Pulsational Instability of Quasi-Stars: Interpreting the Variability of Little Red Dots

TL;DR

The paper tests whether pulsations in quasi-star envelopes around growing black-hole seeds can explain the variability of JWST-detected Little Red Dots (LRDs). By coupling MESA stellar evolution with GYRE non-adiabatic stability analyses, the authors map a blue edge near $T_{ m eff} \approx 5000-5200\ \mathrm{K}$ and identify a Quasi-Star Instability Strip where radial modes become unstable with periods of $\sim 20-180$ yr (fundamental) and $\sim 10-30$ yr (first overtone). Non-linear MESA hydrodynamics reproduce RX1-like hysteresis and decadal-scale pulsations, predicting overtone-driven variability around $P\approx 24$ yr for representative high-mass quasi-stars and motivating a pulsation-driven superwind scenario. The work links the observed LRD variability to a mechanism that can regulate envelope lifetime and seed BH mass, offering a discriminant against AGN interpretations through a population of variable, pulsating quasi-stars.

Abstract

The JWST discovery of "Little Red Dots" (LRDs) has revealed a population of compact, red sources at $z \sim 5-10$ that likely host supermassive black holes (SMBHs). Recent observations of the gravitationally lensed LRD R2211-RX1 reveal century-scale photometric variability and a hysteresis loop in the luminosity-temperature plane, strongly suggesting that the optical emission originates from a pulsating, stellar-like photosphere rather than an accretion disk. This supports the "quasi-star" hypothesis, where a rapidly growing black hole seed is embedded within a massive, radiation-pressure supported envelope. In this work, we investigate the stability of these envelopes using the stellar evolution code MESA coupled with the non-adiabatic oscillation code GYRE. We identify a theoretical "Quasi-Star Instability Strip" with a blue edge at $T_{\mathrm{eff}} \approx 5000-5200$ K. Models hotter than this threshold are stable, consistent with the non-variable LRD R2211-RX2 ($T_{\mathrm{eff}} \approx 5000$ K), while cooler models are unstable to radial pulsations driven by the $κ$-mechanism in helium and hydrogen ionization zones. For quasi-star masses in the range $M_\star \sim 10^4-10^5 M_\odot$, we find that the unstable fundamental radial modes ($\ell =0$, n$_{\rm p}=1$) have periods in the range $\sim 20-180$ years. The first overtone ($\ell =0$, n$_{\rm p}=2$) is also unstable or marginally stable in some of our models, with typical pulsation timescales $\sim 10-30$ years. These oscillations match the co-moving frame variability timescale of RX1. We argue that these violent pulsations likely drive enhanced mass loss analogous to super-AGB winds, which could affect the duration of the quasi-star phase and regulate the final mass of the seeded black hole.

Figures (6)

• Figure 1: Hertzsprung--Russell diagram evolution for our quasi-star models. Tracks show models with different total masses and a central black hole growing from an initial seed of $M_{\rm BH} = 100\,\mathrm{M}_\odot$ to $M_{\rm BH} \approx 0.34\,M_\star$ via accretion. The two highest mass models terminate a bit earlier due to numerical issues. The line color indicates the instantaneous black hole mass, while white markers denote selected evolutionary times. Dashed lines indicate constant stellar radii.
• Figure 2: GYRE stability analysis for a quasi-star model sequence with $M_\star = 10^5 M_\odot$. Top panel: Dimensionless growth rate $\Im(\omega)$ as a function of effective temperature for the fundamental mode ($n_{\rm p}=1$, blue circles) and first overtone ($n_{\rm p}=2$, orange squares). The horizontal dashed line marks the stability boundary at $\Im(\omega)=0$. Positive values (green shading) indicate unstable, driven modes, while negative values (red shading) indicate stable, damped modes. The fundamental mode is unstable across most of the temperature range, becoming stable only at $T_{\rm eff} \gtrsim 5300$ K. Bottom panel: Pulsation period as a function of effective temperature for the same model sequence. The horizontal green band marks the observed $\sim$30-year variability timescale.
• Figure 3: Non-adiabatic pulsation analysis of a quasi-star model with mass $2\times10^5 \,\mathrm{M}_\odot$ and $T_{\mathrm{eff}} = 4682\,{\rm K}$. Top panel: radial eigenfunction $\xi_r$ as a function of normalized radius $x = r/R_\star$ for the radial ($\ell =0$) fundamental mode. Bottom panels: opacity, opacity derivatives $(\partial \ln \kappa/\partial \ln T)_\rho$ and $(\partial \ln \kappa/\partial \ln\rho)_T$, differential work and its integral W as a function of $\log_{10} T$. Regions of driving are shown in green, while damping regions are shown in purple. The mode is unstable (W$>$0) and most of the driving occurs at the location of helium recombination around $\log_{10}(T/{\rm K}) \sim 4.4$, with some driving also due to hydrogen recombination at $\log_{10}(T/{\rm K}) \sim 4$. The reported pulsational period for this mode is P = 73.2 yr.
• Figure 4: Same as Fig. \ref{['fig:gyre_stack_fundamental']}, but for the first overtone. This mode is marginally stable according to GYRE non-adiabatic calculations (W$\simeq$0). The predicted pulsation period is P = 21.5 yr. MESA hydrodynamic calculations show this mode to be unstable, with P = 23.5 yr.
• Figure 5: Hydrodynamic evolution of a pulsating quasi-star model with envelope mass $M_\star = 2\times10^5\,M_{\odot}$ and black hole mass $M_{\rm BH} = 4.5\times10^4\,M_{\odot}$ (red star symbol in Fig. \ref{['fig:instability_strip']}). Top panel: The trajectory in the luminosity--temperature plane. The system traces counter-clockwise hysteresis loops, a signature of the thermodynamic "heat engine" cycle driving the pulsation. Colored circles along the track mark 10-year intervals during the final 100 years of the simulation. Middle and Bottom panels: Time evolution of the photospheric radius and the surface Mach number ($v_{\rm surf}/c_s$), respectively. The simulation resolves the rapid growth of an unstable overtone mode ($P \simeq 24$ yr). The surface velocity eventually becomes highly supersonic, leading to the formation of strong shocks in the envelope. The dotted lines represent results for a model extracted in the stable region (white star symbol in Fig. \ref{['fig:instability_strip']}).