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

Abstract

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.

Figures (4)

• Figure 1: Kippenhahn diagram showing the mass coordinate as a function of time for the model with $\dot{M}_{\rm gain,max} = 1$${\rm M}_{\odot}$/yr, $Z=10^{-4}$ and $Y=0.25$. The nitrogen mass fraction is color-coded; convection zones are indicated by cyan dots. The diamond shows the instant of GRI. The black filled region shows the BH mass. The non-accreting QS model is shown by the dashed orange line, and the corresponding BH mass by the solid grey line. The extrapolated QS mass for the accreting model is shown by the dotted orange line; that of the non-accreting model remains constant (orange dashed). The extrapolated BH masses are plotted with black and grey dotted lines, respectively; in each case, the three lines correspond to different estimates assuming $\alpha = 0.5,\ 1,\ {\rm and}\ 1.5$. The star and the upward triangle indicate the crashing points of the accreting and non-accreting QS models. The downward triangles indicate the extrapolated masses of the object when the envelope has been entirely swallowed by the BH.
• Figure 2: Evolution in the HRD of the $Z=10^{-4}$ models with the accretion rates color-coded. The approximate total mass of the star, or QS, is given by the right vertical axis (estimated by Eq. \ref{['eq:ledd']}). The solid lines represent the continuously accreting models. The non-accreting QSs are shown in dashed lines inside the nested plot. The diamonds, star, and triangles correspond to the same phases as in Fig.\ref{['fig:kipp_1']}. The maximum values of the luminosity for the accreting QSs are estimated by the extrapolation of the QS mass and considering a constant $T_{\rm eff}$. The gray dashed line is a fit to the ending points of the QS models by santarelli2026evolutionary. The red shaded region corresponds to the effective temperature range of the Hayashi line as considered by inayoshi2025critical. The observed LRD sample from de-Graaff2025Little-Red-Dots is shown with red dots.
• Figure 3: Luminosity as a function of stellar mass for the continuously accreting models: 1 ${\rm M}_{\odot}$/yr (orange), 0.1 ${\rm M}_{\odot}$/yr (blue), and 0.01 ${\rm M}_{\odot}$/yr (mint). The instant when the GRI criterion is met is marked by diamond symbols in the corresponding colours. The grey shaded region denotes the mass range where the GRI is expected to occur, for main-sequence stars with accretion rates from 0.1 to 1 ${\rm M}_{\odot}$/yr haemmerle2018evolutionnagele2022stabilityherrington2023modelling, and their corresponding luminosities. The black dashed line represents the mass–luminosity relation obtained by setting the stellar luminosity equal to the Eddington luminosity.
• Figure 4: Similar to Fig. \ref{['fig:HRD']}, showing accreting models with $\dot{M}_{\rm gain,max} = 1$${\rm M}_{\odot}$/yr and different metallicities color-coded.