Long-term eclipse time variations in white dwarf binaries

Abstract

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.

Figures (6)

• Figure 1: Grid of the O$-$C plots for the WD binaries in the ETV programme with > 2 measured eclipse times. The y-axis is the O$-$C value, measured in seconds. The x-axis is the MJD(BTDB) time. The red dashed line at y=0 is added to highlight the deviations from the expected O$-$C value if no variation in eclipse time was present. The ID number in each plot corresponds to the binary's ID number listed in Table \ref{['tab:targets']}.
• Figure 2: The log of the RMS of the O$-$C values as a function of the baseline of observation, measured in years. The shape of the points indicates the type of binary - a circle means the binary is WDMS, a square means WDBD, and a triangle indicates a DWD binary. The colour of the point indicates the mass of the companion following the colour bar on the right side of the plot. The grey tracks show the evolution of the RMS with baseline for each point.
• Figure 3: The log of the RMS of the O$-$C values as a function of the mass of the companion ($M_{\mathrm{sec}}$) measured in solar masses. The shape of the points indicates the type of binary, with circles representing WDMS binaries, squares representing WDBD binaries, and triangles representing DWD binaries. The colour of the points represents the orbital period following the colour bar on the right of the plot. Errors on the x-axis are shown in grey. The vertical grey, dotted line represents the convective boundary at 0.35$M_{\odot}$.
• Figure 4: The log of the RMS of the O$-$C values as a function of log($M^{3.45}/a^{2}$). The shape of the points indicates the type of binary, with circles representing WDMS binaries, squares representing WDBD binaries, and triangles representing DWD binaries. The colour of the points represents the orbital period following the colour bar on the right of the plot, and the size of the points represents the mass of the companion, with larger companion masses shown as larger points. Errors on the x-axis are shown in grey. Smaller values on the x-axis mean a larger fraction of the available energy is needed to drive ETVs via the Applegate mechanism.
• Figure 5: The log of the RMS of the O$-$C values as a function of log($M^{1.6}a$). The shape of the points indicates the type of binary, with circles representing WDMS binaries, squares representing WDBD binaries, and triangles representing DWD binaries. The colour of the points represents the orbital period following the colour bar on the right of the plot, and the size of the points represents the mass of the companion, with larger companion masses shown as larger points. Errors on the x-axis are shown in grey. Smaller values on the x-axis mean a larger fraction of the available energy is needed to drive ETVs via the Lanza mechanism.