ARlogo Annu. Rev. Astron. Astrophys. 1998. 36: 599-654
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2.3. Additional Physics

Besides gravity and adiabatic gas dynamics, atomic and radiative processes are very important in the formation of galaxies and the evolution of the intergalactic medium. In particular, radiative cooling is thought to be primarily responsible for the condensation and survival of galaxies within larger virialized structures (e.g. White & Rees 1978, Blumenthal et al 1984). The processes included in state-of-the-art cosmological simulation codes include optically thin radiative cooling, multispecies chemistry, a phenomenological treatment of star formation and its associated energy feedback, and approximate radiative transfer.

The simplest way to incorporate radiative cooling is by means of an equilibrium cooling function Lambda(T) such that the cooling rate per unit volume is nenp Lambda(T), plus a contribution proportional to ne(T - Tgamma) from Compton cooling of ionized gas by the microwave background radiation. In this approach, the number densities of free electrons and protons, ne and np, respectively, are computed assuming equilibrium between recombination and collisional ionization at temperature T (with Tgamma the microwave background temperature), which eliminates the need to follow rate equations for multiple species. Cooling functions were used in many early dissipative simulations, e.g. by Cen et al (1990), Katz & Gunn (1991), and continue to be adequate for many applications.

The cooling function approach breaks down when ionization equilibrium breaks down, as can happen behind shocks or in dense cooling regions, and when photoionization becomes more important than collisional ionization, as it does in the tenuous intergalactic medium. Gnedin (1996a) accounted for the second effect by generalizing the cooling function to depend on the photoionization rate while retaining a one-fluid treatment of the gas. However, a full treatment of cooling requires following the nonequilibrium abundances of free electrons and all atomic, ionic, and molecular species relevant for cooling. Cen (1992) was the first to implement such a treatment in a cosmological simulation code, including rate equations for electrons and all ionization states of hydrogen and helium. Haehnelt et al (1996b) added heavier elements ("metals"), with their photoionization equilibria computed using the code CLOUDY (Ferland et al 1998).

Because of the importance of molecular hydrogen as a coolant of primordial (i.e. metal-free) gas below 104 K (e.g. Peebles & Dicke 1968, Shapiro & Kang 1987), recent treatments add H-, H2+, and H2 (Haiman et al 1996, Abel et al 1997, Anninos et al 1997, Gnedin & Ostriker 1997). All species are treated as though they are in the ground electronic state (although recombination rates are computed including cascades from excited states), which is a good approximation at the low densities of cosmological and intergalactic gas (Abel et al 1997).

Gas heating can also be important, both in raising the Jeans mass enough to suppress dwarf galaxy formation (e.g. Couchman & Rees 1986, Dekel & Silk 1986, Kepner et al 1997a) and in reionizing the intergalactic medium (Shapiro & Giroux 1987, Ostriker & Gnedin 1996). Heating by star formation (ultraviolet radiation from hot stars, stellar wind bubbles, and supernovae) has been included in a phenomenological way, along with the conversion of gas into collisionless particles representing stars or galaxies, by many workers, e.g. Katz (1992), Cen & Ostriker (1992a, 1993b), Navarro & White (1993), Mihos & Hernquist (1994).

Radiative transfer has been treated so far only in relatively crude approximations because the specific intensity is computationally infeasible, as it is a function of six variables (position, photon frequency, and direction) and time. Cen (1992) treated the radiation field as spatially homogeneous and isotropic while allowing for its detailed energy dependence, an approximation that has been used frequently since. Gnedin & Ostriker (1997) treated radiative emission as uniform and isotropic but allowed absorption to vary locally depending on the gas density, using a clever scheme they call the local optical depth approximation.

In one (Ducloux et al 1992) or two (Stone et al 1992) space dimensions, improved treatments of radiative transfer have been developed using a variable Eddington factor (the ratio of radiation stress to energy density). In these codes, the Eddington factor, needed to close the radiation moment hierarchy at second order, is provided by approximate integrations of the radiative transfer equation that are valid in both the optically thick and thin regimes. So far this very promising method has not included the full frequency dependence of the radiation, nor has it been extended to three dimensions, which both require substantial increases in computation.

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