Tag Archives: gravity darkening

CHEOPS observes WASP-189b

ESA’s CHEOPS satellite was launched to produce high-quality light-curves of exoplanet systems. A new paper led by Adrien Deline of the University of Geneva now reports CHEOPS observations around the orbit of the ultra-hot-Jupiter WASP-189b. The figure shows the transit (planet passing in front of the star), the eclipse (the planet passing behind the star) and a slower variation caused by the varying visibility of the heated face of the planet.

One notable feature of the transit of WASP-189b is that it is distinctly asymmetrical. This is caused by gravity darkening, which occurs when a star is rapidly rotating. The centrifugal forces cause the equatorial regions to be pushed outwards, producing an equatorial bulge. Since the bulge is then further from the star’s centre, the surface gravity will be lower, and that means that the surface will be cooler and thus dimmer.

The illustrations below show the asymmetry, where the dashed line in the lowest panel shows the difference between a transit model both with and without gravity darkening. The right-hand panel illustrates the polar orbit of the planet.

Gravity darkening of planet-host MASCARA-4

MASCARA is one of WASP’s competitor transit-search projects, so let’s celebrate a neat result from TESS data of transits of MASCARA-4b. The host star, MASCARA-4, is a hot, fast-rotating A-type star. As a result of its fast rotation, the equatorial regions are being flung outwards by centrifugal forces, such that the star has a flattened, oblate shape. As a result, the force of gravity will be less at the equator than at the poles of the star, and that means that the equatorial regions will be slightly cooler and so a bit dimmer (in outline, that’s because gravity inward pull is balanced by gas pressure, and so lower gravity means lower pressure, and the temperature of a gas is related to its temperature through the perfect gas law). This effect is called “gravity darkening”.

The star spins around its axis (thick line) while the planet orbits at an oblique angle.

In a new paper, John Ahlers et al have detected the effect of gravity darkening on a transit lightcurve of the hot Jupiter MASCARA-4b. The planet has a misaligned orbit, first coming onto the stellar face near the equator, and then moving towards a pole. That means it moves from slightly cooler regions to slightly hotter regions, and that changes the amount of light occulted by the planet.

If gravity darkening is not taken into account then the model fit is a bit too deep at the start and a bit too shallow at the end of the transit. One of the benefits of detecting this effect of gravity darkening is that it then tells us the true angle between the star’s spin axis and the planet’s orbit (whereas other methods, such as Doppler tomography, only tell us the projection of that angle onto the sky).