J. Roman-Garza, D. Schaerer, C. Charbonnel, T. Fragos, E. Cenci, R. Marques-Chaves, P. Oesch, M. Xiao

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 $T_\mathrm{eff}\sim4000$-9000~K. The general relativistic instability leading to central BH formation occurs at $M_\star\sim3.5\times10^4$ M$_{\odot}$ ($6.6\times10^4$ M$_{\odot}$) for $\dot{M}_{\rm acc}=0.1$ 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 $z<4.5$ ($L_\mathrm{bol}\sim10^{9.5}$-$10^{11.5}$ L$_{\odot}$) yields quasi-star masses $10^{4.5}$-$10^{6.5}$ M$_{\odot}$. The observed minimum luminosity of $\sim10^{9.5}$~\Lsun\ implies accretion rates $\gtrsim0.1$ 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.