Inside the cocoon: a comprehensive explanation of the spectra of Little Red Dots

JWST has revealed a population of compact galaxies in the early Universe with broad emission lines and strong Balmer breaks; among them the so-called ''little red dots'' (LRDs). Their nature remains uncertain with hypotheses including exotic phenomena. We assemble a sample of LRD-like objects at $z>3$ and use self-consistent radiative-transfer calculations to show that a supermassive black hole accreting from a dense gas cocoon accurately reproduces the detailed spectra. We show that the cocoons must be non-spherical, with comparable amounts of inflowing and outflowing material. And we predict correlations between Balmer break strength, Balmer line-absorption and scattering line width, which we confirm in our observed sample. We reproduce all LRD-like properties without requiring star-like atmospheres and we determine the typical black hole in our sample to be of order a million solar masses, with ionized cocoon masses of tens of solar masses potentially supplied from a much larger cold-gas reservoir.