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In the canonical picture of galaxy formation, the initial distribution of baryons in the universe matched that of the dark matter, such that when dark matter overdensities collapse and virialize, gas is also affected by the same large–scale tidal fields as the dark matter, resulting in a similar distribution of baryonic matter as that of the dark matter. However, since the halo gas is dissipational (unlike dark matter), it is capable of radiating away orbital and thermal energy, sinking to the center of the halo's gravitational potential, until it is ultimately cold and dense enough to form stars. Thus, all galaxies are thought to be embedded at the center of a massive dark matter halo, with the sizes, luminosities, morphologies and angular momentum content of those galaxies owing to the details of their formation — which are likely to be correlated in some way with the formation of the dark matter halo. In this section, we will detail the canonical model for how this link between dark matter halo formation and galaxy formation is thought to operate, including the importance of this model in laying the foundation for semi-analytic models (SAMs) of galaxy formation, and discussing the levels of agreement between such models and observations. We will then give a brief review of the challenges and achievements in attempting to simulate galaxy formation directly with hydrodynamic cosmological simulations.

3.1. Modeling Gas Accretion onto Galaxies

The classic picture of galaxy formation (e.g., Fall & Efstathiou, 1980, White & Frenk, 1991, Mo et al., 1998) attempts to model the formation of galactic disks inside the hierarchical framework of LCDM by making a few assumptions about the relationship between the baryons and dark matter. In these relatively simple models it is possible to reproduce a number of observable properties of spiral galaxies (e.g., the slope and scatter of the Tully–Fisher relation) as well as damped Lyα absorbers, while making as few underlying assumptions as possible. For example, Mo et al. (1998) use the following fundamental assumptions:

  1. As the halo forms, the gas initially relaxes into an isothermal distribution. Further gas accretion is shocked to the virial temperature of the halo. Virialized gas subsequently cools, conserving angular momentum.
  2. The specific angular momenta of galaxy disks are thus similar to their parent halos, jdj (alternatively, λd ≃ λ). As a result, the total angular momenta of disks is expected to be a fixed fraction of that of the halo: Jd / JMd / M.
  3. Galaxy disks have masses that are a fixed fraction of roughly a few percent of the mass of their parent halos: Md / M ≤ 0.05
  4. The resulting disk is assumed to be rotationally supported with an exponential surface density profile and Rd ≃ λ Rvir.

Building on this approach, more recent semi-analytic models include additional physical models such as supernova feedback that expels gas from galaxies, black hole growth and feedback that heats gas in galaxy clusters, estimation of the cooling radius and cooling rate out of the hot halo, as well as effects of galaxy mergers such as starbursts and morphological transformation (recently, e.g., Cattaneo et al., 2006, Croton et al., 2006, Somerville et al., 2008, Dutton, 2012, Somerville et al., 2012). By tuning the input parameters of these models on certain observational constraints (e.g. tuning the chemical yield of supernovae to reproduces metallicities of stars in galaxies in Somerville et al., 2008), it is possible to produce modeled galaxy populations that reproduce a great number of physical properties of galaxies: e.g., cold gas fractions, stellar ages, specific star formation rates, stellar mass functions, etc.

While it is beyond the scope of this chapter to provide a more comprehensive review of semi-analytic models of galaxy formation, one important point for consideration (especially for our discussion in § 4) is that while some more recent models do implement a distinction between “cold mode” accretion that does not shock–heat to the virial temperature, versus “hot mode” gas accretion which does shock–heat, the angular momentum of the halo gas (regardless of which “mode” is used) is still modeled by λd = λgas = λDM. However, hydrodynamic simulations suggest that galactic outflows may preferentially expel low angular momentum gas from the centers of galaxies, keeping galaxy formation inefficient and stopping forming galaxies from universally creating massive bulges at early times. In this case, even if galaxies initially form with λd = λDM at early times, this similarity would be expected to break over cosmic time, as outflows continue to preferentially remove low angular momentum gas from the galaxy (without similarly removing dark matter from the halo). Furthermore, while one might expect the overall spin of halo gas and dark matter to be in rough agreement, we will see in § 4.2 that the detailed accretion geometry of different modes of of gas accretion (particularly the contribution of dense filamentary “cold mode” gas) results in a scenario where λgas ≠ λDM.

3.2. Hydrodynamic Simulations of Galaxy Formation

Early work in cosmological hydrodynamic simulations showed great difficulty in successfully simulating disk dominated galaxies. In what is often referred to as the “angular momentum catastrophe”, simulations produced either spherical galaxies or disks with significantly lower angular momentum than the halo, with orbital angular momentum being transferred to the dark matter by dynamical friction before the baryons reach the center of the halo (e.g. Katz, 1992, Navarro & White, 1994, Sommer-Larsen et al., 1999, Steinmetz, 1999, Navarro & Steinmetz, 2000, D'Onghia et al., 2006). Not surprisingly, these simulated galaxies also produced unrealistic rotation curves and failed to match other observational constraints, such as the Tulley–Fisher relation.

The alleviation of this problem seemed to be the inclusion of efficient star formation feedback, which preferentially removes low angular momentum gas (that would otherwise form stars) from the centers of galaxies during the formation process (e.g. Governato et al., 2007, Scannapieco et al., 2008, Brook et al., 2011, Guedes et al., 2011, Governato et al., 2010, Übler et al., 2014, Christensen et al., 2016). This feedback makes galaxies considerably less efficient at forming stars, also keeping them gas–rich for longer. This, in turn, also helps alleviate the tension between the observed abundance of disk dominated galaxies (e.g., Weinmann et al., 2006) with the frequency of major mergers derived from N-body simulations (e.g., Stewart et al., 2008, Fakhouri et al., 2010), as both direct hydrodynamic simulation as well as semi–empirical galaxy formation models suggest that gas–rich major mergers may help build angular momentum supported disks from the surviving merger remnant, rather than transforming pre-existing disks into spheroids Robertson et al. (2006), Stewart et al. (2009), Hopkins et al. (2009), Governato (2009). With these advances in star formation and feedback prescriptions (as well as more advance computational power), recent simulations have essentially eliminated the early angular momentum problem, allowing hydrodynamic simulations to successfully produce bulgeless exponential disk galaxies with properties quite similar to those observed in the real universe (e.g., Governato et al., 2010, Brook et al., 2011, Guedes et al., 2011).

Most importantly for our discussion of angular momentum acquisition in galaxies (and their halos), recent hydrodynamic simulations have also begun to place growing emphasis on the different “modes” of gas accretion onto galaxies, especially at high redshift. In what is labeled “hot–mode” accretion, gas continues to behave in the manner previously described, shock–heating to the virial temperature of the halo, mixing, and eventually cooling on the galaxy. However, the main mode of gas accretion for most galaxies is thought to be via “cold–mode” (or “cold flow”) accretion — where the inflowing gas streams originating from filamentary accretion are dense enough at high redshift to have cooling times shorter than the shocking compression timescales, resulting in direct gas accretion from the cosmic web, through the galaxy halo, and onto the outskirts of the galaxy (e.g., Kereš et al., 2005, Dekel & Birnboim, 2006, Brooks et al., 2009). As a result, this cold mode gas does not necessarily mix with the existing gaseous halo, and so the specific angular momentum of gas that accretes onto the central galactic disk might not be well matched by that of the dark matter halo, as previously assumed. We will discuss possible implications of this dual mode of accretion for understanding angular momentum in galaxy halos in § 4.2.

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