The quasi-star model for Little Red Dots: potential and challenges

(Abridged) Little Red Dots (LRDs) are a class of sources discovered by JWST observationally defined by a "V-shaped" rest-frame UV-Optical SED, a compact or unresolved morphology, and for having, frequently, broad hydrogen emission lines. Among various models, those involving a quasi-star interpret LRDs as an intermediate stage in the evolution of a super-massive black hole (SMBH) seed into a classic AGN. In this paper, we employ the radiative-transfer code \texttt{Cloudy} to study whether this model is able to reproduce the spectral features commonly observed in LRDs. The model consists of an accreting SMBH ($M_{\rm BH}\sim10^{5-6} \ M_\odot$) surrounded by a convective layer where a black-body (BB) spectrum with $T\sim5000 \ {\rm K}$ and $L\sim10^{44.4} \ {\rm erg \ s}^{-1}$ is produced. This BB is then reprocessed by a concentric thick ($\Delta R\sim1000 \ {\rm AU}$) shell of dense ($n_{\rm H}\sim10^{11} \ {\rm cm}^{-3}$) gas partially ionised by thermal collisions. The emerging radiation is further reprocessed by a diffuse clumpy medium surrounding the quasi-star. We fit this model to JWST/NIRSpec spectra of LRDs from the literature, deriving the main physical parameters and the SMBH masses. Once coupled with the UV emission from a host galaxy, this model is able to reproduce the shape of the UV-to-NIR continuum, including the presence of a Balmer break, as well as the luminosity of the hydrogen emission lines. However, this quasi-star model does not natively account for the presence of broad helium lines and for the possible presence of hot dust, needing additional components to match these observables. Our main result is to show how some LRDs can be modeled as quasi-stars, highlighting that a significant degeneracy exists among different LRD models. This has important consequences for our understanding of the mechanisms driving black hole growth in the early Universe.