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 ∼ 5–10 that likely host supermassive black holes. 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. Here, we investigate the pulsational stability of these envelopes using the stellar evolution code MESA coupled with the nonadiabatic oscillation code GYRE . We identify a theoretical “quasi-star instability strip” with a blue edge at T eff ≈ 5000 − 5200 K. Models hotter than this threshold are stable, consistent with the nonvariable LRD R2211-RX2 ( T eff ≈ 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 ⋆ ∼ 10 4 –10 5 M ⊙ , we find that the unstable fundamental radial modes ( ℓ = 0, n p = 1) have periods in the range ∼20–180 yr. The first overtone ( ℓ = 0, n p = 2) is also unstable or marginally stable in some of our models, with typical pulsation timescales ∼10–30 yr. These oscillations match the comoving 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.