Long-term eclipse time variations in white dwarf binaries

The overwhelming majority of eclipsing white dwarf (WD) binary systems show quasi-periodic variations in eclipse timings on many year timescales. Currently, the mechanism behind these eclipse time variations (ETVs) is not known, with the main competing theories being the planetary hypothesis and the Applegate/Lanza mechanisms. Here, we present a comprehensive study of 43 WD binary systems, the vast majority of which have more than a decade of eclipse timing measurements, analysing their global properties to determine which driving force is the likely origin of the observed ETVs. Long-term, high-speed photometry data obtained with ULTRACAM, ULTRASPEC and HiPERCAM have allowed us to track the evolution of the ETVs in these systems, and analyse any previously unseen trends. From this analysis, we find a clear difference in the level of observed ETVs past the fully convective boundary, where systems with partially radiative companion stars consistently showing high levels of variation. While some systems may be affected by the presence of an unknown planet, the results from this study strongly indicates that an Applegate- or Lanza-like mechanism is the most likely driving force for the timing variations seen in the majority of systems in this sample. However, as found in previous studies, the Applegate/Lanza mechanisms are still not able to reproduce the large and rapid timing variations seen in the vast majority of systems, with the companion star to the WD unable to provide sufficient energy on these short timescales.

💡 Research Summary

This paper presents a comprehensive investigation of eclipse timing variations (ETVs) in 43 eclipsing white‑dwarf (WD) binary systems, the majority of which have more than a decade of high‑speed photometric coverage. The sample comprises three double‑WD binaries, five WD‑brown‑dwarf (WDBD) pairs, and thirty‑five WD‑main‑sequence (WDMS) systems (34 M‑dwarfs and one K‑dwarf). Using ULTRACAM, ULTRASPEC, and HiPERCAM, the authors obtained sub‑second time resolution of ingress and egress, allowing eclipse mid‑times to be measured with typical uncertainties of 0.1–0.3 s.

The authors first fitted a linear ephemeris to each system and constructed O–C (observed minus calculated) diagrams. The majority of O–C curves display quasi‑sinusoidal behaviour with periods ranging from a few years to several decades, while a subset shows abrupt, large‑amplitude deviations (several seconds to tens of seconds) that cannot be described by a simple parabola.

Two competing explanations for the observed ETVs are examined: (1) the light‑travel‑time (LTT) effect caused by one or more circumbinary planets, and (2) variations in the stellar quadrupole moment driven by magnetic activity in the non‑degenerate companion (the Applegate and Lanza mechanisms).

Planetary models were fitted to the O–C data, but in most cases the required orbital parameters are dynamically implausible (extremely high eccentricities, unstable multi‑planet configurations) or fail to predict future eclipse times. In particular, systems with long‑term, multi‑decade variations cannot be reproduced by a single planetary companion.

The magnetic‑activity hypothesis was evaluated by calculating the energy budget needed for the Applegate (1992) and Lanza (2020) mechanisms, using measured companion masses, radii, and estimated magnetic cycle periods. For fully convective M‑dwarfs (M ≲ 0.35 M⊙) the required energy exceeds the star’s total luminosity by one to two orders of magnitude, especially for those showing rapid, large‑amplitude ETVs. Conversely, systems with partially radiative companions (e.g., the K‑dwarf V471 Tau and several >0.5 M⊙ main‑sequence stars) have energy requirements that are comparable to the available stellar output, and these systems consistently exhibit the highest ETV amplitudes.

A statistical analysis reveals a clear trend: binaries whose secondary lies above the fully convective boundary display significantly larger and more complex O–C variations than those below the boundary. This supports the notion that the internal structure of the active star governs the efficiency of quadrupole‑moment fluctuations.

Nevertheless, even the refined Lanza model, which reduces the energy demand by invoking localized magnetic flux tubes and a modest asynchronism between stellar rotation and orbital motion, still struggles to account for the most extreme variations. The required asynchronism is at odds with the very short tidal synchronisation timescales (∼10⁵ yr) expected for close WD binaries.

The authors conclude that while the majority of observed ETVs are most plausibly driven by an Applegate‑ or Lanza‑type magnetic mechanism, the classic formulations cannot fully explain the magnitude and rapidity of the variations in many systems. They advocate for next‑generation magnetohydrodynamic simulations that incorporate realistic flux‑tube dynamics, possible differential rotation, and more accurate stellar interior models. Simultaneous monitoring of magnetic activity indicators (e.g., Hα emission, X‑ray flux) would also help to correlate activity cycles with eclipse timing behaviour.

In summary, this work provides strong statistical evidence that magnetic activity in the non‑degenerate companion is the dominant source of eclipse timing variations in white‑dwarf binaries, especially for systems with partially radiative secondaries, while also highlighting the persistent energy‑budget problem that must be resolved by future theoretical and observational efforts.