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Theory lacks adequate resolution and physics. Of course these issues are intricately connected. One needs to tackle baryon physics and the associated possibilities for feedback. At this point in time, the leading simulations, such as the ERIS cosmological simulation of the MW (Guedes et al. 2011), provide at best 10 pc resolution in a state of the art simulation with gas and star formation. The gas and star formation physics is included in an ad hoc way, because of the resolution limitation. For example, while stars are known to form in the dense cores - of density 105 cm-3 - of Giant Molecular Clouds, the current hydrodynamical simulations adopt SF thresholds of typically 1 cm-3 and always 102 cm-3. Sharp increases of the SF density threshold result in moving the SF regions outside of the nucleus (Teyssier et al. 2010). However, in reality, it is the unresolved subgrid physics that determines the actual threshold, if one even exists. Mastery of the required subparsec-scale physics will take time, but there is no obvious reason why we cannot achieve this goal with orders of magnitude improvement in computing power.

For the moment, phenomenology drives all modelling. This is true especially for local star formation. A serious consequence is that physics honed on local star-forming regions, where one has high resolution probes of star-forming clouds and of ongoing feedback, may not necessarily apply in the more extreme conditions of the early universe.

One issue that arises frequently is whether the perceived challenges to LambdaCDM justify a new theory of gravity. From MOND (Milgrom 1983) onwards, there are any number of alternative theories that are designed to explain certain observations. However, none can explain the ensemble of observations any better than LambdaCDM, nor do they rely on solid physical grounds. But to the extent that any unexplained anomalies exist, these are invariably at no more than the 2sigma level of significance. It seems that such "evidence" is not adequate motivation for abandoning Einstein-Newton gravity. Indeed, while it is overwhelmingly clear that there are many potential discrepancies with LambdaCDM, we have certainly not developed the optimal LambdaCDM theory of galaxy formation: the current models do not adequately include the baryons nor do we reliably understand star formation, let alone feedback. Other MOND-related issues are reviewed in Famaey & McGaugh (2011), including challenges raised by the apparent emptiness of local voids and satellite phase space correlations. However, we regard these as more a matter of absorbing the significance of ever deeper galaxy and 21 cm surveys, on the one hand (for example, deep blind HI surveys show that gas-rich galaxies are the least clustered of any galaxy population Martin et al. 2012), and on the other hand, of questioning the details of hitherto inadequately modelled baryonic physics, as developed for example in Zolotov et al. (2012). Whether appeal to alternative gravity is justified by inadequate baryonic physics is a question of judgement at this point. Here is a summary of many of these failures: we cite some key reasons why LambdaCDM does not yet provide a robust explanation of the observations: we list below several examples that represent challenges for theorists.

  1. Massive bulgeless galaxies with thin disks are reasonably common (Kormendy et al. 2010). Simulations invariably make thick disks and bulges. Indeed, the bulges are typically overly massive relative to the disks for all galaxies other than S0s. Massive thin disks are especially hard to simulate unless very fine-tuned feedback is applied. A consensus is that the feedback prescriptions are far from unique (Scannapieco et al. 2012). One appealing solution involves SN feedback. This drives a galactic fountain that feeds the bulge. A wind is driven from the bulge where star formation is largely suppressed for sufficiently high feedback (Brook et al. 2012). Another proposal includes radiation pressure from massive stars as well as SNe. The combined feedback helps expand the halo expansion, thereby limiting dynamical friction and bulge formation (Macciò et al. 2012).
  2. Dark matter cores are generally inferred in dwarf spheroidal galaxies, whereas LambdaCDM theory predicts a cusp, the NFW profile. Strong SN feedback can eject enough baryons from the innermost region to create a core (Governato et al. 2010, Pontzen & Governato 2012), but this requires high early SN feedback or a series of implausibly short bursts of star formation.
  3. The excessive predicted numbers of dwarf galaxies are one of the most cited problems with LambdaCDM. The discrepancy amounts to two orders of magnitude. The issue of dwarf visibility is addressed by feedback that ejects most of the baryons and thereby renders the dwarfs invisible, at least in the optical bands. There are three commonly discussed mechanisms for dwarf galaxy feedback: reionization of the universe at early epochs, SNe, and (ram pressure and tidal) stripping. AGN-driven outflows via intermediate mass black holes provide another alternative to which relatively little attention has been paid (Silk & Nusser 2010).

