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

TL;DR

This study extends transit timing data for WD 1856+534 b, constrains its orbital evolution, and rules out additional massive companions, supporting a history of high-eccentricity tidal migration with minimal current eccentricity.

Contribution

It provides the longest transit timing baseline for WD 1856+534 b, refines the orbital period stability, and constrains the presence of additional planets, advancing understanding of its migration history.

Findings

Transit timing data extended to 1498 epochs.

Orbital period appears stable with no significant change.

No additional planets with >4.1 M_J within 1500 days period.

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.