A quasi-star is born: formation and evolution of accreting quasi-stars as a metallicity-independent pathway to Little Red Dots

To investigate the rest-frame optical emission of “Little Red Dots”, we model the formation of and evolution of quasi-stars, i.e. stellar envelopes supported by the accretion luminosity onto a central black hole, originating from rapidly accreting proto-stars reaching the supermassive star regime ($>{10}^4$ M${}_{\odot }$) and undergoing general relativistic instability. We compute stellar evolution models with net mass gain rates $=0.01$, 0.1, and 1 M${}_{\odot }$/yr and metallicities $Z=0$-0.01. For the mass gain rates $\ge 0.1$ M${}_{\odot }$/yr, stars remain nearly fully convective with $T_{\mathrm{e}\mathrm{f}\mathrm{f}}\sim 4000$-9000~K. The general relativistic instability leading to central BH formation occurs at $M_{\star }\sim 3.5\times {10}^4$ M${}_{\odot }$ ($6.6\times {10}^4$ M${}_{\odot }$) for ${\dot{M}}_{\mathrm{a}\mathrm{c}\mathrm{c}}=0.1$ M${}_{\odot }$/yr (1 M${}_{\odot }$/yr), at luminosities $L\sim {10}^9$ L${}_{\odot }$. The lifetime of quasi-stars is estimated to be ${10}^7$-${10}^8$~yr, $\sim$100-1000 times longer than their progenitors. In an environment allowing for rapid accretion the formation, evolution, and properties of quasi-stars are found be essentially independent of metallicity. Comparing the luminosities of our models with those of Little Red Dots at $z<4.5$ ($L_{\mathrm{b}\mathrm{o}\mathrm{l}}\sim {10}^{9.5}$-${10}^{11.5}$ L${}_{\odot }$) yields quasi-star masses ${10}^{4.5}$-${10}^{6.5}$ M${}_{\odot }$. The observed minimum luminosity of $\sim {10}^{9.5}$~\Lsun\ implies accretion rates $\gtrsim 0.1$ M${}_{\odot }$/yr for Little Red Dots progenitors. Our models offer a metallicity-independent framework supporting quasi-stars as the source of Little Red Dot optical emission, and provide insights into their lifetimes, composition, and progenitor environment.