## Appendix A: model equationsThe radiative transition probability for downward transitions is
where and
are the Einstein coefficients for spontaneous
and stimulated emission, and is the mean
integrated radiation field intensity at the line frequency. For the
LVG model with expansion velocity increasing
with radius where is the escape probability for , and for other values of , is given as a function of by equation (A1) of Castor (1970). Here the optical depth is where is the line excitation temperature, and is the filling factor for the H II region. is the cosmic background radiation temperature, and , so for example and 17294 K for the 12.178 GHz and 6.668 GHz lines, respectively. The brightness temperature of the line above the continuum is where © European Southern Observatory (ESO) 1997 Online publication: May 26, 1998 |