(2.1) |

The opacity of the multiplet is the sum of the
opacities:

(2.2) |

(2.3) |

where the last equality holds in the optically thin regime.

This implies that the physical meaning of depends on the value of : If the relative intensities are normalized to unity, then and equals the sum of all centerline opacities.

The results of the HFS fitting procedure are:

Line T ant * Tau V lsr Delta V Tau main 1 1.313 ( 0.018) 3.783 ( 0.001) 0.589 ( 0.003) 0.230 ( 0.006)where

`T ant * Tau`

=, `V lsr`

=, `Delta V`

=
and `Tau main`

=.
According to assumptions A1 and A5, the hyperfine structure
fitting procedure allows you to deduce the excitation
temperature, since (assuming the Rayleigh-Jeans regime is
valid, which is not true at mm...):

(2.4) |

(2.5) |

**Note**: the main group opacity is limited to
the range since outside these limits, the problem
becomes degenerate because the opacity no longer appears in
the equations (in the optically thin limit, line ratio no
longer depend on the opacity, and in the thick limit,
).