Inflated Supermassive Stars as Little Red Dots and Progenitors of Supermassive Black Holes

JWST has uncovered an abundant population of compact, red sources at high redshifts, termed little red dots (LRDs). We study whether they could be explained by thermally relaxed, hydrogen-burning, metal-enriched supermassive stars (SMSs). We construct 1D models in hydrostatic and thermal equilibrium, including a radiation-pressure-dominated, CNO-burning core and an outer envelope with metallicity-dependent opacity, non-adiabatic convection, and an effective treatment of super-Eddington surface layers. The luminosity is close to the Thomson-scattering Eddington limit. The Fe-opacity bump drives the formation of a strongly inflated, low-mass envelope, while hydrogen recombination terminates the envelope at a bound photosphere. For M=${10}^4$ to ${10}^6$ Msun and metal mass fractions $Z={10}^{-4}$ to ${10}^{-2}$, we find that the most metal-rich models (Z ~ ${10}^{-2}$) develop highly inflated envelopes and reach Teff ~ 7000 K. We suggest that such enriched SMSs could instead be assembled through runaway stellar collisions in compact star clusters. The GR instability sets a maximum mass that depends on the core rotation rate. The nonrotating and rotating models have maximum masses $3\times {10}^5$ to $3\times {10}^6$ Msun, and maximum luminosity of the order ${10}^{44}$ erg/s, comparable to the observed bright-end cutoff of the LRD luminosity function. Core hydrogen depletion can drive initially stable SMSs across the instability threshold after a lifetime of order 1 Myr. If each LRD leaves a black hole retaining most of its mass, the observed LRD abundance implies a present-day remnant density of order ${10}^{-2}\mathrm{c}\mathrm{M}\mathrm{p}{\mathrm{c}}^{-3}$, consistent with the local abundance of supermassive black holes. Cool SMSs naturally produce weak X-ray and weak high-ionization lines. Non-LTE effects may significantly modify the Balmer features and the continuum opacity, and may lower Teff below our LTE value.