Free-Free Radio Emission Proposed to Constrain Ionized Gas Properties in Little Red Dots

Little red dots discovered by JWST exhibit broad emission lines and compact sizes that current models attribute to rapidly accreting black holes embedded in dense neutral and ionized gas. The paper calculates that free-free self-absorption produces a turnover whose frequency scales with emission measure, allowing radio data to break degeneracies that plague optical-infrared line profile fitting alone. Predicted SEDs for representative local and z~6 LRDs show detectable flux densities above 10 GHz under plausible n_e ~ 10^4-10^6 cm^-3 conditions. This approach accesses spatial scales of tens of parsecs inaccessible to current or planned optical interferometers. Radio observations therefore supply an independent geometric constraint on the ionized envelope geometry. Existing VLA upper limits already exclude the highest-density extreme models, while ngVLA sensitivity forecasts indicate turnover detection thresholds reachable within 10-hour integrations for the brightest LRDs. The method also predicts a low-frequency spectral index that encodes the radial density power-law index, offering a direct test of outflow versus inflow geometries proposed in the literature.