It is fair to say that the progress achieved by several groups in simulating galaxy formation is quite remarkable. Just a decade ago the spatial resolution of cosmological simulations barely reached a kiloparsec, which corresponds to the characteristic exponential scale length of galactic disks. Today simulations are approaching a resolution better than a hundred parsecs, an improvement of more than an order of magnitude. Therefore we have moved from a situation in which the process of disk galaxy formation was barely within the reach of cosmological calculations to a situation in which the simulations can effectively target such process. At the same time, sub-grid models of those astrophysical mechanisms that determine the thermodynamics of the interstellar medium, and consequently the process of star formation, are becoming increasingly more realistic. Furthermore, as the resolution of simulations increases further we might enter a regime in which the multi-phase ISM and the bulk effect of supernovae explosions can be modeled directly rather than being incorporated in a sub-grid fashion. Indeed the most recent (AMR) cosmological simulations at the time of writing suggest that the many assumption of sub-grid models cease to be required if a resolution of at least 50 pc can be achieved 43. Finally, we have gained a much better understanding of the various numerical effects that can dramatically affect the results of the simulations and render a comparison with observed galaxies quite meaningless.
Yet, despite the tremendous improvement in numerical resolution, cosmological simulations are still affected by resolution issues in the early phase of galaxy assembly, namely during the fist few billion years of evolution. The latter phase is characterized by frequent mergers (the merger rate of dark halos declines dramatically after z = 1, about 8 billion years ago, in the CDM model) and is responsible for the build up of the central region of galaxies, including their bulge 48, 55. The central region of a virialized object indeed assembles earlier because it corresponds to the peak of the local density field, which becomes gravitationally unstable and collapses earlier than the the outer, lower density regions. The collapse of the central region is of course lumpy; many small halos, each of them possibly already hosting a previously assembled small galaxy, come together and merge. Even in the best cosmological simulations currently available, these "primordial" halos are poorly resolved due to their small masses. Each object being resolved by only a few tens of thousand particles, spurious angular momentum loss, two-body heating and other numerical effects are particularly severe 46, 47, 48. This lack of resolution at early times probably explains why the same simulations that are finally producing disks with realistic structural properties 58, 59, 34, 55, 60 still exhibit central regions with an excess of low angular momentum material and an ubiquitous massive, dense spheroidal bulge component. Since bulgeless galaxies are abundant in the present-day Universe as well as several billions of years ago 5, here we are facing a major problem.
5.1. Origin of bulgeless galaxies
The ubiquitous bulge component in simulated galaxies triggers the following question; can a disk galaxy without a bulge ever be formed in a CDM Universe? Answering this question using the current simulations seems a daunting task. The situation becomes even worse if we consider that halos with larger angular momentum, thus favourable to the formation of large, dominant disks, are also those that are more prone to form a massive bulge because they undergo a larger number of major mergers 108. If the main problem is resolution during the early phase of structure formation, one could hope to minimize numerical loss of angular momentum by increasing the resolution further. However, due to the scale-free nature of collapse in a cold dark matter Universe, when the mass resolution is increased not only previously resolved halos are sampled by more particles, but also new, previously unresolved halos appear that are once again modeled with too few particles. In other words, in cold dark matter simulations of any resolution there will always be some epoch at which most lumps of dark matter and baryons become small enough to be poorly resolved, thus biasing the angular momentum content of the final galaxy. The latter argument, however, strictly applies only to dark matter. As we have seen, mechanisms such as supernovae feedback can decouple the collapse history of baryons from that of the dark matter. In addition, as the mass of the progenitor lumps decreases there is another important process that can lead to a significant decoupling. Between one and five billion years after the Big Bang, namely between z = 3 and z = 1, both the formation rate of stars in galaxies and the mass growth of supermassive black holes that shine as quasars at the center of them reach their peak, producing so much ultraviolet radiation to ionize most of the hydrogen in the Universe 109, 110, 111, 112. This ubiquitous ultraviolet radiation, known as the photoionizing background, keeps the intergalactic gas at a temperature exceeding 104 K, suppressing the collapse of baryons in halos with masses below 108 solar masses (deeper potential wells are needed to confine gas that cannot coolbelow 104 K) 113, 114, 115, 116. The ionizing background also causes photoevaporation of gas that has previously collapsed in such small halos 117. The net result is that halos with masses below 108 solar masses become nearly empty of baryons during this epoch, retaining only the stars that were formed before the rise of the ultraviolet background; when they merge, they bring very little baryonic mass and thus should contribute little to the formation of bulges. Interestingly, galaxies with little or no bulge are mostly found among the lowest mass disk galaxies (Figure 2), which were formed by the hierarchical merging of smaller lumps, as expected if the photoionizing background played a key role in suppressing bulge formation early on.
