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

Matteo Cantiello, Jake B. Hassan, Rosalba Perna, Philip J. Armitage, Mitchell C. Begelman, Yan-Fei Jiang, Taeho Ryu, Richard H. D. Townsend

First listed 2025-12-19 | Last updated 2025-12-19

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.

Short digest

Uses MESA+GYRE to test whether quasi-star envelopes that could power Little Red Dots become radially unstable and pulsate. Finds a Quasi-Star Instability Strip with a blue edge at Teff ≈ 5000–5200 K: hotter models are stable (consistent with non-variable R2211‑RX2 at ≈5000 K), cooler ones are κ‑driven unstable in H/He ionization zones. Fundamental modes have 20–180 yr periods and first overtones 10–30 yr, matching the co-moving variability and L–T hysteresis of lensed LRD R2211‑RX1. The implied pulsation-enhanced winds could shorten the quasi-star phase and regulate the seed BH’s terminal mass.

Key figures to inspect

• Figure 1 (HR diagram tracks): Identify where models cross Teff ≈ 5000–5200 K and how radius lines and BH-mass color coding map onto the proposed blue edge of the instability strip; compare stable (hotter) versus unstable (cooler) track segments relevant to RX2 vs RX1.
• Instability-strip map (Teff–Lum or Teff–parameter plane): Locate the ‘Quasi-Star Instability Strip,’ mark the blue edge near 5000–5200 K, and see which envelope masses fall into unstable territory.
• Mode stability and growth-rate diagram (GYRE): Inspect which radial modes (ℓ=0, n_p=1 and 2) are unstable and their e-folding rates across Teff; confirm κ‑mechanism driving regions from work integrals in H/He ionization zones.
• Period–mass (or period–Teff) scaling: Read off fundamental (20–180 yr) and first-overtone (10–30 yr) periods versus M⋆ ≈10^4–10^5 M⊙ and check consistency with RX1’s co-moving timescale.
• Nonlinear pulsation cycle: Follow time-dependent MESA loops in the luminosity–temperature plane to verify the clockwise/counter-clockwise hysteresis morphology and amplitude compared to RX1.