class Continuum and Line Analysis Single-dish Software - IRAM

2.5. FITTING AN HYPERFINE STRUCTURE 7
From these equations, we deduce:
τ(vi + p2) = p4 · ri (assumption A4)
�
τi = p4 · S
i
Tant(vi + p2) = p1 � −p4ri 1 − e �
p4
Tant(vi + p2) ≈ p1 · ri
where the last equality holds in the optically thin regime.
This implies that the physical meaning of p4 depends on the value of S: If the relative
intensities are normalized to unity, then S = 1 and p4 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=p1, V lsr=p2, Delta V=p3 and Tau main=p4.
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 λ < 3mm...):
Tant(v) = T ∗ A(v) = Beff
Finally, the excitation temperature is given by:
[Tex − Tbg](1 − e
Feff
−τ(v) ) (2.4)
Tex = Tbg + Feff p1
Beff p4
Note: the main group opacity is limited to the range 0.1 − 30 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, exp(−τ) ≪
1).
2.5.4 Typical Analysis Sequence
This routine produces the figure 2.1.
1 set plot histo
2 set format brief
3 clear
4 clear alpha
5 file in prov.30m
6 find
7 get f
8 modify source TOTO
9 set unit v c
10 method hfs hfs-n2hp.lin
11 minimize
(2.5)