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4.3. Additional Heating and Ionization Processes

The following are additional processes that are likely to be important in AGN clouds.

4.3.1. Dielectronic recombination. Radiative recombination is the term used to describe the interaction of the ion Xi+1 with a free electron, leading to the ion Xi in a ground or excited state below the ionization limit. Recombination can also proceed via autoionization states, above the ionization limit, in which case it is called dielectronic recombination. At high temperatures the free electrons cover an infinite number of autoionization states. Dielectronic recombination, in this case, is fast but density dependent. At low temperatures individual autoionization states are the main contributors to the recombination rate. The process is important in AGN clouds and can also result in emission lines of ion Xi. Such lines are weak but are of great importance in determining the chemical composition of the gas.

4.3.2. Collisional ionization and three-body recombination. The rates of collisional ionization and its inverse process, three-body recombination, depend on Ne2, Te, and the statistical weight of the level in question. Such processes are not very important in photoionized galactic nebulae, where the density is low and most ions are in their ground state. This is not the case in the broad line clouds, where many atoms are in excited states, due to the high density and large optical depth. For example, in the BLR clouds, the n geq 10 levels of hydrogen, helium and some metals are collisionally coupled to the continuum and their populations are completely controlled by such processes. The n < 10 levels of hydrogen are affected too.

The treatment of these processes is rather tricky. A very large number of levels must be considered, and many unknown cross sections must be guessed. As a general rule, three-body recombination is faster than radiative recombination, for many ions, at Ne geq 1011 cm-3. The process is therefore important in the very dense parts of the BLR.

4.3.3. Compton heating-cooling and ionization. Compton scattering by bound and free electrons can be an important ionization and heating source for the gas, because of the intense X-ray radiation in AGNs. For nonrelativistic electrons, the energy transfer per scattering is approximately

Equation 20 (20)

thus photons with energies greater than about 2.6 keV can ionize hydrogen from its ground level. Heavier elements can be ionized too, at higher energies, with an effective cross section which is proportional to the number of bound electrons. In realistic situations, the process is important only for mostly neutral gas, and hydrogen ionization is the only important source of free electrons because of the small abundance of the heavier elements.

The Compton heating rate is

Equation 21 (21)

Compton cooling ("inverse Compton") occurs when a low energy photon, (h nu < 4kTe) is scattered by an electron. The cooling rate is

Equation 22 (22)

In these expressions sigmah and sigmac are heating and cooling effective cross sections that agree with the Thomson cross section at low photon energy and with the Klein-Nishina formula at h nu ~mec2. The correction due to stimulated processes, that can be important in intense radiation fields, was not included in these equations.

Compton heating and cooling is most important for the (hypothetical) hot gas suggested as a confining medium for AGN clouds (chapter 9).

4.3.4 Secondary electrons. Photoionization by high energy photons results in the ejection of an energetic electron. Because of the smaller Coulomb-scattering cross section at high energies, the mean free path of such electrons is long and several other reactions can occur before thermalization takes place. Most important are collisional ionization (leading to more secondary electrons) and collisional excitation. The result is more ionizations and less heating per incident high energy photon. The process is well known in the interstellar medium.

Secondary electrons related processes are very important in the partly neutral zone of AGN broad line clouds. The fast electrons are produced mainly by photoionization of He0 and some metals, and they loose much of their energy by collisional excitation and collisional ionization of hydrogen. Calculations giving the number of extra ionizations, and the effective heating due to such electrons, are available. Care must be taken in calculating the cooling rate since excitation to high levels may be followed by collisional de-excitation, i.e. additional heating. There is also some extra line emission due to this process.

4.3.5 Charge exchange. These are reactions of the type

Equation 23 (23)

where X and Y are two ions. The most important cases at Te ~ 104 K, involve neutral hydrogen. Well known examples are charge exchange reactions of H0 with O+ and N+, that control the ionization of oxygen and nitrogen near the hydrogen ionization front.

Atomic calculations show that charge exchange with hydrogen, at a rate of 10-9 cm+3 s-1 or larger, is common for many ions. The typical recombination coefficients for metals, at Te = 104 K, are about 10-12 cm+3 s-1, and charge exchange with hydrogen is therefore an important process for all regions where N(H0) / N(H+) geq 10-3. For example, the charge exchange of H0 with Fe++ is an important factor in increasing the Fe+ fraction in AGN clouds.

Charge exchange can proceed via excited states, leading to some line emission. There is not yet any clear evidence that this is important in AGN clouds.

4.3.6 H- and molecules. In large column density clouds, a trace amount of hydrogen can be in the form of H- and H2. This can be an important opacity source at infrared frequencies that increases the amount of infrared heating. The expected amount of H- and H2 must therefore be considered.

An important creation mechanism for H- is collisions with free electrons

Equation 24 (24)

Several other processes, such as charge exchange of H- with positively charged ions (charge neutralization), can be important too. Out of the possible heating-cooling processes applicable to H- and H2, those associated with bound-free and free-free transitions in H- are probably the most important.

The H- and H2 related processes are of marginal importance in AGN clouds, unless the column density is extremely large (~ 1025 cm-2).

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