Left panel: from top to bottom are the full NOEMA spectrum at ν_rest ~ 750 GHz of NCv1.143, G09v1.97 and G15v2.779, respectively. The reference frequency is the redshifted frequency of the line H₂O(2₁₁–2₀₂). The frequencies of the main H₂O⁺(2₁₁–2₀₂) _(5/2−5/2) and H₂O⁺(2₀₂–1₁₁) _(5/2−3/2) lines are indicated by grey vertical dashed lines. The three dashed squares in the spectrum of NCv1.143 show the position of each zoom-in spectrum of the H₂O⁺ (or the HO) as displayed in the right panel indicated by the A, B or C. The superposed blue dashed histograms represents the spectra of H₂O(2₁₁–2₀₂)centred at the frequencies of the H₂O⁺ lines. Note that, in many cases, the observed frequency ranges (yellow histograms) do not include the full expected profiles for the H₂O⁺ lines. The red curve represents the Gaussian fitting to the spectra. We have detected both H₂O⁺ lines in NCv1.143, and tentatively detected H₂O⁺(2₀₂–1₁₁) _(5/2−3/2) in G09v1.97 and H₂O⁺(2₁₁–2₀₂) _(5/2−5/2) in G15v2.779. Right panel: from top to bottom are the spectra dominated by lines of H₂O⁺(2₁₁–2₀₂) _(5/2−5/2), H₂O⁺(2₀₂–1₁₁) _(3/2−3/2) and HO(2₁₁–2₀₂), respectively, displayed as the filled yellow histograms. The reference frequency is the frequency of each of these lines. Weaker H₂O⁺(2₀₂–1₁₁) _(3/2−3/2) and H₂O⁺(2₁₁–2₀₂) _(5/2−3/2) components are indicated by additional grey vertical dashed lines. The superposed blue dashed histograms represent the spectra of para-H₂O(2₁₁–2₀₂)in NCv1.143 centred at each line frequency. The red curve represents the Gaussian fitting to the spectra, and the green dashed curves are the decomposed Gaussian profiles for each fine structure line. The violet error bar indicates the ±1σ uncertainties of the spectrum.