*Astron. Astrophys. 327, 1262-1270 (1997)*
## 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
where *n* is the total number density of hydrogen nuclei and
is the relative number density of the *i*
-th species. In Eq. (1), and
are, respectively, the formation and destruction
rates of the *i* -th species due to double collisions, whereas,
and 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
where U is the internal energy by unit mass,
is the net cooling rate by unit mass (
), *P* is the pressure,
is the mass density, and *V* is the
specific volume. Assuming that and
, with R the gas constant, and
the molar mass, Eq. (2) can be written as
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
where, or in the
constant density or in the constant pressure approximations,
respectively.
Variations of the external ionizing sources flux produces direct
variation on the rates and
, and on the heating rate
, whereas, variations of the presure affect
density and temperature. Notice that variations of *n* or
provoke a variation of the chemical state of
the gas, and therefore produce a variation of the cooling rate
. 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).
© European Southern Observatory (ESO) 1997
Online publication: April 6, 1998
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