The modeled emissivities of CO and HCN in units of M_⊙ (K km s⁻¹ pc²)⁻¹ as a function of CO and HCN intensity, respectively. Left: Inverse of the CO emissivity (in units of the CO conversion factor) as a function of CO intensity, ⟨α_CO⟩=⟨ϵ_CO⟩⁻¹. We include the fit to our models (Eq. (17), solid line) and the 1σ uncertainty on the fit (gray shaded area). We also include the results of several numerical studies (Narayanan et al. 2012; Hu et al. 2022a; Gong et al. 2020, red dashed line, cyan dotted line, brown dash-dotted line, respectively) as well as the results of observational studies at ∼150 pc scales in the Antennae (pink dashed line, He et al. 2024) and PHANGS galaxies (purple dotted line, Teng et al. 2024). We note that we have recast the α_CO − σ_v fit from Teng et al. (2024) in terms of I_CO using the fit between I_CO and σ_v from our models. Right: Inverse of the HCN emissivity (in units of the HCN conversion factor) as a function of HCN intensity, ⟨α_HCN⟩=⟨ϵ_HCN⟩⁻¹. We include a fit to our models (Eq. (18), solid line) and the 1σ uncertainty on the fit (gray shaded area). For comparison, we include several published values of α_HCN from observations of Milky Way clouds (Dame & Lada 2023; Shimajiri et al. 2017), and we show the Gao & Solomon (2004a,b) value as the black dashed line. This figure demonstrates how well our models are able to reproduce previous numerical prescriptions of α_CO, as well as observationally constrained values of α_CO and α_HCN. The formatting of the model output is the same as in Fig. 3.