a correlation of a steeper IMF with the densest massive galaxies (Dutton et al. 2012a). All of these studies report increasing M/L with increasing spheroid velocity dispersion and / [Fe].

Figure 18. Stellar mass-to-light ratio inferred from kinematical modeling (after subtracting off the contribution of the DM component), normalized to Salpeter ratio inferred from stellar populations versus stellar M/L from kinematical modeling, for six DM models (Cappellari et al. 2012).

The possible degeneracy between IMF and DM fraction and shape is a concern because the DM profile steepens as a consequence of adiabatic contraction. While, Cappellari et al. (2012) tried a variety of DM models that do not significantly influence their result (since they only probed the region where dark matter accounts for at best 20% of the mass), only one study (Sonnenfeld et al. 2012) so far has cleanly broken the degeneracy with the dark matter profile: By using a double Einstein ring, Sonnenfeld et al. (2012) found a strong case for a Salpeter IMF. The adiabatic contraction of the DM is within the range found by Gnedin et al. (2004).

The implications of a steeper IMF in massive galaxies for galaxy formation models remain to be explored. The increased efficiency of star formation required at early epochs will certainly provide further tensions with the need to leave a substantial gas supply at late epochs for the observed late evolution observed for low mass galaxies, as discussed below.

4.5. Feedback and AGN

Quenching of star formation has been largely motivated by the apparent success of SMBH feedback in reproducing the scaling and normalization of the black hole mass-spheroid velocity dispersion M_BH - _v) relation, as first proposed by Silk & Rees (1998). SAMs indeed demonstrate that AGN feedback is able to quench star formation in massive elliptical galaxies (Croton et al. 2006, Bower et al. 2006, Cattaneo et al. 2006, Somerville et al. 2008). One can reproduce the fairly sharp cut-off in the bright end of the galaxy luminosity function (Bell et al. 2003, Panter et al. 2007). These SAMs do not require "quasar mode" AGN feedback with Eddington luminosities.

High resolution hydrodynamical cosmological simulations indeed show that while cold streams initially feed the black hole, transferring angular momentum to produce central disks (Dubois et al. 2012a) that become gravitationally unstable and feed the compact bulge through migration of clumps (see Bournaud et al. 2011a), the cold flows are eventually interrupted by AGN-driven super-winds (Dubois et al. 2012b).

However the physics of driving SMBH outflows is still not well understood. One issue is that momentum-driven winds fail to account for the normalization of the M_BH - _v relation (Silk & Nusser 2010, Debuhr et al. 2012), with the shortfall being about a factor of 10. This momentum deficit can be supplied by radio jet-driven outflows (Wagner & Bicknell 2011), which also account for the observed high velocities of entrained cold gas (Wagner et al. 2012). Alternative or complementary possibilities, possibly more relevant to radio-quiet quasars, include positive feedback from outflow-triggered star formation (Silk & Norman 2009, Gaibler et al. 2011, see Fig. 19) and energy-driven outflows (Faucher-Giguere & Quataert 2012). Nearby AGN show dense molecular rings surrounding circumnuclear rings of star formation (Sani et al. 2012), reminiscent of the simulated triggering of star formation (Gaibler et al. 2011).

Figure 19. Simulations (in 32 kpc box) of AGN feedback at 14 (left) and 22 Myr (right) after the onset of the jet, in edge-on (top) and face-on (bottom) views of log density (Gaibler et al. 2011)

SMBHs are generally found to correlate with bulges rather than with disks, pseudobulges or dark halos (Ho 2007, Kormendy et al. 2011, Kormendy & Bender 2011), although disk galaxies appear to follow a similar M_BH - _v relation, albeit with more scatter (Graham et al. 2011). This would simplify formation mechanisms, suggesting that bulges and SMBH grow together, perhaps self-regulating each other. Massive black hole growth at early epochs seems to be (just) achievable by gas accretion. Large cosmological simulations (Di Matteo et al. 2012, see also Li et al. 2007, Sijacki et al. 2009, Khandai et al. 2012) have shown that primordial massive BHs can grow by cold filamentary infall, and acquire masses of up to several billion solar masses by z = 6 in the most massive halos (M_vir 10^12-13 M).

Insight into black hole growth is provided by looking for extreme deviations in the M_BH - _v relation. Massive black holes seem to be in place at high redshift before spheroids (Wang et al. 2011). This is also the case for a nearby starbust galaxy containing an AGN but without any matching spheroid or indeed massive stellar component (Reines & Deller 2012). On the other hand, SMGs seem to contain relatively low mass black holes for their stellar content (Alexander et al. 2008).