Table 5: Optical depths accounting for source coveragea.
Line Observed Model Model Model
    III IV V
110-111 (O) $0.113\pm0.032$ 0.046 0.086 0.120
211-212 (O) $0.016\pm0.006$ 0.017 0.020 0.024
212-111 (O) $0.539\pm0.098$ 0.726 0.641 0.610
211-110 (O) $0.941\pm0.160$ 0.710 0.591 0.533
101-000 (P) $0.503\pm0.103$ 0.286 0.285 0.283
202-101 (P) $0.335\pm0.061$ 0.393 0.393 0.392

$\chi^2_{\rm reduced, ortho}$
- 4.9 3.5 4.4
$\chi^2_{\rm reduced, para}$ - 5.3 5.4 5.4
N(H2CO) - 5.4 5.2 4.8
Ortho/Para - 3.0 2.8 2.5
a Column 1: H2CO transition with O and P denoting ortho- and para-H2CO, respectively. The upper two lines refer to K-doublet transitions. In the lower part of the table, reduced $\chi^2$ values, total H2CO column densities from the +7 km s-1 component in units of 1013 cm-2, and H2CO ortho-to-para abundance ratios are given. Column 2: observed apparent optical depths (see Table 4), but accounting for a frequency dependence of the continuum source covering factor, $f_{\rm c}$ = ( $\nu_{\rm GHz}/100)^{0.5}$. Column 3: LVG results exclusively accounting for microwave background excitation ( $T_{\rm CMB}$ = 4.6 K =  $T_{\rm ex}$; Model III). Columns 4 and 5: same as Col. 3, but including collisional excitation with n(H2) = 200 and 500 cm-3, respectively (Models IV and V). For details, see Sect. 4.2.3.

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