Hot-Jupiters are a class of exoplanets that share similar characteristics to Jupiter (i.e. they are all gas giant planets), but have extraordinarily high surface temperatures because they orbit very close to their parents stars. On a hot-Jupiter, the intense heating on the planet’s dayside drives powerful winds that tear continually around the planet, transporting heat from the dayside and dumping it on the nightside. These hellacious winds whip around the planet from west to east, generating what is known as superrotation. The winds extend from the planet’s equator to latitudes of typically 20° to 60°. Because a hot-Jupiter orbits so close to its parent star, the planet is most likely tidally-locked and presents the same hemisphere towards its parent star all the time. Superrotation on a tidally-locked hot-Jupiter tends to produce an eastward displacement of the planet’s hottest region from the substellar point by up to 10° to 60° of longitude.
Figure 1: Artist’s impression of a gas giant planet.
S. Faigler & T. Mazeh (2014) analysed the Kepler light-curves of four transiting hot-Jupiters - KOI-13b, HAT-P-7b, TrES-2b and Kepler-76b. The light-curves of these four planets show beaming, ellipsoidal and reflection/emission (BEER) phase modulations. As a hot-Jupiter circles its parent star, it gravitationally tugs at the star, causing the star to “wobble”. From an observer’s point of view, the star would appear to approach and recede in a periodic fashion as the hot-Jupiter orbits around it. In the BEER phase modulations, the beaming effect, also know as Doppler boasting, is caused by an increase (decrease) in the brightness of the parent star as it approaches (recedes from) the observer. The ellipsoidal effect is caused by the tidal distortion of the star by the hot-Jupiter. Both the beaming and ellipsoidal phase modulations are proportional to the hot-Jupiter’s mass. Finally, the reflection/emission phase modulations are the result of a combination of light reflected from the planet’s dayside (reflection) and thermal radiation that is re-emitted by the planet (emission).
The back and forth motion of a star induced by the gravitational tugging of an orbiting hot-Jupiter also causes the star’s spectrum to be blue-shifted (red-shifted) when the star is observed to approach (recede from) the observer. This results in a radial velocity signature that is proportional to the planet’s mass and it serves as an independent measure of the planet’s mass in addition to the BEER phase modulations. Radial velocity measurements available for the hot-Jupiters - HAT-P-7b, TrES-2b and Kepler-76b show that the planetary-mass derived from the beaming amplitude is noticeably larger than from the radial velocity measurements. Also, for all four hot-Jupiters - KOI-13b, HAT-P-7b, TrES-2b and Kepler-76b, the planetary-mass derived from the beaming amplitude is larger than from the ellipsoidal amplitude.
S. Faigler & T. Mazeh (2014) suggests that the apparent planetary-mass discrepancy is found to be caused by superrotation, whereby the eastward displacement of the planet’s hottest spot from the substellar point induces an angle shift in the planet’s reflection/emission phase modulation which “leaks” into the beaming modulation and artificially boosts its observed amplitude. As a consequence, the planetary-mass estimated from the beaming amplitude is somewhat larger than the real one. When the effect of superrotation is included in a modified “BEER model”, the apparent planetary-mass discrepancies disappear. This study shows that hot-Jupiter superrotation may be a rather common phenomenon that can be identified in the Kepler light-curves of hot-Jupiters that exhibit considerable BEER phase modulations. For each of the four hot-Jupiters in this study, the hottest spot is estimated to be displaced eastwards from the substellar point by 0.8° ± 0.9° for KOI-13b, 5.4° ± 1.5° for HAT-P-7b, 38° ± 18° for TrES-2b and 9.2° ± 1.3° Kepler-76b.
Figure 2: The four panels correspond to the four hot-Jupiters - KOI-13b, HAT-P-7b, TrES-2b and Kepler-76b. For each panel, the solid line represents the best-fit superrotating BEER model of the corresponding hot-Jupiter’s light-curve. The residuals are shown below each panel. On each panel, the dashed, dash-dot and dotted lines represent the shifted reflection/emission, beaming and ellipsoidal models, respectively. The vertical red dashed line marks the phase of maximum reflection/emission. Notice that the phase of maximum reflection/emission of each planet comes before phase 0.5. This is consistent a superrotation-induced eastward displacement of the planet’s hottest spot from the planet’s substellar point. S. Faigler & T. Mazeh (2014).
S. Faigler & T. Mazeh (2014), “BEER analysis of Kepler and CoRoT light curves: II. Evidence for emission phase shift due to superrotation in four Kepler hot Jupiters”, arXiv:1407.2361 [astro-ph.EP]