We present new transit and occultation times for the hot Jupiter WASP-12b. The data are compatible with a constant period derivative:Ṗ = −29 ± 3 ms yr −1and P/Ṗ = 3.2 Myr. However, it is difficult to tell whether we have observed orbital decay or a portion of a 14-year apsidal precession cycle. If interpreted as decay, the star's tidal quality parameter Q ⋆ is about 2 × 10 5 . If interpreted as precession, the planet's Love number is 0.44 ± 0.10. Orbital decay appears to be the more parsimonious model: it is favored by ∆χ 2 = 5.5 despite having two fewer free parameters than the precession model. The decay model implies that WASP-12 was discovered within the final ∼0.2% of its existence, which is an unlikely coincidence but harmonizes with independent evidence that the planet is nearing disruption. Precession does not invoke any temporal coincidence, but it does require some mechanism to maintain an eccentricity of ≈0.002 in the face of rapid tidal circularization. To distinguish unequivocally between decay and precession will probably require a few more years of monitoring. Particularly helpful will be occultation timing in 2019 and thereafter.

We present the discovery of a transiting exoplanet candidate in the K2 Field-1 with an orbital period of 9.1457 hr: K2-22b. The highly variable transit depths, ranging from ∼0% to 1.3%, are suggestive of a planet that is disintegrating via the emission of dusty effluents. We characterize the host star as an M-dwarf with T eff ; 3800 K. We have obtained ground-based transit measurements with several 1-m class telescopes and with the GTC. These observations (1) improve the transit ephemeris; (2) confirm the variable nature of the transit depths; (3) indicate variations in the transit shapes; and (4) demonstrate clearly that at least on one occasion the transit depths were significantly wavelength dependent. The latter three effects tend to indicate extinction of starlight by dust rather than by any combination of solid bodies. The K2 observations yield a folded light curve with lower time resolution but with substantially better statistical precision compared with the ground-based observations. We detect a significant "bump" just after the transit egress, and a less significant bump just prior to transit ingress. We interpret these bumps in the context of a planet that is not only likely streaming a dust tail behind it, but also has a more prominent leading dust trail that precedes it. This effect is modeled in terms of dust grains that can escape to beyond the planetʼs Hill sphere and effectively undergo "Roche lobe overflow," even though the planetʼs surface is likely underfilling its Roche lobe by a factor of 2.

We have searched for short periodicities in the light curves of stars with T eff cooler than 4000 K made from 2-minute cadence data obtained in TESS sectors 1 and 2. Herein we report the discovery of 10 rapidly rotating M-dwarfs with highly structured rotational modulation patterns among 371 M dwarfs found to have rotation periods less than 1 day. Star-spot models cannot explain the highly structured periodic variations which typically exhibit between 10 and 40 Fourier harmonics. A similar set of objects was previously reported following K2 observations of the Upper Scorpius association (Stauffer et al. 2017). We examine the possibility that the unusual structured light-curves could stem from absorption by charged dust particles that are trapped in or near the stellar magnetosphere. We also briefly explore the possibilities that the sharp structured features in the lightcurves are produced by extinction by coronal gas, by beaming of the radiation emitted from the stellar surface, or by occultations of spots by a dusty ring that surrounds the star. The latter is perhaps the most promising of these scenarios. Most of the structured rotators display flaring activity, and we investigate changes in the modulation pattern following the largest flares. As part of this study, we also report the discovery of 17 rapidly rotating M-dwarfs with rotational periods below 4 hr, of which the shortest period is 1.63 hr.