Recent cosmological simulations by the major groups involved in this area of research include the effect of the photoionizing background 56, 58, 59, 34, 55, 60. The inclusion of the ultraviolet background in the picture introduces a scale, ~ 108 solar masses, in an otherwise scale-free structure formation model. This suggests that simulations should try to obey the following resolution requirement in order to avoid spurious angular momentum loss during the early phase of galaxy formation; the smallest baryon-rich lumps, namely those with masses > 108 solar masses, should be resolved by about a million SPH particles, and a few 105 dark matter particles, as suggested by resolution studies 46, 48. The latter resolution requirement translates into an SPH particle mass of about 102 solar masses, a couple of orders of magnitude higher than that currently achieved in cosmological simulations of galaxy formation 55.
Provided that resolution issues are solved, a conceptual problem still remains. It is a common assumption, supported by a large number of detailed three-dimensional simulations, that mergers between nearly equal mass disk-dominated galaxies would produce a spheroidal, bulge-dominated system 118, 119, 120. These nearly equal-mass mergers are frequent in hierarchical assembly, especially early on. A bulgeless galaxy should only arise if the last major merger occurs when the cosmic ultraviolet flux is still high, at z > 1, i.e. more than ten billions of years ago, and involves lumps small enough to be nearly devoid of baryons. Major mergers between more massive lumps, that were barely affected by the ultraviolet flux, and/or occurring later, when the flux has declined, will inevitably build a bulge; the bulge will only become less concentrated as the resolution increases but will not disappear. This means that forming bulgeless galaxies in CDM needs a requirement on the merging history in addition to that on the resolution 121. The fact that major mergers cease to be common after z = 2-3 122 is quite encouraging in this respect. This figure becomes even more favourable, at least qualitatively, for halos with masses below that of the Milky Way halo, which would be consistent with the fact that most bulgeless galaxies are of low mass (Figure 2). Yet, at the moment it is unclear how these figures on halo merger rates can be compared quantitatively with the fraction of bulgeless galaxies seen both today and at z=1 in large galaxy surveys such as COSMOS 5.
The final structure of the galaxy is strongly dependent on its merging history not only because the latter contributes to determine its bulge-to-disk ratio but also because it affects the structure of the disk itself 123. After the last major merger the galaxy grows via accretion of smaller lumps of dark matter and baryons (usually referred to as satellites) and gas accretion from the hot gas cooling from the halo. We could name this second phase "oligarchic growth", using a terminology well known in the field of planet formation, where a similar switch between modes of growth occurs in the case of colliding km-sized rocky bodies (planetesimals). Bulgeless galaxies should arise in those systems that switch to "oligarchic growth" earlier than the rest of the galaxy population based on our previous argument. However this simple prediction is complicated by the fact that a bulge could also arise during the "oligarchic growth" phase as a result of bar formation and subsequent buckling 54. Therefore, one should require that the fraction of CDM halos that switch to "oligarchic growth" at high redshift be comfortably larger than the observed fraction of bulgeless disk galaxies since some of them might have formed their bulge later via internal evolution.
