Negative superhumps in cataclysmic variables driven by retrograde apsidal disk precession

Abstract

Negative superhumps are photometric modulations in cataclysmic variables with periods slightly shorter than the orbital period. They are usually attributed to retrograde nodal precession of a tilted accretion disk, although the origin and persistence of the tilt remains unexplained. We propose instead that negative superhumps arise from retrograde apsidal precession of an eccentric disk. Using linear eccentric disk theory, we show that the direction of apsidal precession is highly sensitive to disk size and temperature, and that pressure effects can drive retrograde precession even in cool disks. In low mass ratio systems where the 3:1 resonance is within the disk, disk expansion during outbursts may produce opposite precession directions in the inner and outer disk, allowing the temporary coexistence of positive and negative superhumps, and driving dissipation in an extended superoutburst. In higher mass ratio systems where the resonance location is outside of the disk, the resonance width can still extend into the outer parts of the disk, excite eccentricity, and drive apsidal precession. This mechanism explains the prevalence of negative superhumps across a wide range of mass ratios and accretion states, without requiring a long-lived disk tilt. It may also explain how positive superhumps can occur in high mass ratio systems if the disk density builds up in the outer parts of the disk.

Figures (5)

• Figure 1: The eccentricity (upper panels) and periapse angle (lower panels) versus radius of the disk for three different values of $H/r$ and $q=0.1$. The outer disk truncation radius is $r_{\rm out}=0.5\,a_{\rm b}$ (left) and $r_{\rm out}=0.48\,a_{\rm b}$ (right). The dotted lines show the solution to the 2D equations and the solid lines show solution to the 3D equations.
• Figure 2: The eccentricity growth rate (upper panel) and precession rate (lower panel) as a function of $H/r$ are shown for various disk outer radii and $q=0.1$. The dotted lines show the solution to the 2D equations and the solid lines show solution to the 3D equations.
• Figure 3: The eccentricity growth rate (upper panel) and precession rate (lower panel) as a function of the disk outer radius, $r_{\rm out}$ with $H/r=0.02$ and $q=0.1$. The dotted lines show the solution to the 2D equations and the solid lines show solution to the 3D equations.
• Figure 4: The location of the 3:1 resonance as a function of binary mass ratio (red dashed lines, equation \ref{['rres']}). The contours show the forcing term, $s$ (equation \ref{['eq:forcing']}), for disk aspect ratios of $H/r=0.01$ (left), 0.03 (middle) and 0.05 (right). The solid orange lines show a typical location of the disk outer radius for a tidally truncated disk at $r_{\rm out}=0.9\,r_{\rm l}$.
• Figure 5: Eccentricity growth rate (upper panel) and the precession rate (lower panel) as a function of the binary mass ratio using the 3D equations. The disk outer radius is $r_{\rm out}=0.9\,r_{\rm l}$.