Studies of Thermally Unstable Accretion Disks around Black Holes with Adaptive Pseudo-Spectral Domain Decomposition Method I. Limit-Cycle Behavior in the Case of Moderate Viscosity

TL;DR

This paper introduces an improved numerical method combining pseudo-spectral and adaptive domain decomposition techniques to study thermally unstable accretion disks around black holes, revealing that such disks have negative Bernoulli functions, implying no outflows.

Contribution

The authors develop a novel adaptive pseudo-spectral domain decomposition method with enhanced interface treatment and physical modeling for accretion disks, enabling more accurate simulations of their limit-cycle behavior.

Findings

Reproduced previous results on limit-cycle behavior of unstable disks.

Discovered that the Bernoulli function remains negative, indicating no outflows.

Validated the numerical method's effectiveness for accretion disk studies.

Abstract

We present a numerical method for spatially 1.5-dimensional and time-dependent studies of accretion disks around black holes, that is originated from a combination of the standard pseudo-spectral method and the adaptive domain decomposition method existing in the literature, but with a number of improvements in both the numerical and physical senses. In particular, we introduce a new treatment for the connection at the interfaces of decomposed subdomains, construct an adaptive function for the mapping between the Chebyshev-Gauss-Lobatto collocation points and the physical collocation points in each subdomain, and modify the over-simplified 1-dimensional basic equations of accretion flows to account for the effects of viscous stresses in both the azimuthal and radial directions. Our method is verified by reproducing the best results obtained previously by Szuszkiewicz & Miller on the limit-cycle behavior of thermally unstable accretion disks with moderate viscosity. A new finding is that, according to our computations, the Bernoulli function of the matter in such disks is always and everywhere negative, so that outflows are unlikely to originate from these disks. We are encouraged to study the more difficult case of thermally unstable accretion disks with strong viscosity, and wish to report our results in a subsequent paper.