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Astron. Astrophys. 327, 1262-1270 (1997)

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2. Basic equations

The thermal and chemical evolution of a gas subjected to variable external conditions are calculated by solving the system of kinetic equations and the equation of energy conservation. The system of kinetic equations can be written in the general form

[EQUATION]

where n is the total number density of hydrogen nuclei and [FORMULA] is the relative number density of the i -th species. In Eq. (1), [FORMULA] and [FORMULA] are, respectively, the formation and destruction rates of the i -th species due to double collisions, whereas, [FORMULA] and [FORMULA] are, respectively, the production and destruction rates of the i -th species due to the interaction of particles with radiation.

The equation of energy conservation equation can be expressed as

[EQUATION]

where U is the internal energy by unit mass, [FORMULA] is the net cooling rate by unit mass ([FORMULA] [FORMULA]), P is the pressure, [FORMULA] is the mass density, and V is the specific volume. Assuming that [FORMULA] and [FORMULA], with R the gas constant, and [FORMULA] the molar mass, Eq. (2) can be written as

[EQUATION]

Two extreme situations that can be used to confine intermediate situations are the constant density and constant pressure approximations. In these approximations, the energy conservation equation can be expressed as

[EQUATION]

where, [FORMULA] or [FORMULA] in the constant density or in the constant pressure approximations, respectively.

Variations of the external ionizing sources flux produces direct variation on the rates [FORMULA] and [FORMULA], and on the heating rate [FORMULA], whereas, variations of the presure affect density and temperature. Notice that variations of n or [FORMULA] provoke a variation of the chemical state of the gas, and therefore produce a variation of the cooling rate [FORMULA]. In the following, we solve the basic equations (1) and (2) with the appropriate assumptions in order to model: a) the evolution of a metal free cloud subjected to a variation of the ionizing and dissociating flux (Sect. 3), and b) the evolution of a solar abundance gas subjected to variations of the primary ionization rate due to cosmic rays (Sect. 4).

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© European Southern Observatory (ESO) 1997

Online publication: April 6, 1998
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