It is important to consider the possibility that the accepted assumption that mergers produce bulge-like, spheroidal components might not be true in general. Recently, it has been shown that if the disks of two galaxies contain a lot of gas a large disk can be produced as a result of the merger 124, 125 This is because the gas dissipates and settles into centrifugal equilibrium at fairly large radii owing to the angular momentum originally locked in the orbital motion of the two galaxies. The disk re-growth might actually increase the disk-to-bulge ratio provided that there is sufficient gas in the original galaxies, but this still needs to be quantified. Now, interestingly galaxies appear to become more gas rich at earlier times and for lower masses. It is thus plausible that at early times galaxies underwent several gas-rich mergers that contributed to building a disk more than to forming a bulge. As a consequence, it seems relevant to carry out simulations that are very accurate in the early phase of galaxy assembly even if this prevents from following the formation of the galaxy until the present epoch (Callegari, Mayer et al., in preparation).
As we have seen in the previous section, mergers are not the only way by which a central mass concentration can arise in galaxies. The non-cosmological simulations also exhibit a profile that becomes steeper than exponential towards the center, although models with blast-wave feedback look very promising as fas as limiting the growth of the central density enhancement. We note, however, that the initial gas density and angular momentum distributions of the isolated models are poorly constrained. Testing different initial conditions can teach us about the physical conditions of the gaseous halo needed in order to be consistent with observations. Preliminary simulations (Kaufmann et al. in preparation) show that an initial gas density profile with a core, and thus a high initial entropy (as expected in scenarios in which some non specified primordial heating mechanism, perhaps feedback by massive central black holes, raised the entropy of the gas already collapsed in halos 126), can lead to disk masses, atomic hydrogen distribution and X-ray emission in better agreement with observations compared to the case in which the gas density follows the cuspy dark matter profile. Comparing the prediction of simulations to observations in different wavelengths, such as radio wavelengths at which the atomic hydrogen is revealed, and X-rays by means of which the hot gas in the halo can be detected, could be a powerful tool to constrain the physics of galaxy formation.
5.2. Additional issues at a glance
There are some aspects of the galaxy formation process that we have not covered in this report and that might have an impact on the problem of disk formation and, in particular, on the origin of bulgeless galaxies. First, gas accretion seems to occur in a different fashion for large and small galaxies. Small galaxies mostly accrete gas that enters already cold (T ~ 104 K) in the dark matter halo following a filamentary, anisotropic flow, while large galaxies tend to be built mostly by accretion of gas that is shock heated to high temperatures (T ~ 106 K) when it enters the halo and later cools down in a smooth, isotropic flow 127, 128. The implications of these two modes of accretion on disk formation, for example their impact on angular momentum transport, are still unclear. The treshold halo mass that decides between cold and hot mode accretion is estimated to be around 1012 solar masses, namely comparable to the mass of the Milky Way or Andromeda halo. This is interesting in the context of bulgeless galaxies. As we already noted, bulge-dominated galaxies such as the Andromeda galaxy, are usually much more massive than bulgeless galaxies such as the M33 galaxy (there are some examples of massive bulgeless galaxies, e.g. M101 in Figure 1), hence their different structure might be, at least partially, a product of these two different gas accretion modes.
Another aspect that needs attention is that for galaxies mainly accreting in the hot mode a thermal instability might develop in the cooling flow 129. As a result of that gas cools faster in slightly more overdense regions, giving rise to dense clouds nearly in pressure equilibrium with the surrounding gas 129, 130 (see Figure 12). In this case the hot mode would not be a smooth cooling flow but would develop into a two-phase medium. Clouds lose orbital angular momentum due to the hydrodynamical drag exerted by the surrounding gas and eventually reach the center at timescales different from gas that started out at the same radius but remained in the diffuse phase. Since there is transfer of angular momentum between the cold and hot phase we expect some effects on disk formation. It is hard to predict, even qualitatively, in which direction the effect will be since both the hot and the cold phase will eventually contribute to the disk assembly. A very high resolution is required to resolve the thermal instability 130 and cosmological simulations are just now becoming capable to do so.
