WD 1054-226 revisited: a stable transiting debris system

Abstract

A growing number of white dwarfs (WDs) exhibit one or more signs of remnant planetary systems, including transits, infrared excesses, and atmospheric metal pollution. WD 1054-226 stands out for its unique, highly structured, and persistent photometric variability. We aim to investigate the long-term stability and nature of the periodic signals observed in WD 1054-226 to better understand the origin and evolution of its transiting material. We analyse all available TESS light curves from Sectors 9, 36, 63, and 90 using Lomb-Scargle (LS), Box-Least-Squares (BLS), and Gaussian process (GP) periodogram analyses. We complement these with multiband, high-cadence ground-based photometry from LCOGT, MuSCAT2, ALFOSC, and ProEM to test for colour dependence and confirm the periodicities. We confirm the persistence of the previously-reported 25.01 h and 23.1 min periodicities over a six-year baseline. The 25.01 h signal shows some temporal evolution, while the 23.1 min dips are highly coherent on long timescales. A transient 11.4 h feature, previously reported, is detected only in early TESS sectors and is absent in recent data. No significant colour dependence is found in the ground-based observations. The stability of both the 25.01 h and 23.1 min signals indicates a long-lived, dynamically sculpted debris structure around WD 1054-226. The lack of colour dependence implies high optical depth, consistent with an opaque, edge-on debris ring rather than an optically thin dust population. This makes WD 1054-226 a key laboratory for testing models of remnant planetary systems around white dwarfs.

Figures (9)

• Figure 1: All $i$ band light curves ordered into groups, and phase-folded to the 25.01 h period, the reference time for phase folding is 2459928.85. The light curves of each group have a y-offset corresponding to the 25.01 h periodic signal cycle.
• Figure 2: Multi-colour photometry from MuSCAT2, ProEM, and ALFOSC shown for filters $g'$ (blue), $r$ (green), $i$, and $i'$ (yellow), and $z_\mathrm{s}$ (red) and phase-folded to the 25.01-h period, the reference time for phase folding is 0.0. The MusCAT2 photometry is binned to 3-min, the ProEM photometry to 2-min, and the ALFOSC photometry is not binned. The light curves have a y-offset corresponding to the 25.01 h periodic signal cycle.
• Figure 3: Lomb-Scargle periodograms of the TESS photometry from Sectors 9, 36, 63, and 90. The known 23.1 min and 25.01 h periodicities are marked with solid orange and blue lines, respectively, while the 11.4 h signal is marked with a solid green line. Dashed and dotted lines indicate harmonics of these signals using the same colour coding.
• Figure 4: Gaussian process periodograms for the long-period searches (3--29 h) from the TESS Sector 9, 36, 63, and 90 photometry. Left column: 1D periodograms for a single-period GP model. The plotted signal amplitude $\Delta\mathrm{BIC}$ is defined as the difference between the BIC of the single-period GP model and that of the aperiodic GP model, i.e. $\Delta\mathrm{BIC}=\mathrm{BIC}_1(p_1)-\mathrm{BIC}_0$. Right column: Conditional 1D periodograms for a two-period GP model where $p_1$ is fixed to 25.01 h. Here, $\Delta\mathrm{BIC}=\mathrm{BIC}_2(p_1=25.01\mathrm{h},p_2)-\mathrm{BIC}_1(p_1=25.01\mathrm{h})$. The known 25.01 h period and its harmonics are marked with solid and dashed blue lines, respectively, while the 11.4 h period and its harmonics are marked with the solid and dotted green lines. The horizontal slashed line shows the $\Delta\mathrm{BIC}$ level of -10, which corresponds to very strong evidence in favour of the periodic signal Kass1995.
• Figure 5: Posterior densities for the GP model hyperparameters estimated from the ground-based LCO observations and from separate TESS sectors. The first column shows the GP coherence scale, the second column shows the GP harmonic complexity, and the third column shows the amplitude of the periodicity. The 11.4 h period is estimated only from the TESS Sectors 9 and 36. The ground-based posterior estimates for the 25.01 h and 23.1 min periodicities are significantly better than the TESS ones due to the significantly higher photometric precision.