Little Red Dot $-$ Host Galaxy $=$ Black Hole Star: A Gas-Enshrouded Heart at the Center of Every Little Red Dot
The central engines of Little Red Dots (LRDs) may be ``black hole stars" (BH*s), early stages of black hole growth characterized by dense gas envelopes. So far, the most direct evidence for BH*s comes from a handful of sources where the host galaxy is completely outshone as suggested by their remarkably steep Balmer breaks. Here we present a novel scheme to disentangle BH*s from their host galaxies assuming that the [OIII]5008Å line arises exclusively from the host. Using a sample of 98 LRDs ($z$~$2-9$) with high quality NIRSpec/PRISM spectra, we demonstrate that the host-subtracted median stack displays a Balmer break $>2\times$ stronger than massive quiescent galaxies, with the rest-optical continuum resembling a blackbody-like SED ($T_{\rm{eff}}$~$4050$ K, $\log(L_{\rm{bol}})$~$43.9$ erg s$^{-1}$, $R_{\rm{eff}}$~$1300$ au). We measure a steep Balmer decrement (H$α$/H$β>10$) and numerous density-sensitive features (e.g., FeII, HeI, OI). These are hallmark signatures of dense gas envelopes, providing population-level evidence that BH*s indeed power LRDs. In the median LRD, BH*s account for $\sim20\%$ of the UV emission, $\sim50\%$ at the Balmer break, and $\sim90\%$ at wavelengths longer than H$α$ with the remainder arising from the host. BH*s preferentially reside in low-mass galaxies ($M_{\rm{\star}}$~$10^{8}\,{\rm M}_{\rm{\odot}}$) undergoing recent starbursts, as evidenced by extreme emission line EWs (e.g., [OIII]5008Å~$1100$Å, CIII]~$12$Å), thereby favoring BH* origins linked to star-formation. We show V-shaped LRD selections are biased to high BH*/host fractions ($\gtrsim60\%$ at 5500Å) -- less dominant BH*s may be powering JWST's blue broad-line AGN. We find BH*s are so commonplace and transient (duty cycle $\sim1\%$, lifetime $\sim10$ Myrs) that every massive black hole may have once shone as a BH*.