    None of these have so far been demonstrated to provide definitive solutions. Reionization only works for the lowest mass dwarfs. The ultrafaint dwarfs in the MW may be fossils of these first galaxies (as checked by detailed models (Koposov et al. 2009, Salvadori & Ferrara 2009, Bovill & Ricotti 2011). It is argued that SN feedback solves the problem for the more massive dwarfs (Macciò et al. 2010). However, this conclusion is disputed by Boylan-Kolchin et al. (2011), who use the Aquarius simulations (Springel et al. 2008) to predict more massive dwarfs in dark-matter-only simulations than are observed. These authors argue that the relatively massive dwarfs should form stars, and we see no counterparts of these systems, apart possibly from rare massive dwarfs such as the Magellanic Clouds. We have previously remarked that omission of baryonic physics biases the dark matter-only simulations to an overstatement of the problem by overpredicting dwarf central densities (Zolotov et al. 2012).

  4. The SFE in dwarfs is highly debated. Let us put aside the high SFE at early epochs that is required to obtain strong feedback in order to generate cores. For example, it is possible that intermediate mass black holes could be invoked to solve this problem and simultaneously generate the required low baryon fraction (Peirani et al. 2012).
  5. In order to obtain the required late epoch evolution (Weinmann et al. 2012), one might appeal to a lower SFE in dwarfs, plausibly associated with low metallicities and hence low dust and H2 content. Models based on metallicity-regulated star formation can account for the numbers and radial distribution of the dwarfs by a decreasing SFE (Kravtsov 2010). This explanation is disputed by Boylan-Kolchin et al. (2011), who infer a range in SFEs for the dwarfs of some two orders of magnitude. A similar result appeals to varying the halo mass threshold below which star formation must be suppressed to account for the dwarf luminosity function, whereas the stellar masses of many observed dwarfs violate this condition (Ferrero et al. 2011). Finally, tidal stripping may provide a solution (Nickerson et al. 2011), at least for the inner dwarfs.

