Transit Timing of the White Dwarf-Cold Jupiter System WD 1856+534

TL;DR

WD 1856+534 b provides a unique testbed for planet survival and inward migration around a white dwarf. The authors extend transit timings to nearly 1500 epochs and compare constant-period and growth models, finding no significant period change. They constrain the planetary tidal quality factor to $Q_p' \gtrsim 3.1\times10^{6}$ and place a weak lower bound on the stellar $Q_*'$, while ruling out close, massive perturbers with $M_p>4.1\,M_J$ and $P<1500$ days. The results favor a past high-eccentricity tidal migration scenario that has since ceased, with the present orbit nearly circular and tides likely dominated by the planet if any. Overall, the study demonstrates the power of long-baseline transit timing to inform migration channels and tidal physics in compact white-dwarf planetary systems.

Abstract

We present new transit timing measurements for the white dwarf-cold Jupiter system WD 1856+534, extending the baseline of observations from 311 epochs to 1498 epochs. The planet is unlikely to have survived the host star's red-giant phase at its present location and is likely too small for common-envelope evolution to take place. As such, a plausible explanation for the short semimajor axis is that the exoplanet started out on a much larger orbit and then spiraled inward through high-eccentricity tidal migration (HETM). A past transit-timing analysis found tentative evidence for orbital growth, which could have been interpreted as a residual effect of HETM, but we find the data are consistent with a constant-period model after adding 18 new transit measurements. We use the estimated period derivative $\dot{P} = 0.04\pm0.43$ ms yr$^{-1}$ to place a lower limit on the planetary tidal quality factor of $Q_p' \gtrsim 3.1 \times 10^6$, consistent with that of Jupiter in our own Solar System. We also test for the presence of companion planets in the system, which could have excited WD 1856 b onto an eccentric orbit via the Kozai-Lidov process, and ultimately rule out the presence of an additional planet with a mass greater than $4.1\,M_J$ and a period shorter than 1500 days. We find no evidence for nonzero eccentricity, with an upper limit of $e\lesssim10^{-2}$. If the planet indeed reached its current orbit through HETM, the low present-day eccentricity indicates that the migration process has now ceased, and any further orbital evolution will be governed solely by weak planetary tides.

Figures (6)

• Figure 1: Stacked light curve of WD 1856+534 b generated from data obtained for this work.
• Figure 2: New WD 1856 b transit light curves obtained with the Lick Nickel telescope. The first and third panels show the data points (black) and fitted light curves (red) with epoch number labeled on the right. The second and fourth panels display the corresponding residuals. Vertical offsets were applied to separate the transits.
• Figure 3: Two-dimensional projection of posterior distribution sampled by emcee when fitting the TTVFast transit-timing model to the observed transit times. The probability distribution function used to color points and compute contours was smoothed using Gaussian Kernel Density Estimation. The lighter colors denote regions of higher probability density. Contours are drawn at $50\%$, $60\%$, $70\%$, $80\%$, and $90\%$ of the peak probability density.
• Figure 4: Log (base 10) likelihood ratio comparing hypothetical companion at $300$ mass points and $100$ period points to the constant-period model. Companion planets in the purple regions of phase space are incompatible with our data. The region outlined in a dashed box is explored further in Figure \ref{['fig:likelihood_ratios_zoom']}.
• Figure 5: Log (base 10) likelihood ratio comparing hypothetical companion at $300$ mass points and $100$ period points to the constant-period model. This plot zooms in on the region outlined by a dashed box in Figure \ref{['fig:likelihood_ratios']}.