Degeneracy among electron temperature, column density, and region size

Characterize or resolve the intrinsic degeneracy among the electron temperature, electron column density, and characteristic size of the ionized region when fitting free-free emission spectra from little red dots.

Background

The paper fits mock multi-band ALMA and ngVLA photometry with a truncated power-law free-free emission model whose free parameters include the electron temperature, electron column density, characteristic ionized-region radius, and density-profile slope. Although physically plausible temperature bounds allow the column density and radius to be constrained to approximately ±0.2 dex, the authors state that the three-way degeneracy involving temperature, column density, and radius cannot be solved in principle. This leaves unresolved the extent to which independent information or additional observables could break the degeneracy and improve parameter recovery.