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

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 $\kappa$-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.