Table 2: Model results for NH3 observations toward $\rho ~ {\rm Oph ~ A}$.
    NH3 modela    

Transition		 $T_{\rm mb}$ $T_{\rm R}$ $\tau_0$ $T_{\rm ex}$ $A_{\rm ul}$ $n_{\rm c}$(H2)b
  (K) (K)   (K) (s-1) (cm-3)

o-(10-00)		 0.40 0.41 4.6 6.5 $1.59 \times 10^{-3}$ $3.6 \times 10^{7}$
p- (11-11)c >0.38 0.88 0.10 11.8 $1.69 \times 10^{-7}$ $2.0 \times 10^{3}$
p- (22-22)c >0.18 0.23 0.012 21.7 $2.26 \times 10^{-7}$ $2.0 \times 10^{3}$
o-(33-33) $\ldots$ 0.04 -0.005 -5.2 $2.59 \times 10^{-7}$ $2.2 \times 10^{3}$
Notes:
a Ortho-to-para of unity is assumed ( $X_{\rm o}/X_{\rm p} = 1$).
b Values of the critical density, $n_{\rm c}$(H2) =  $A_{\rm ul}/C_{\rm ul}(T_{\rm k})$, for 20 K.
c Data estimated from Fig. 2 of Zeng et al. (1984) and scaled to the Odin beam size, i.e. multiplied by (43/120)2.

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