Non-Stationary Discs and Instabilities

TL;DR

This review analyzes when and how accretion discs around compact objects become thermally or viscously unstable, tracing the evolution from classical α-prescription models to modern MRI/MHD frameworks. It integrates analytic time-dependent disc theory, disc-instability modeling for outbursts in binaries, and MRI-informed simulations to explain outburst phenomenology and inner-disc stability, including radiation-pressure–dominated regimes. The authors highlight magnetic stresses, winds, and convection as pivotal factors that can stabilize or modify disc behavior, challenging the notion that radiation-pressure instabilities necessarily produce runaway variability. They call for global radiation-MHD simulations and new observational probes to resolve remaining tensions between theory and high/soft-state observations, and to understand the impact of composition and magnetic topology across astrophysical discs. Overall, the work underscores the intricate coupling between thermodynamics, magnetic fields, and angular-momentum transport in shaping disc evolution from CVs to AGN.

Abstract

We review our current knowledge of thermal and viscous instabilities in accretion discs around compact objects. We begin with classical disc models based on analytic viscosity prescriptions, discussing physical uncertainties and exploring time-dependent solutions of disc evolution. We also review the ionization instability responsible for outbursting dwarf nova and X-ray binary systems, including some detailed comparisons between alpha-based models and the observed characteristics of these systems. We then review modern theoretical work based on ideas around angular momentum transport mediated by magnetic fields, focusing in particular on knowledge gained through local and global computer simulations of MHD processes in discs. We discuss how magnetohydrodynamics (MHD) may alter our understanding of outbursts in white dwarf and X-ray binary systems. Finally, we turn to the putative thermal/viscous instabilities that were predicted to exist in the inner, radiation pressure-dominated regions of black hole and neutron star discs, in apparent contradiction to the observed stability of the high/soft state in black hole X-ray binaries.

Figures (8)

• Figure 1: Green function $G(h,1,t)$ versus specific angular momentum $h$ for freely expanding disc (left) and for disc with the outer radius fixed so that $h_{\rm out}=2$. Thicker curves correspond to later times. For the bounded disc, the condition of zero accretion rate is applied at the outer radius.
• Figure 2: Distributions of viscous torque $F$ versus angular momentum $h$ at two moments of time in $\alpha$-discs, freely-expanding (dashed) and limited by the outer radius with $h_{\rm out} = 1$ (solid). The accretion rate on the center decays with time.
• Figure 3: Comparison of analytic solutions \ref{['eq:LBP_mdot']}, \ref{['eq:texp']}, \ref{['eq:Mdot_law_unbounded']}, and \ref{['eq:Mdot_fixedRout_alpha']} for the evolution of the accretion rate onto a 10 $M_\odot$ black hole with different viscosity and disc outer boundary (freely expanding or fixed). The viscosity in each solution is chosen to approximate the law in the zone of dominant gas pressure and opacity according to the Kramers formula. At late times, the time-dependencies tend to $(t/\tau_\mathrm{pl})^{-7/5}$, $\exp(-t/t_\mathrm{exp})$, $(1+t/\tilde{t}_0)^{-5/4}$, and $(1+t/t_0)^{-10/3}$, respectively. The input parameters are $M_{\rm disc} = 6\times 10^{24}~$g, $R_{\mathrm{out}}=2\times 10^{11}$ cm and $t_{\rm vis} = 60^{\mathrm d}$. The corresponding $e$-decay time is $t_\mathrm{exp}\approx 27^{\mathrm d}$; the bounded $\alpha$-disc's solution is close to the linear-problem solution for about $3\, t_\mathrm{exp}$.
• Figure 4: Snapshot of the three dimensional structure of mass density (top) and radiation energy density (bottom) of a global simulation of MRI turbulence in a disk around a supemassive black hole jia20. In addition to MHD, this simulation incorporates angle-dependent radiation transport with frequency-averaged (grey) opacities.
• Figure 5: Mass transfer rates of CVs compared to the stability criterion Eq. (\ref{['eq:stabCV']}). Systems above the upper (red) solid line are hot and stable. Systems below the lower (blue) line indicate cold, stable discs if the white dwarf magnetic field $B \geq 10^5$ G. The dashed line represents the expected secular mass transfer rate (Knigge0611). Square symbols indicate Z Cam type dwarf novæ; (red) stars indicate nova-likes. Dwarf novae shown in black have a more complete observed light-curve than those in grey.