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

TL;DR

This paper investigates the pulsational stability of quasi-stars, proposing that their oscillations can explain observed variability in early universe red sources and influence black hole seed growth.

Contribution

It introduces a theoretical instability strip for quasi-stars and links pulsations to observed variability, advancing understanding of early black hole formation.

Findings

Unstable radial pulsations occur in quasi-star models with T_eff ~ 5000-5200 K.

Pulsation periods range from 10 to 180 years, matching observed variability.

Pulsations may drive mass loss, impacting black hole seed growth.

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.