Cooling function

The rate of cooling per H2 molecule (erg s-1) is defined as

\begin{displaymath}W({\mathrm H}_2) = 1/n({\mathrm H}_2) \sum _{vJ,v'J'} (E_{vJ} - E_{v'J'}) n_{vJ} A(vJ \rightarrow v'J')\; ,\end{displaymath}


where EvJ > Ev'J' are the energies (erg) of the levels, expressed relative to the v = 0, J=0 ground state, nvJ (cm -3) is the population density of the level (v,J), and $A(vJ \rightarrow v'J')$ (s-1) is the spontaneous transition probability; $n({\mathrm H}_2) = \sum_{vJ} n_{vJ}$ is the total H2 number density.

The Fortran program interp.f prerforms an interpolation to any given set of values of the following parameters, within their specified ranges:

$\displaystyle 1 \le$nH$\displaystyle \le 10^8 {\mathrm cm}^{-3}$(1)
$\displaystyle 100 \le$T$\displaystyle \le 10^4 {\mathrm K}$(2)
$\displaystyle 10^{-8} \le$n(H)/n(H2)$\displaystyle \le 10^6$(3)
$\displaystyle 0.1 \le$n(ortho)/n(para)$\displaystyle \le 3 .$(4)


These parameters are, successively: nH = n(H) + 2n(H2), the gas density; the kinetic temperature, T; the H to H2 density ratio; the ortho- to para-H2 density ratio. The program interp.f prompts for values of these four parameters. The cooling function is calculated by interpolation of the data contained in the file le_cube and is returned as $\log _{10} [ W ({\mathrm{erg \; s}}^{-1}) ] $. The ranges specified above are exceeded at the risk of the user: no guarantee of the reliability of the result is given, even if the output value appears "reasonable". The subroutines used to evaluate the cooling function may be incorporated (along with the data set le_cube) in the user's own astrophysical model.