Towards Self-consistent Modeling of Quasi-Stars and their NLTE Spectra: Implications for Little Red Dots
Quasi-stars, massive envelopes surrounding rapidly accreting black hole (BH) seeds, are promising candidates for explaining the rapid formation of supermassive black holes in the early Universe and may account for some of the JWST-discovered Little Red Dots (LRDs). We present a self-consistent framework combining stellar evolution calculations with non-local thermodynamic equilibrium (NLTE) spectral synthesis to test this connection. Our models drop the polytropic assumptions of previous work: the envelope is described entirely by mixing-length theory, with saturated convection and radiative energy setting the luminosity at an inner boundary a few hundred Schwarzschild radii from the BH. This removes the BH-mass limits of earlier models, and we follow the evolution up to BH-to-total mass ratios approaching unity. We then use TLUSTY to compute the first converged NLTE atmospheric models for the surface conditions and primordial hydrogen-helium composition expected in quasi-stars. Our models produce cool photospheres, prominent Balmer breaks, and Balmer and Paschen absorption features. NLTE effects substantially modify line strengths, increasing Balmer absorption depths by $\sim 35-55\%$ relative to LTE models, while having a minor effect on the continuum. Comparison with observed LRD spectral energy distributions shows broad agreement in continuum shape, although our models do not reproduce their commonly observed strong emission lines. Under the quasi-star interpretation, comparisons with individual LRDs suggest characteristic quasi-star masses of approximately $10^5-10^7 M_\odot$. These results establish a physically motivated connection between quasi-star evolution and observable spectra, providing a framework for testing quasi-stars as progenitors of LRDs while identifying limitations of current atmospheric models.