Tag Archives: tidal interaction

The tidal shape of the exoplanet WASP-121b

The moon’s gravity causes a tidal bulge in Earth’s oceans, so that the water facing the moon is raised several metres. Similarly, close-orbiting exoplanets will have a tidally distorted shape, with a tidal bulge facing the host star. The amount of distortion can be quantified by the “Love number” h (named after the mathematician Augustus Love)

Specifically, h2 tells us the relative height of the tidal bulge, and would be zero for a perfectly rigid body that did not distort at all, and would be 2.5 for a perfectly fluid body that adapted fully to the tidal potential. Gas-giant planets have large envelopes of gaseous fluid, so would be expected to have fairly high values of h2. However, they also might have rocky or metallic cores, and so would have values less than 2.5. For example Jupiter has h2 = 1.6 while Saturn has h2 = 1.4.

Transit of WASP-121b observed by HST with a model fit by Hellard et al.

A new paper by Hugo Hellard et al discusses whether h2 for a hot-Jupiter exoplanet can be measured from the shape of the transit lightcurve, given good-enough photometry such as that from the Hubble Space Telescope.

The main problem is that the transit profile is heavily affected by variations in the brightness of the stellar disc, in particular the limb darkening (a star’s limbs appear a bit dimmer, because a tangential line-of-sight into a gas cloud skims only the cooler, upper layers). Thus the Hellard et al paper discusses at length different ways to model the limb darkening.

A star’s disk is dimmer at the edges, so a transiting exoplanet removes less light (here Venus, top right, is transiting the Sun).

The end-result, however, is a claim to have measured h2 for WASP-121b, with a value of h2 = 1.4 ± 0.8. This is not (yet) a strong constraint, but points to the potential in the future, and also flags up the need to understand and properly parametrise limb darkening.

The orbit of WASP-12b is decaying

Here’s the latest update on the changes in the orbital period of WASP-12b, from a new paper by Samuel Yee et al.

The times of transit are getting earlier, which means that the period is decreasing slightly. By also considering the times of occultation (when the planet passes behind the star), and also the radial-velocity measurements of the system, the authors deduce that the changes are not the effect of some other planet, but are a real decay in the orbit of WASP-12b. This is expected to occur as a result of tidal interactions between the planet and its host star.

One notable conclusion is that the rate of period decay in WASP-12b is much faster than that in WASP-19b, which shows no detectable period change yet, despite it being an even shorter-period hot Jupiter, which should increase tidal interactions. Yee et al suggest that the difference could arise if the host star WASP-12 is a sub-giant star, whereas WASP-19 is not.

Update: Following an article on WASP-12b’s orbital decay, supplied by Liz Fuller-Wright of Princeton University, and appearing in phys.org and Science Daily, the work has gained media attention from CNN, Science Times, Universe Today, and the UK’s Metro.

WASP-18 is observed by TESS

The TESS mission will survey the entire sky for new transiting exoplanets, and as a by-product will produce space-quality lightcurves of all the WASP exoplanet systems. The first such paper has just appeared on arXiv, where Avi Shporer et al report on the TESS lightcurve of WASP-18.

WASP-18b is the most massive planet found by WASP, a 12-Jupiter-mass planet in a very tight orbit lasting only 0.94 days. This means it has the strongest planet–star tidal interaction of any known planetary system, such that the planet’s gravity gives rise to large tidal bulges on the host star. Here are the TESS data folded on the orbital cycle:

The out-of-transit data are clearly not flat (shown on a larger scale in the middle panel), and show the “ellipsoidal modulation” caused by the tidal bulges on the star. The heated face of the planet is also eclipsed by the star at phase 0.5, producing a secondary eclipse.

By analysing the lightcurve the authors conclude that very little heat is being redistributed from the heated face of the planet. Strong winds could carry heat to the un-irradiated cooler hemisphere, but there is little sign of this in the data.

So far the results of the analysis are in line with theoretical expectations, though the work points to the potential for similar analyses of other previously-known exoplanet systems.

The rigidity of hot-Jupiter exoplanet HAT-P-13b

It is fairly amazing what one can deduce about planets orbiting distant stars. A new paper by Peter Buhler et al reports constraints on the rigidity of the hot-Jupiter exoplanet HAT-P-13b.

The essential data comes from an observation of the occultation of the planet (when it passes behind the host star), as observed in infra-red light by the Spitzer Space Telescope.

Occultation of HAT-P-13b

If the planet’s orbit were exactly circular the occultation would occur exactly half a cycle after the transit. But this occultation is 20 minutes early. That means that the orbit is slightly elliptical, amounting to an eccentricity of 0.007 +/– 0.001, a small but non-zero value.

Most hot Jupiters are expected to have orbits which have been completely circularised by tidal forces. Thus an eccentric orbit implies either that the planet has only relatively recently moved into that orbit, or that the eccentricity is being maintained by the gravitational effects of a third body.

In this case another planet, HAT-P-13c, a 14-Jupiter-mass planet in a longer 446-day orbit, is thought to be perturbing the close-in hot Jupiter HAT-P-13b.

The extent of the perturbation then tells us about the rigidity of the hot Jupiter. Tidal forces result from the fact that gravity differs across an extended body such as a planet, and how a planet reacts to the tidal stress depends on its rigidity.

The rigidity is parametrised by the “Love number”, and the authors find that the eccentricity of HAT-P-13b’s orbit implies a Love number of 0.3. This in turn implies that the planet likely has a rocky core of about 11 Earth masses, with the rest being an extended gaseous envelope.