The disc instability model: original recipe and additional ingredients

TL;DR

The paper assesses the Disk Instability Model (DIM) and its extensions for cataclysmic variables, focusing on how additional ingredients—disc truncation, irradiation (hot-white-dwarf and self-irradiation), mass-transfer variations, stream overflow, and winds—alter stability and light-curve behavior. It discusses a 1D adaptive-grid implementation with a two-value $ ext{α}$ viscosity and an $S$-curve, showing that each ingredient shifts the stability boundaries and can reproduce diverse outburst morphologies, including long recurrence times and complex rebrightenings. However, the proliferation of poorly constrained parameters limits predictive power, and multiple mechanisms can explain similar phenomena (e.g., long outbursts via tidal instabilities or irradiation-driven mass transfer). The author argues for progress through intermediate 2D simulations that relax axisymmetry while leveraging accurate vertical structure, and for addressing outstanding issues such as low states, disc truncation physics, and the role of magnetic fields, to solidify the physical basis of the DIM.

Abstract

The disc instability model successfully reproduces many of the observed properties of cataclysmic variables. However, additional ingredients such as mass-transfer variations, disc irradiation, stream-disc overflow, or inner-disc truncation must be included to explain certain systems. The physics underlying these processes is often poorly constrained, and our lack of knowledge is typically absorbed into extra free parameters, much like the $α$-prescription for viscosity. In this paper, I examine how each of these ingredients affects the predicted light curves and discuss the limitations that arise from the growing number of unconstrained parameters on the model's predictive power.

Figures (8)

• Figure 1: Influence of $\alpha_{\rm c}$ on the light curve. The primary mass is $M_1=0.6$ M$_\odot$, the orbital period is 4 hr, and the viscosity parameter is $\alpha_h=0.2$ on the hot branch.
• Figure 2: Influence of the truncation of the inner disc on the light curve. The primary mass is $M_1=1$M$_\odot$, the orbital period is 4 hr; $\alpha_c=0.04$ on the cold branch and $\alpha_h=0.2$ on the hot branch.
• Figure 3: Irradiation by a hot white dwarf. Here, $M_1=0.6$M$_\odot$, the orbital period is 4 hr, $\alpha_c=0.04$, and $\alpha_h=0.2$ as in Fig. \ref{['fig:visc']}. The disc albedo is zero. The bottom panels zoom on the major outburst, and show that the luminosity reaches its quiescent level before reflares.
• Figure 4: Self irradiation of the disc. The binary parameters are those of Fig. \ref{['fig:visc']}.
• Figure 5: Self irradiation of the disc when the inner disc radius is small. The binary parameters are those of Fig. \ref{['fig:rin']}.