2. Radiative excitation of OH-FIR lines
We first examine a simple radiative pumping scheme of the OH-FIR lines by photons emitted by the circumstellar dust grains. Fig. 1 shows the six lowest OH rotational states. OH molecules pumped to the (J = 5/2) level by the absorption of photons return to the ground (J = 3/2) state through the cascades in the and ladders to invert the populations of the ground state hyperfine levels. The populations of the upper levels are assumed to be negligible. In this case the FIR rotational line fluxes can be easily calculated by considering the routes downward through various rotational states. A photon can give rise to 3 photons at , and and the conservation of the number of absorbed photons can be expressed as follows:
We use the usual convention of line flux (negative value for absorption). The emission lines are optically thin, as a result, the number of photons emitted is proportional to the line strength.
where , and are the branching ratios:
, and are the transition probabilities. The flux of the line is directly related to the flux of the line because of the conservation of the number of photons:
The photons absorbed or emitted at alter the intensities of the and lines.
where is the branching ratio of the transition = /( + ) = 0.88
Similarly, the fluxes of the and the lines are calculated as follows
If the fluxes of the absorption line and the line are known, we can derive all the other FIR lines in the pumping cycle of the OH maser, by using formulae 2-7.
© European Southern Observatory (ESO) 1998
Online publication: February 4, 1998