Energy level diagrams of OH⁺, H₂O⁺, and H₃O⁺, showing with arrows the transitions that lie within the PACS range; colored numbers indicate round-off wavelengths in μm. The fine-structure splitting of the OH⁺ and H₂O⁺ levels is out of scale. Solid-red arrows mark the lines detected in NGC 4418 and/or Arp 220; dashed-red arrows indicate marginal detection in any of the sources; green arrows indicate blended lines, and black arrows show undetected lines.