HCN excitation ladder (spectral line energy distribution; points) and LVG models (lines) for APM 08279+5255, accounting for both collisional and radiative excitation. The HCN( J = 5→4) data point is from Weiß et al. (2007). The models give n _gas = 10 ^4.2 cm ⁻³, T _kin = T _IR = 220 K, and infrared field-filling factors of IR _ff = 0.3–0.7 (shown in steps of 0.1).