Doomed Worlds I: No new evidence for orbital decay in a long-term survey of 43 ultra-hot Jupiters

Ultra-hot Jupiters are likely doomed by tidal forces to undergo orbital decay and eventual disruption by their stars, but the timescale over which this process unfolds is unknown. We present results from a long-term project to monitor ultra-hot Jupiters transits. We recovered WASP-12 b's orbital decay rate of dP/dt = -29.8 +/- 1.6 ms yr-1, in agreement with prior work. Five other systems initially had promising non-linear transit ephemerides. However, a closer examination of two -- WASP-19 b and CoRoT-2 b, both with prior tentative detections -- revealed several independent errors with the literature timing data; after correction neither planet shows signs of orbital decay. Meanwhile, a potential decreasing period for TrES-1 b, dP/dt = -16 +/- 5 ms yr-1, corresponds to a tidal quality factor Q*' = 160 and likely does not result from orbital decay, if driven by dissipation within the host star. Nominal period increases in two systems, WASP-121 b and WASP-46 b, rest on a small handful of points. Only 1/43 planets (WASP-12 b) in our sample is experiencing detectable orbital decay. For nearly half (20/42) we can rule out dP/dt as high as observed for WASP-12 b. Thus while many ultra-hot Jupiters could still be experiencing rapid decay that we cannot yet detect, a sizeable sub-population of UHJs are decaying at least an order of magnitude more slowly than WASP-12 b. Our reanalysis of Kepler-1658 b with no new data finds that it remains a promising orbital decay candidate. Finally, we recommend that the scientific community take steps to avoid spurious detections through better management of the multi-decade-spanning datasets needed to search for and study planetary orbital decay.