Free-Free Radio Emission from Little Red Dots as a Probe of Ionized Gas

Recent studies have hypothesized that little red dots (LRDs) are rapidly accreting black holes surrounded by dense gaseous environments. Both neutral and ionized gas play a key role in explaining many of the puzzling spectral features of LRDs, including the emission line profiles in the optical-infrared bands, although the physical conditions required for these gas components remain poorly constrained. We propose that free-free emission provides a robust, independent probe of ionized gas in LRDs. Free-free self-absorption produces a characteristic spectral turnover whose critical frequency and luminosity depend on the electron column density and the characteristic size of the ionized region, such that radio observations simultaneously constrain both quantities. The spectral slope at frequencies below the turnover further probes the radial density distribution on spatial scales far below those achievable by current and future optical-infrared observatories. We also present predicted free-free spectral energy distributions for two representative LRDs in the local and high-redshift universe and show that future radio-to-millimeter observations with ALMA and ngVLA can probe the range of ionized-gas parameters inferred from current observations. Free-free emission therefore offers a unique way to probe the geometry and physical conditions of the ionized gas surrounding LRDs.