Superhumps and their Relation to the Disk Instability Model

TL;DR

This review consolidates decades of time-resolved photometry showing that superhumps illuminate the disk instability dynamics in cataclysmic variables, anchored by the thermal-tidal instability framework and the 3:1 resonance. It highlights three key advances: (1) the stage A–B–C evolution of superhumps and its physical interpretation, (2) a practical mass-ratio estimator from Stage A superhumps, and (3) the extension of superhump phenomenology to intermediate polars, AM CVn systems, and black-hole X-ray binaries. It also documents new phenomena, such as standstill-triggered superoutbursts and negative superhumps, while identifying unresolved issues in period changes, high-q transitions, and long-period resonances. Overall, superhumps serve as a powerful diagnostic of accretion-disk structure, informing binary parameters and the interplay of thermal, tidal, and geometric effects across diverse accreting systems.

Abstract

Since the discovery of superhumps in 1974, these photometric modulations have provided a crucial observational window into disk instabilities in cataclysmic variable stars, particularly the tidal instability associated with the 3:1 resonance. Over the past few decades, extensive time-resolved photometry has revealed a rich diversity of superhump-related phenomena, including delayed superhump development, early superhumps in WZ Sge-type dwarf novae, systematic stage A-B-C evolution, negative superhumps, and superhumps observed in related systems such as intermediate polars and AM CVn stars. In this invited review, we summarize key observational advances since the establishment of the thermal-tidal instability framework, discuss their theoretical interpretations within the disk instability model, and highlight remaining open problems. These developments have been driven by coordinated networks of amateur observers, wide-field robotic surveys, and continuous high-precision space-based photometry from Kepler and TESS. Together, they demonstrate that superhumps remain a powerful probe of disk dynamics, binary parameters, and the interplay between thermal, tidal, and geometric effects in accretion disks.

Figures (8)

• Figure 1: $\dot{M}$-$P_{\rm orb}$ diagram. The acronyms of NL, ZC, UG, PS, ER, SU and WZ present nova-likes, Z Cam-type stars, U Gem(SS Cyg)-type stars, permanent superhumpers, ER UMa-stars, SU UMa-stars and WZ Sge-type stars. CVs in the upper and lower regions separated by the oblique line are thermally stable and unstable, respectively. CVs in the right and left regions are tidally stable and unstable, respectively. Systems with lower mass transfer rates have longer (super)outburst-recurrence cycles. This figure was created based on Figure 3 in osa96review.
• Figure 2: (top) O-C diagram of the superhump maximum timing, (middle) superhump amplitude, and (bottom) superhump amplitude, (bottom) superoutburst light curve after subtraction of a linear decay trend. The horizontal axis represents the superhump cycle ($E$) starting from the first observed superhump. This figure is Figure 3 in Pdot.
• Figure 3: (right) ASAS-SN light curve in $V$ and $g$ bands of NY Ser from 2015 to 2018. (left) Enlarged light curve in 2018. Two superoutbursts occurred directly following standstills. This figure was created based on Figures 1 and 2 in kat19nyser.
• Figure 4: (upperleft) Light curve of two days around the superoutburst maximum in a WZ Sge star V455 And in 2007. (lowerleft) Its detrended one. The evolution of the early superhumps in a very short time ($<$ one day) was clearly observed. (right) Folded superhump profiles in different objects and superoutburst. All have double-peaked shapes, though the details of these profiles are slightly different. This figure was created based on Figures 11 and 12 in kat15wzsge.
• Figure 5: (a) Long-term light curve of ASASSN-16eg during the superoutburst in 2016, which is a typical one of WZ Sge stars. (b) Folded light curve of early superhumps having a double-peaked shape. (c) O-C diagram of the superhump maximum timing (upper), amplitude of the superhump, and (c) light curve of the superoutburst having a common horizontal axis. This figure was created based on Figures 1, 2 and 3 in wak17asassn16eg.