Theoretical radio SEDs (bottom) and their local spectral indices (top), which emulate different optical-depth scenarios by assuming a range of Σ_dust values. The spectral index, α_Δ5GHz, is calculated at 5 GHz intervals along the radio SED and plotted against the midpoint of the frequency range. We annotate τ ∼ 1 in each model with a dashed line, showing the optically thick to optically thin transition. Each model has a constant T_dust =  21 K, ﹩{a}_{{\rm{\max }}}=﹩ 0.8 mm, and Ω_dust = 1 × 10¹¹ Sr for the dust component and a constant EM  =  9 × 10⁸cm⁻⁶ pc and Ω_ionized = 13 × 10⁻¹ Sr for the ionized gas (black dotted line).