The Eccentric Disk Model for Superhumps

Abstract

An important goal of the disk instability model is to explain the superhump phenomenon. Superhumps are features found in the light curves of binary systems, characterized by a period slightly different from the binary orbital period. In cases where the superhump period is longer than the orbital period (positive superhumps), they have been interpreted as arising from an eccentric, precessing disk. This paper reviews the theory and simulations that indicate that the disk's eccentricity originates from a dynamical instability at the 3:1 resonance. The instability is described by a mode-coupling process involving the interaction of the disk eccentricity with the binary tidal potential. This instability provides critical constraints on the nature of the disk turbulence that enables the disk to reach this resonance.

Figures (2)

• Figure 1: Diagram of the eccentricity instability cycle. The eccentric and tidal modes interact to generate a spiral wave at the 3:1 resonance that in turn interacts again with the tidal field to generate a stress that amplifies the eccentricity.
• Figure 2: Eccentricity $e=|E|$ of the fastest growing eigenmodes that are normalized by their values at the disk outer edge $e_{\rm o}$ plotted as a function of dimensionless radius $r/a_{\rm b}$. The binary mass ratio is $q=0.1$ in all cases. The red dashed lines are for 2D disks, while the solid blue lines are for 3D disks. The black dashed and dotted lines plot the resonant growth and precession terms, respectively, given by the real and imaginary parts of Equation (\ref{['s']}) in units of $\Omega_{\rm b}$. The left panel is for a disk with aspect ratio $h=0.02$, similar to what is expected during a superoutburst, while the right panel is for a warmer disk with aspect ratio $h=0.05$.