A Spectral Framework for Testing the Quasi-Star Hypothesis in Little Red Dots I: Weighing LRDs by Their Super-Eddington Luminosity Ratios---No Signs of Overmassive Black Holes
We present a spectral test of the quasi-star hypothesis for Little Red Dots (LRDs) whereby a black hole grows inside a stellar-like envelope. We use Prospector to fit host galaxies and TLUSTY photospheres to 5 LRDs that show strong molecular or atomic absorption. We approximate each object's electron-scattered Eddington luminosity ratio, $ϕ\equiv κ_{\rm es}σT_{\rm eff}^{4}/(gc)$, and we use MESA-QUEST to simulate their envelopes. All 5 are super-Eddington at $ϕ= {87}$--$299$, with the caveat that the largest sources sit at the edge of our atmosphere grid and beyond our simulations. We derive envelope masses between $700$--${15{,}000}\,M_\odot$, where quasi-star theory requires the black hole to be less than a third of that. GN-28074 falls 5 decades below its published virial mass estimate, alleviating the overmassive black hole problem. Their black holes double every $\sim0.05$--${0.2}$~Myr and can produce intermediate-mass black holes in $\lesssim30$~Myr. Our 3 water-absorbing objects have cold components that are $2$--$3$~dex denser than their hot components, which we interpret as the water forming in cold dense clouds. We then extend our measurements to 82 archival LRDs, finding that the population has super-Eddington photospheres and wind speeds that increase with $ϕ$, which implies that LRDs evolve from massive sources with slow winds to having more eruptive winds as they mature and shed their outer envelopes. We thus constrain the Eddington ratios and masses of LRDs and show self-consistently that quasi-stars may be the central engines powering LRDs.