HCN, HCO⁺, and HNC SLEDs of PLCK_G244.8+54.9 (black points). Gray triangles in the lower left of the first two panels refer to the dense-gas mid-J to J = 1–0 flux ratios in the local ULIRG Arp 220 (Imanishi et al. 2007; Greve et al. 2009), after normalizing to the HCN(4–3) and HCO⁺(4–3) line fluxes in PLCK_G244.8+54.9. Colored curves show a range of solutions to our collisional excitation models with RADEX, combining the spatially-integrated intensity ratios of HCN, HCO⁺, and HNC. These curves fit the three SLEDs reasonably well and illustrate the n–T_kin parameter degeneracies shown in more detail in Fig. 8. Lowering flux uncertainties and covering additional dense-gas transitions around the peak would improve the constraints.