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Appendix A: Spectra of the ground-state HO lines

In Sect. 3, we present the ground-state lines of ortho- and para-HO observed with Herschel/HIFI toward the Orion Bar (Fig. A.1) and Orion S (Fig. A.2).

	Fig. A.1 Spectra of the ground-state HO lines in the Orion Bar. The weak continuum has been subtracted.
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	Fig. A.2 Spectra of the ground-state HO lines toward Orion S. For the o-HO line, the continuum has been subtracted. The p-HO line shows absorption against the continuum.
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Appendix B: Column densities derived by non-LTE RADEX code

In Sect. 4, for the non-LTE calculations of ortho- and para-H₂¹⁸O lines, we generate a grid of models with values of T_kin = 20, 60, and 100 K and values of n(H₂) = 10⁴, 10⁶, and 10⁸ cm^-3, and fix the background radiation temperature at 2.73 K for the Orion Bar and Orion S using the RADEX code (van der Tak et al. 2007). Table B.1 presents the derived column densities for the adopted conditions from a full grid non-LTE calculations as examples. The p-HO 1₁₁−0₀₀ line in Orion S appears in absorption so we derive the column density using the optical depth (see Sect. 4.2 for details).

As an additional model for the Orion Bar, for the background radiation field we adopt a modified blackbody distribution with a dust temperature of T_d = 49 K and a dust emissivity index of β = 1.6 by Arab et al. (2012) for the interior of the Orion Bar, so that the absolute dust opacity of τ_d = 0.21 at 971 GHz. This RADEX model shows that ortho- and para-HO lines appear in absorption at low density and low temperature (at T_kin = 20 K & n(H₂) = 10⁴ cm^-3), which is not consistent with our observations.

Appendix C: Further constraints on the OPR in Orion S

In Sect. 4.2, we estimate the intensity of the ground-state line of ortho-H₂¹⁸O 2₁₂−1₀₁ (1655.9 GHz) assuming that this line appears in absorption to constrain the OPR in Orion S. In Fig. C.1 we present four absorption lines on top of the ground-state ortho-H₂¹⁸O 2₁₂−1₀₁ line. The green, red, yellow, and blue lines represent absorption lines with optical depth of 0.08, 0.16, 0.20, and 0.24, respectively.

	Fig. C.1 Four absorption lines on top of spectra of the ground-state ortho-HO 212−101 line (black), with continuum in Orion S. Assuming that the OPRs are 1, 2, 2.5, and 3, the derived optical depth of 0.08, 0.16, 0.20, and 0.24 are presented, respectively, as green, red, yellow, and blue.
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© ESO, 2014