4. THE DARK SIDE OF DISK FORMATION

Several fundamental problems have arisen in detailed attempts to implement disk formation. The baryons undergo excessive cooling. The highest resolution simulations to date have revealed that as a consequence of the unresolved clumpiness of the dark matter, most of the baryonic angular momentum is lost to the dark halo by dynamical friction of infalling baryon clumps. The final specific angular momentum is only twenty percent or less of what is observed. The angular momentum distribution also does not match that of dark halos if the baryon angular momentum distribution tracks that of the dark matter, there being far too much low angular momentum gas at small galactocentric radii in the models. Even if angular momentum is assumed to be conserved by the baryons, the final disk in a Milky Way-like galaxy is about twice as massive as observed.

One issue is generic to hierarchical formation models with a specified efficiency of turning gas into stars. The most massive systems form late, and hence are expected to be younger and therefore bluer than less massive disks. The opposite trend is seen in the disk colour-magnitude relation [van den Bosch2002].

A further difficulty arises from the substructure in the dark halos that results in the formation of many satellite halos. These are not observed as stellar systems, for example in the distribution of Local Group dwarf galaxies. Another problem concerns the density distribution of the dark matter halos. The dark matter halos seem to be too concentrated compared to actual galaxies. Cusps are predicted in the halo cores that are not seen in nature, and the ratio of dark mass to baryonic mass is excessive in the vicinity of the baryon-dominated disk.

Several galaxies have been modelled in detail and illustrate these various trends. The Milky Way has the best studied rotation curve. Binney and Evans combined the inner rotation curve with microlensing data to infer that the observed microlensing optical depth towards the galactic centre requires so many stars that one has difficulty in acommodating a diffuse cold dark matter component. No more than 10 percent of the dark matter within 5 kpc can be diffuse and non-baryonic [Binney & Evans2001]. In particular, the NFW profile ( r^-1 for r < r_s with r_s ~ 0.1r₂₀₀) is not allowed. Indeed, the highest resolution simulations require an even steeper dark matter cusp; r^-1.5. This certainly would not allow enough bulge and inner disk stars to give a reasonable microlensing optical depth.

A complementary study by Klypin et al focuses on the outer Milky Way rotation curve. They argue that up to half of the mass within 10 kpc may be contributed by the dark halo, thereby allowing a NFW profile [Klypin, Zhao and Somerville2002]. However this conclusion comes at a cost. Only 60 percent of the baryons inferred by the model to be within the virial radius can be accomodated in the bulge, stellar halo and disk, including interstellar matter. Most of the observed mass of course is in stars, which are measured directly for stars of order a solar mass or larger, and via rotation curve modelling, diffuse infrared emission and bulge microlensing for the least massive stars. All disk formation and evolution simulations seem to run into a similar difficulty, as for example in a recent discussion of colour evolution [Westera et al.2002].

Several of these issues are manifestations of the overcooling problem that is generic to hierarchical structure formation models. The cooled baryon fraction in cluster simulations is about 30 percent, whereas the global CDM prediction is about 5 percent for the baryon fraction, which for _m 0.3 predicts 15 percent for rich clusters, as indeed is observed. About half of the cooled baryons remain on the peripheries of clusters as the warm/hot intergalactic medium at T ~ 10⁵ - 10⁶ K. Numerical SPH simulations find such a WIGM, although the physics of how this gas is heated yet remains outside the cluster virial radius is not completely clear. Shock heating is obviously important, but there are numerical issues that need to be clarified. The WIGM however only acccounts for about 30 percent of the total baryon content of the low redshift universe. The cluster x-ray luminosity-temperature correlation, which monitors the mass in virialised gas, does not satisfy the simple scaling expected in hierarchical collapse models, but rather suggests that preheating, preferentially in the lower mass clusters, may have helped to steepen the luminosity-temperature correlation from L_x T² to L_x T².

Another probe of dark matter in reasonably luminous disks comes from studying the kinematics of barred galaxies. Debattista and Sellwood argued that a maximal disk is required, eg for NGC 3198, in order to maintain a self-gravitating bar [Debattista & Sellwood2000]. On the other hand, Kranz et al. find varying results for the disk mass fraction by modelling the detailed kinematic structure, for example the (unbarred) galaxy NGC 4254 requires a submaximal disk [Kranz, Slyz and Rix2002].

The colour-magnitude relation (B-K versus K) reveals another difficulty [van den Bosch2002]. The more luminous galaxies, the redder they are, indicative of less vigorous recent star formation. SEmi-analytical disk models, even when feedback is included, give the inverse correlation. This is another manifestation of the overcooling problem. The oldest early-type galaxies are found to be the most massive, and these have the highest [ / Fe], indicative of the shortest star formation time-scales. The opposite trend is expected in hierarchical models [Thomas, Maraston and Bender2002].