  6. Another long-standing problem relates to downsizing. Massive galaxies are in place before lower mass galaxies as measured by stellar mass assembly, and their star formation time-scales and chemical evolution time-scales at their formation/assembly epoch are shorter. One popular explanation (Cattaneo et al. 2008) is that galaxies cannot accrete/retain cold gas in massive halos, either because of AGN feedback or because of virial shocks that prevent the gas supply of the disk in cold filaments (Birnboim & Dekel 2003).
  7. It is possible to develop galaxy formation models with suitable degrees and modes of feedback that address many of these issues. However, a major difficulty confronted by all SAMs is that the evolution of the galaxy luminosity function contradicts the data, either at high or at low redshift. The SAMs that are normalized to low redshift and tuned to account for the properties of local galaxies fail at high redshift by generating too many red galaxies (Fontanot et al. 2009). Too few blue galaxies are predicted at z = 0.3. This problem has been addressed by including AGB stars in the stellar populations. This fix results in a more rapid reddening time-scale by speeding up the evolution of the rest-frame near-infrared galaxy luminosity function (Henriques et al. 2011). There is a price to be paid however: now there are excess numbers of blue galaxies predicted at z = 0.5.
  8. There is a well-known difficulty in matching both the galaxy luminosity function and Tully-Fisher scaling relation, even at z = 0. Reconciliation of the Tully-Fisher zero point with the galaxy luminosity function requires too high an efficiency of star formation (Guo et al. 2010). In fact, the problem is even worse: the models of massive spirals tuned to fit the Tully-Fisher relation are too concentrated (McCarthy et al. 2012). This is a reflection of the over-massive bulge problem in disk galaxies that simply refuses to go away (Navarro & Steinmetz 2000, Abadi et al. 2003).
  9. The luminosity function problem is most likely related to another unexplained property of high redshift galaxies. The SSFR evolution at high z is very different from that at low z. Essentially, it saturates. One finds an infrared Main Sequence of galactic SFRs: SFR versus M* (Elbaz et al. 2011). Neither the slope nor the scatter are adequately understood. Starburst galaxies lie above the Main Sequence, but the fraction of cosmic star formation in these systems depends on inadequately justified assumptions about starburst duration. For example, nebular emission and dust extinction affect infrerred ages, and one cannot easily understand the blue continuum slopes oberved at high redshift and lower UV luminosities (Bouwens et al. 2011).
  10. The observed rapid growth of early-type galaxy sizes since z = 2 for fixed stellar mass cannot be reproduced in SAMs or analytical models (Cimatti et al. 2012): at z = 2 galaxies are too compact.
  11. Much has been made of nearby rotation curve wiggles that trace similar dips in the stellar surface density that seemingly reduce the significance of any dark matter contribution. Maximum disks optimize the contribution of stars to the rotation curve, and these wiggles are most likely associated with spiral density waves. A similar result may be true for low surface brightness gas-rich dwarf galaxies (Swaters et al. 2011).
  12. High mass-to-light ratios are sometimes required for maximum disk models of spiral galaxy rotation curves, but these are easily accommodated if the IMF is somewhat bottom-heavy. The case for IMF variations has been made for several data sets, primarily for early-type galaxies (e.g., see van Dokkum & Conroy 2011). The LSB dwarfs are plausible relics of the building blocks expected in hierarchical formation theories.
  13. Spiral arms are seen in the HI distribution in the outer regions of some disks. This tells us that significant angular momentum transfer is helping feed the optical inner disk. The baryonself-gravity is large enough that one does not for example need to appeal to a flattened halo, which might otherwise be problematic for the DM model (Bertin & Amorisco 2010).
  14. The slope and normalization of the baryon Tully-Fisher relation do not agree with the simplest LambdaCDM prediction. The observed slope is approximately 4, similar to what is found for MOND (Milgrom 1983), whereas LambdaCDM (without feedback) gives a slope of 3 (McGaugh 2011, McGaugh 2012), but fails to account for the observed dispersion and curvature.
  15. The baryon fraction in galaxies is some 50% of the primordial value predicted by light element nucleosynthesis. These baryons are not in hot gaseous halos (Anderson & Bregman 2010). Convergence to the universal value on cluster scales is controversial: convergence to the WMAP value is seen for X-ray clusters above a temperature of 5 keV (Dai et al. 2010), but could be as large as 30% even for massive clusters (Andreon 2010, Scannapieco et al. 2012). If the latter discrepancy were to be confirmed, one would need significant bias of baryons relative to dark matter, presumably due to feedback, on unprecedentedly large scales.
  16. The distribution of the MW satellite galaxies in a great circle (Lynden-Bell 1982) is unexpected in the LambdaCDM context (Kroupa et al. 2005). However, infall onto halos is not spherically symmetric (Aubert et al. 2004), and subhalos tend to lie in a plane (Libeskind et al. 2005). The details of the thickness of this plane remained to be settled (e.g., Kroupa et al. 2010 versus Libeskind et al. 2011).
  17. There is a significant lack of galaxies in comparison with standard expectations in the Local Void close to the Local Group (Peebles 2007, Tikhonov & Klypin 2009). But it is not yet clear whether this region fairly low galactic latitude region has been surveyed as closely as other regions.
  18. Bulk flows are found over 100 Mpc scales that are about two standard deviations larger than expected in LambdaCDM (Feldman et al. 2010). The technique primarily uses Tully-Fisher and Fundamental Plane galaxy calibrators of the distance scale. An X-ray approach, calibrating via the kinetic (Sunyaev & Zeldovich 1972) effect (kSZE), claims the existence of a bulk flow out to 800 Mpc (Kashlinsky et al. 2010). However the discrepancies with LambdaCDM are controversial because of possible systematics. A recent detection of kSZE confirms pairwise bulk flows of clusters at 4sigma and is consistent with LambdaCDM (Hand et al. 2012).

Several of these issues may be linked. For example, the analysis of (Cappellari et al. 2012) that the IMF is non-universal, with shallower (top-heavy) IMFs for galaxies of lower velocity dispersion, can be linked with the known relations between velocity dispersion and metallicity (e.g., Allanson et al. 2009) to produce a relation between IMF and metallicity, which goes in the right direction: low-metallicity systems have top-heavy IMFs. Until now, observers assumed a universal IMF when deriving stellar masses. They have therefore overestimated the stellar masses of low-metallicity systems. We would like to think that this overestimation of M* might explain at the same time the evolution of the cosmic SSFR and that of galaxy sizes. Indeed, at high redshift, galaxies are expected to be more metal-poor, and the overestimate of their typical stellar masses will lead to an underestimate of their SSFRs, relative to those of lower-redshift galaxies. Therefore, the cosmic SSFR may not saturate at high redshift, which will make it easier to fit to models. At the same time, if high redshift galaxies have lower stellar masses than inferred from a universal IMF, then for a given stellar mass, they have larger sizes than inferred, and the too rapid evolution of galaxy sizes (relative to models) might disappear. We propose that observers replace stellar mass by K-band rest-frame luminosity, which, if properly measured, can serve as a useful proxy for stellar mass, independently of any assumed IMF.

In summary, it is clear that many problems await refinements in theoretical understanding. No doubt, these will come about eventually as numerical simulations of galaxy formation are refined to tackle subparsec scales.

We are grateful to A. Cattaneo, B. Famaey, A. Graham, J. Kormendy, P. Kroupa, S. McGaugh, A. Pontzen and A. Tutukov for very useful comments.

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