§3.11 气体冷却

Hot gas cooling enters the right-hand side of equation equation:firstlaw, as well as the equations describing mass and energy flows among different gas phases which may be present in sub-resolution models.

In cosmological simulations, the focus is usually on structures whose virial temperature exceeds $\sim 10^4$ K. Common assumptions in standard implementations of the cooling function $\Lambda(u,\rho)$ is that the gas is optically thin and in ionization equilibrium. It is also usually assumed that three-body cooling processes are unimportant so as to restrict the treatment to two-body processes. For a plasma with primordial composition of H and He, these processes are: collisional excitation of H$^0$ and He$^+$, collisional ionization of H$^0$, He$^0$, and He$^{+}$, standard recombination of H$^+$, He$^+$, and He$^{++}$, dielectric recombination of He$^+$, and free--free emission (bremsstrahlung). The collisional ionization and recombination rates depend only on temperature. Therefore, should an ionizing background radiation be absent, the resulting rate equations can be solved analytically. This leads to a cooling function $\Lambda(u)/\rho^2$ as illustrated in the left panel of Fig. 9. On the other hand, in the presence of ionizing background radiation, the rate equations can be solved iteratively. Note that for a typical cosmological radiation background (e.g., UV background from star-forming galaxies and quasars, see ^[118] ,^[119] ,^[120] ,^[121] ), the shape of the cooling function can be significantly altered, especially at low densities. For a more detailed discussion, see, for example, 星系形成章节 and ^[17] .

Additionally, the presence of metals will drastically increase the number of possible processes by which gas can cool. As it becomes computationally very demanding to calculate the cooling function in this case, cosmological simulations usually rely on a pre-computed, tabulated cooling function. As an example, the right panel of Fig. 9 shows the tabulated cooling function from ^[123] , for temperatures above $10^5$ K, for different metallicities of the gas, keeping the ratios of different metal species fixed to solar values. A refinement that is nowadays often exploited in simulations consists in using the `Cloudy` code (^[124] ), which allows users to tabulate the cooling and heating rates, individually for a grid of UV intensities and for various different chemical elements. In this way, cooling rates are self-consistently calculated for arbitrary chemical % compositions. Note that almost all the implementations solve the above rate equations (and therefore the cooling of the gas) as a ``subtime step'' problem, decoupled from the hydrodynamical treatment. This translates in assuming that the density is fixed across the time step. Furthermore, the time step of the underlying hydrodynamical simulation is in general, for practical reasons, not controlled by nor related to the cooling time scale. The resulting uncertainties introduced by these approximations have not yet been deeply explored and clearly leave room for future investigations.

For the formation of the first objects in halos with virial temperatures below $10^4$ K, the assumption of ionization equilibrium no longer holds. In this case, the non-equilibrium reactions have to be considered, by solving the balance equations for the individual levels of each species during the cosmological evolution. In the absence of metals, the main coolants are H$_2$ and H$_2^+$ molecules (see ^[125] ). HD molecules can also play a significant role. When metals are present, many more reactions are available and some of these can contribute significantly to the cooling function below $10^4$ K. This effect is clearly visible in the right panel of Fig. 9 for $T<10^4$ K. For more details, see 星系形成章节, Refs. ^[126] ,^[122] , and references therein.