Furthermore, another issue concerns a dynamical mechanism called adiabatic contraction. Indeed the dark matter halo should slowly contract in response to the baryonic mass collapsing within it 131. This is a standard assumption of the one dimensional numerical models that we discussed earlier in this review (see section 1). Different researchers who have developed numerical models of gas collapse within isolated spherical halos disagree slightly on the magnitude of the effect, i.e. on how strongly the overall potential well of the galaxy is modified 132. In any case, the effect of adiabatic contraction is to increase the maximum rotational velocity of the galaxy and to reduce the size of the disk because the overall potential well becomes deeper (hence the radius at which a gas parcel can be in centrifugal equilibrium diminishes 8). This has an impact on any observed correlation between galaxy properties that involves the disk rotational velocity, for example the Tully-Fisher relation (see previous section). Recent work with one-dimensional numerical models has pointed out that, if adiabatic contraction is effective, it is impossible to match the observed Tully-Fisher relation even in the case that the angular momentum of the gas is perfectly conserved during the collapse - the resulting galaxies always rotate too fast 13. The fact that recent cosmological simulations are able to roughly match the Tully Fisher relation 55 is thus not expected. However, this discrepancy might suggest that one-dimensional models cannot capture the dynamics and thermodynamics of the three-dimensional collapse in a cosmological context. In particular, it is possible that the concept of adiabatic contraction is not appropriate for a structure formation model like CDM in which a large fraction of the baryonic mass is added not via slow, smooth accretion of gas but rather via mergers and/or cold flows on timescales short enough to violate the assumption of adiabaticity in the first place.
Finally, even if realistic disks could form it is not clear that they will survive intact until the present epoch in a Universe where structure grows hierarchically. In a hierarchical Universe a galaxy is always surrounded by smaller galaxies that will eventually perturb it during close fly-bies by raising tides, or even merge with it. Cosmological simulations predict that these satellite galaxies have very eccentric, plunging orbits 133 which should take them close to the disk of the primary galaxy. The tidal perturbations will deposit kinetic energy in the stellar disk, raising the random velocities of its stars and increasing its scale height 134. This is confirmed by recent three-dimensional simulations, although the extent of the damage, especially whether or not most of the disk survives intact despite the intruders, is still debated 135, 136. Tidal interactions will also trigger bar formation and eventually produce a bulge via the buckling instability (see section 4.1). The disk might eventually re-growth as new gas is accreted from the halo or a gas-rich companion is digested, but this is still unclear at the moment. The study of disk heating by satellites is a difficult problem that requires a resolution beyond that currently possible in cosmological simulations.
In summary, there are several aspects of galaxy formation that still need to be understood in depth, and their overall impact on disk formation thus still awaits a clear assessment. This deeper understanding demands a substantial improvement in the resolution of the simulations and in the sub-grid recipes that describe the ISM, star formation and feedback. Yet, in our opinion, simply more computing power and better sub-grid methods are not going to solve many of the pressing issues in this field, such as the origin of bulgeless galaxies. Instead, there is still room, and need, for new ideas and new approaches to the open questions. Provided that this happens, computer simulations will then continue to play a central role in advancing our understanding of how disk galaxies form.
We thank Volker Springel and Elena d'Onghia for reading an earlier version of the manuscript and returning very helpful comments. We also thank all the people that have had a long term collaboration with the authors and contributed to many of the results discussed in this review; Alyson Brooks, Chris Brook, James Wadsley, Joachim Stadel, Tom Quinn, Greg Stinson, Beth Willman, Neal Katz, George Lake and Ben Moore. We also acknowledge useful and stimulating discussions on galaxy formation, star formation and computer modeling issues with James Bullock, Stefano Borgani, Marcella Carollo, Stephane Courteau, Victor Debattista, Avishai Dekel, Aaron Dutton, Andrea Ferrara, Nick Gnedin, Dusan Keres, Ralf Klessen, Andrey Kravtsov, Stelios Kazantzidis, Simon Lilly, Aryeh Maller, Francesco Miniati, Julio Navarro, Padelis Papadopoulos, Cristiano Porciani, Matthias Steinmetz, Romain Teyssier, Frank van den Bosch and Keichi Wada.