Modified models of radiation pressure instability applied to 10, 10⁵, and 10⁷ M_⊙ accreting black holes

¹ Nicolaus Copernicus Astronomical Center (PAN), ul. Bartycka 18, 00-716 Warsaw, Poland
e-mail: msniegowska@camk.edu.pl
² Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
³ School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel

Received: 21 April 2022
Accepted: 21 January 2023

Abstract

Context. Some accreting black holes exhibit much stronger variability patterns than the usual stochastic variations. Radiation pressure instability is one of the proposed mechanisms that might account for this effect.

Aims. We model luminosity changes for objects with a black hole mass of 10, 10⁵, and 10⁷ solar masses, using the time-dependent evolution of an accretion disk that is unstable as a result of the dominant radiation pressure. We concentrate on the outburst timescales. We explore the influence of the hot coronal flow above the cold disk, the inner purely hot flow, and the effect of the magnetic field on the time evolution of the disk-corona system. For intermediate-mass black holes and active galactic nuclei, we also explore the role of the disk outer radius because a disk that is fed by tidal disruption events (TDE) can be quite small.

Methods. We used a 1D vertically integrated time-dependent numerical scheme that models the simultaneous evolution of the disk and corona, which is coupled by the vertical mass exchange. We parameterized the strength of the large-scale toroidal magnetic fields according to a local accretion rate. We also discuss a possible inner optically thin flow, the advection-dominated accretion flow (ADAF). This flow would require modification of the inner boundary condition of the cold disk flow. For the set of the global parameters, we calculated the variability timescales and outburst amplitudes of the disk and the corona.

Results. We found that the role of the inner ADAF and the accreting corona are relatively unimportant, but the outburst character strongly depends on the magnetic field and on the outer radius of the disk if this radius is smaller (due to the TDE phenomenon) than the size of the instability zone in a stationary disk with infinite radius. For microquasars, the dependence on the magnetic field is monotonic, and the period decreases with the field strength. For higher black hole masses, the dependence is nonmonotonic, and an initial rise of the period is later replaced with a relatively rapid decrease as the magnetic field continues to rise. A still stronger magnetic field stabilizes the disk. When we assumed a smaller disk outer radiusfor 10⁵ and 10⁷ M_⊙, the outbursts were shorter and led to complex multiscale outbursts for some parameters, thus approaching the behavior of deterministic chaos.

Conclusions. Our computations confirm that the radiation pressure instability model can account for heartbeat states in microquasars. The rapid variability detected in intermediate-mass black holes in the form of quasi-periodic eruptions can be consistent with the model, but only when it is combined with the TDE phenomenon. The yearly repeating variability in changing-look active galactic nuclei in our model also requires a small outer radius either due to the recent TDE or due to the gap in the disk that is related to a secondary black hole.