Radiation pressure instability: from heart-beat states in black hole binary systems to Quasars and Changing-Look AGN

Radiation-pressure instability was identified soon after the seminal classical accretion disk models of Shakura & Sunyaev and Novikov & Thorne, yet its full implications remain an active area of investigation. These models form the backbone of our understanding of accretion onto compact objects and successfully describe the phenomenology of black hole and neutron star X-ray binaries, as well as luminous active galactic nuclei (AGN), in the regime of high mass accretion rates. At luminosities approaching a significant fraction of the Eddington limit (L/L_Edd ≥ 0.1), standard thin disks are predicted to become thermally unstable due to the dominance of radiation pressure. This prediction has found empirical support in several Galactic stellar-mass black hole systems, where the instability manifests as quasi-periodic, large-amplitude luminosity oscillations, so-called “heartbeat states”, and has been proposed as a driver of observed signatures of deterministic chaos in accretion-driven light curves. The scope of radiation-pressure-induced variability extends beyond stellar-mass black holes: both black holes across mass scales and accreting neutron stars can exhibit related behavior, though the presence of a boundary layer in neutron stars adds complexity and offers a unique laboratory for testing the interplay between accretion dynamics and the central object. On extragalactic scales, the instability has been invoked to explain the duty cycles and apparent short lifetimes of radio-loud AGN, as well as the dramatic spectral-state transitions seen in Changing-Look AGN. Despite these advances, the theoretical picture remains unclear. State-of-the-art magnetohydrodynamic (MHD) simulations have not yet reached consensus on the conditions under which the radiation-pressure instability fully develops or is suppressed. Magnetic fields, which mediate angular momentum transport and couple to both gas and radiation, emerge as a potentially critical factor in modulating the instability's onset and nonlinear evolution. This lecture will revisit the historical development of the instability concept, survey the current observational and theoretical status across different classes of accreting compact objects, and highlight the key open questions in the theory and the connection to observed variability phenomenology, that will shape the next fifty years of disk instability research.