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The radial surface density profiles of galactic disks are determined by the gravitational potential of the galaxy that is dominated in the outer parts by dark matter and the specific angular momentum distribution of the infalling gas that dissipates its potential and kinetic energy while settling into centrifugal equilibrium in the inner regions of a dark matter halo. In addition one has to consider the secular evolution of galactic disks. Viscous angular momentum redistribution and selective gas loss in galactic winds strongly affects the evolution of disks making it difficult to infer the initial conditions from their presently observed structure.

Angular momentum is an important ingredient in order for galactic disks to form. It is generally assumed that, before collapse, gas and dark matter are well mixed and therefore acquire a similar specific angular momentum distribution (Peebles 1969; Fall & Efstathiou 1980; White 1984). If angular momentum would be conserved during gas infall, the resulting disk size should be directly related to the specific angular momentum lambda' of the surrounding dark halo where (Bullock et al. 2001)

Equation 1 (1)

with Rvir and Vvir2 = GMvir / Rvir the virial radius and virial velocity of the halo, respectively, and Mvir its virial mass. Adopting a flat rotation curve, the disk scale length is (Mo et al. 1998; Burkert & D'Onghia 2004)

Equation 2 (2)

where vmax is the maximum rotational velocity in the disk.

Figure 1 shows the correlation between the disk scale length Rdisk and the maximum rotational velocity vmax for massive spiral galaxies (Courteau 1997) which is consistent with a mean value of lambda' approx 0.025. The observationally derived average peak value of lambda' = 0.025 is somewhat smaller than the theoretically predicted value of lambda' = 0.035, indicating that the gas could on average have lost some amount of angular momentum during the phase of decoupling from the dark component and settling into the equatorial plane.

Figure 1

Figure 1. The observed scale lengths versus the maximum rotational velocities of galactic disks are shown for the Courteau (1997) sample. The sold line shows the theoretically predicted correlation for lambda' = 0.035. The dashed curve corresponds to lambda' = 0.025.

This result is promising. The situation is however far less satisfactory when we consider more detailed numerical models of gas infall and accumulation in galactic disks. Many simulations of galactic disk formation suffer from catastrophic angular momentum loss which leads to disks with unreasonably small scale lengths and surface densities that are too large. The origin of this problem has been attributed to a strong clumping of the infalling gas which looses angular momentum by dynamical friction within the surrounding dark matter halo (Navarro & Benz 1991, Navarro & Steinmetz 2000). Other possibilites are low numerical resolution (Governato et al. 2004, 2007), the effect of substantial and major mergers (d'Onghia et al. 2006) or artificial secular angular momentum transfer from the cold disk to its hot surrounding (Okamoto et al. 2003). Over the years many groups have tried to solve this problem by including star formation and energetic feedback (e.g. Sommer-Larsen et al. 2003, Abadi et al. 2003, Springel & Hernquist 2003, Robertson et al. 2004, Oppenheimer & Dave 2006, Dubois & Teyssier 2008). The results are however confusing. First of all the origin of the angular momentum problem is not clearly understood. Secondly, no reasonable, universally applicable feedback prescription has been found that would lead to the formation of large-sized, late-type disks, not only for one special case, but in general.

Progress in our understanding of the cosmological angular momentum problem has recently been achieved by Zavala et al. (2008) who confirmed that the specific angular momentum distribution of the disk forming material follows closely the angular momentum evolution of the dark matter halo. The dark matter angular momentum grows at early times as a result of large-scale tidal torques, consistent with the prediction of linear theory and remains constant after the epoch of maximum expansion. During this late phase however angular momentum is redistributed within the dark halo with the inner dark halo regions loosing up to 90% of their specific angular momentum to the outer parts. The process leading to this angular momentum redistribution is not discussed in details. It is however likely that substantial mergers with mass ratios less than 10:1 that are expected to occur frequently even at late phases during galaxy formation perturb the halo and generate global asymmetries in the mass distribution that are known to be an efficient mechanism for angular momentum transfer. Small satellite infall is probably of minor importance. It would be interesting to study the role of major and minor mergers in this process in greater details.

It is then likely that any gas residing in the inner regions during such an angular momentum redistribution will also loose most of its angular momentum, independent of whether the gas resides already in a protodisk, is still confined to dark matter substructures or is in an extended, diffuse distribution. Zavala et al. (2008) (see also Okamoto et al., 2005 and Scannapieco et al., 2008) show that efficient heating of the gas component can prevent angular momentum loss, probably because most of the gaseous component resides in the outer parts of the dark halo during its angular momentum redistribution phase. The gas would then actually gain angular momentum rather than loose it and could lateron settle smoothly into an extended galactic disk in an ELS-like (Eggen, Lynden-Bell & Sandage 1962) accretion phase.

Unfortunately little is known about the energetic processes that could lead to such an evolution. Obviously, star formation must be delayed during the protogalactic collapse phase in order for the gas to have enough time to settle into the plane before condensing into stars. However star formation is also required in order to heat the gas preventing it from collapsing prior to the angular momentum redistribution phase. Scannapieco et al. (2008) show that their supernova feedback prescription is able to regulate star formation while at the same time pressurizing the gas. Their models are however still not efficient enough in order to produce disk-dominated, late-type galaxies. Large galactic disks are formed. The systems are however dominated by a central, massive, low-angular momentum stellar bulge component. This is in contradiction with observations which indicate a large fraction of massive disk galaxies with bulge-to disk ratios smaller than 50% (Weinzirl et al. 2008) that cannot be produced currently by numerical simulations of cosmological disk formation.

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