Tag Archives: orbital obliquity

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).

WASP-43b has an aligned orbit

WASP-43b is the hot Jupiter that is closest to its parent star, around which it orbits in only 19 hours. At such a close location, tidal interactions between the planet and the star will be intense. That means that we expect the planet to be phase locked (with its rotation period equalling the orbital period, so that the same side always faces the star), and we expect the orbit to be circular (any eccentricity having been damped by tides), and we expect the orbit to be aligned with the rotation axis of the star.

Tidal damping of the alignment of the orbit is the subject of much investigation. It seems to be most efficient if the planet orbits cooler stars, and much less efficient if the planet orbits a hotter star. This might be because cooler stars have large “convective zones” in their outer layers, which can efficiently dissipate tidal energy, whereas hotter stars have only very shallow convective zones with little mass in them.

Since WASP-43b orbits a cool star, a K7 star with a surface temperature of only 4400 Kelvin, that’s another reason for expecting its orbit to be aligned. This has now been confirmed by observations with the Italian Telescopio Nazionale Galileo. The way to measure the orbital alignment of a transiting exoplanet is by the Rossiter–McLaughlin effect. As the planet transits a rotating star, it first obscures one limb and then the other, and since the different limbs will be either blue-shifted or red-shifted, according to how the star is spinning, the effect on the overall light of star will reveal the path of the orbit.

Rossiter-McLaughlin effect

A new paper by Esposito et al reports R–M measurements for three planets including WASP-43b. The data show the classic R–M signature of an aligned planet.

Rossiter-McLaughlin effect for exoplanet WASP-43b

The upper panel shows the change in stellar radial-velocity around the planet’s orbit, caused by the gravitational tug of the planet. The lowest panel highlights the data through transit, showing the expected excursion first to a redder light (when blue-shifted light on the approaching limb is occulted) and then to blue light (when the red-shifted receding limb is occulted).