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

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 study 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 P ̇ = 0.04 ± 0.43 ms yr −1 to place a lower limit on the planetary tidal quality factor of Q p ′ ≳ 3.1 × 1 0 6 , if the planet has not already achieved spin–orbit synchronization. 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 mass greater than 4.0 M J and period shorter than 1500 days. We find no evidence for nonzero eccentricity, with an upper limit of e ≲ 10 −2 . If the planet reached its current orbit through HETM, the low present-day eccentricity indicates that the migration process has now ceased, and any further orbital evolution, if any, will likely be governed by weak planetary tides.