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Most of the stars in spiral galaxies reside in remarkably thin disks. In a photometric study of edge-on galaxies, Yoachim & Dalcanton (2006) found that the fraction of the baryons in the thin disk component is in the range 70% to 90%, with higher fractions being characteristic of more massive galaxies. The so-called superthin disks are even more extreme; the disk of the low-luminosity galaxy UGC 7321, for example, has a radial scale-length some 14 times that of its characteristic thickness (Matthews 2000).

Hierarchical galaxy formation scenarios (see chapter by Steinmetz) predict that galaxy formation is far from monolithic, with occasional major mergers with other halos, and frequent minor mergers. Stellar disks that have formed in the centers of the halos are torn apart in major mergers (Barnes & Hernquist 1992), but the consequences of minor mergers are harder to determine from simulations (e.g. Walker et al. 1996). Tóth & Ostriker (1992) argued that the existence of thin disks in galaxies can be used to constrain the rate of minor mergers. Their numerical estimates have been criticized on various grounds (e.g. Huang & Carlberg 1997, Sellwood et al. 1998, Velázquez & White 1999), but it is clear that a tight constraint remains.

Wyse (this volume) stresses that the thick disk of the MW contains only very old stars, and that the ages of thin disk stars stretch back 10 Gyr. This fact would seem to imply that the last galactic merger to have stirred the MW disk occurred some 10 Gyr ago, and that no comparable disturbance could have occurred since. The MW may not be unique in this respect, as Mould (2005) found that thick disks in four nearby galaxies also appear to be old.

Stewart et al. (2008) estimated the rate of mergers in the current LambdaCDM cosmology. They concluded that 95% of parent halos of some 1012h-1 Modot will have merged with another halo of at least 20% of its mass in the last 10 Gyr, and consequently the disk hosted by the parent must somehow survive in most cases.

Possibly only a small fraction of infalling satellites pose a real threat to a disk. All satellites will be tidally stripped as they fall into the main halo, and some may even dissolve completely before they can affect the disk - the Sagittarius dwarf galaxy appears to be a good example (Law et al. 2005). A massive satellite loses orbital energy through dynamical friction (Section 9.8) causing it to settle deeper into the main halo. Its survival depends on its density (see BT08, Section 8.3); it will be stripped of its loosely bound envelope until its mean density, rho, is about one third the mean density of the halo interior to its orbital radius (BT08 eq. 8.92), and disrupted entirely as it reaches a radius in the main halo where even its central density falls below the mean interior halo density. This process has been studied in more detail by Boylan-Kolchin & Ma (2007) and by Choi et al. (2009). Thus the vulnerability of disks depends on the inner densities, in both dark matter and baryons, of the accreted sub-halos.

If even a single, moderately massive core survives to the inner halo, it could cause an unacceptable increase in the disk thickness. Vertical heating of the disk occurs when a passing or penetrating satellite is able to increase the vertical motions of the disk stars. High speed passages therefore deposit little energy into disk motions, but if the satellite's orbit remains close to the disk mid-plane, then its vertical frequency will couple strongly to that of some of the disk stars and heating will be rapid. Indeed, Read et al. (2008) argued that the accretion event(s) that created the thick disk of the MW most probably resulted from the infall of a subhalo whose orbit plane was inclined at 10 - 20 to that of the disk. The energy deposited could take the form of exciting bending waves in the disk that can propagate radially until they are damped at vertical resonances (Sellwood et al. 1998).

Kazantzidis et al. (2009) simulated several minor mergers with sub-halos in detailed models with plausible parameters. They found that the disk is substantially thickened and heated by the mergers, although they noted that their simulations lacked a gaseous component. Simulations that include a gas component cannot resolve the small-scale physical processes of gas fragmentation, star formation, feedback, etc., and therefore the behavior of the dissipative gas component necessarily includes somewhat ad hoc prescriptions for these aspects of sub-grid physics. Hopkins et al. (2009) stressed that gas in mergers settles quickly to begin to form a new disk; however, it is the fate of the stars that had been formed prior to the merger that is the principal concern. Kazantzidis et al. (2009) argued it is possible that a dissipative component in the disk could absorb some of the orbital energy of the satellite which would reduce the heating of the stellar disk, and such an effect appears to have occured in the simulations by Moster et al. (2010). A clear conclusion has yet to emerge from this on-going research effort, but exclusively old thick disks together with the prevalence of thin disks poses a substantial, though perhaps surmountable, challenge to the LambdaCDM model.

It should be noted that ideas to reduce the density of the inner main halo through frictional energy loss to halo (e.g. El-Zant et al. 2001, Mashchenko et al. 2006, Romano-Díaz et al. 2008a) require the kinds of dense massive fragments that are themselves a danger to the disk. This will be of less importance in the early stages of galaxy assembly, but disk survival adds the requirement that any such process be completed quickly.

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