Far-UV radiation (G) and gas density (n) from PDR models, with constraints from the HCN, HCO⁺, HNC, and CO(5–4) observations. Individual panels show models for Z = 0.1, 0.2, 0.5, 1.0, 2.0 Z_⊙. Different colours denote the different levels of mechanical heating contribution α (0%–100%); the coloured squares denote models consistent with the observed line ratios within 50%; grey shaded contours show the G and n inferred from high-resolution imaging of SDP.81 by Rybak et al. (2020). Only the Z = 0.5 Z_⊙, α = 0, 10% models are consistent with the data. The most direct interpretation is that SDP.81 has sub-solar metallicity and only limited mechanical heating. Lower right: histogram of mechanical heating factor α for the Z = 0.5 Z_⊙ model. All PDR models consistent with the line data are shown in grey; the models consistent with G and n inferred from Rybak et al. (2020) are highlighted in blue.