Little Red Dots host Black Hole Stars: A unified family of gas-reddened AGN revealed by JWST/NIRSpec spectroscopy

Abstract We construct and characterise a sample of 146 little red dots (LRDs) across 2.0 < z < 9.3, selecting all sources with v-shaped UV-optical continua from JWST NIRSpec/PRISM spectra and compact morphologies in NIRCam/F444W imaging. We show that LRD continuum spectra are well described by modified blackbodies across $\sim 0.4-1.0\, \hbox{$\umu $m}$, with typical T ~ 5000 K ($\lambda _{\rm peak}\sim 0.65\, \hbox{$\umu $m}$) across 2 dex in luminosity, and a tail toward T ~ 2000 K. LRDs therefore trace a locus in the Hertzsprung-Russell diagram that is analogous to stars on the Hayashi track, strongly supporting the picture that LRDs are AGN embedded in optically-thick dense gas envelopes. Hotter LRDs with $\lambda _{\rm peak}<0.65\, \hbox{$\umu $m}$ typically have strong Balmer breaks, redder UV slopes and high optical luminosities; other LRDs show weak or no Balmer breaks, and wide variety in βUV and L5100. Crucially, we demonstrate that the UV-optical continua are strongly linked to the Hα, Hβ, [O iii] and O i line properties. There is a tight linear relation between the Hα and optical continuum luminosities, as well as Hα and $\textrm {O\, {\small I} }_{\lambda 8446}$, indicating that Balmer, O i and optical emission must primarily be powered by the same source. The Balmer decrement increases strongly toward higher LHα, L5100 and Balmer break strength, providing key evidence for luminosity-dependent effects of collisional (de-)excitation and resonant scattering in the gaseous envelopes. In contrast, we show that [O iii] emission likely originates from star-forming host galaxies, with strong variation in the AGN-to-host ratio among the LRD population. Our work presents an empirical description of the nature and structure of LRDs, defining a new benchmark for ongoing LRD model developments.