Tag Archives: tidal damping

How fast do the orbits of hot Jupiters decay?

Tidal interactions between close-in, gas-giant exoplanets and their host star should cause the orbits of the planets to decay. The crucial number in determining how fast that happens is the “quality factor”, Q, which tells us the fraction of the tidal energy that is dissipated in each cycle. A high value of Q, say 107, means that only 1 part in 107 of the energy is dissipated, giving a low rate of orbital decay. A smaller value gives a faster decay.

A new study by Kaloyan Penev et al suggests that Q varies a lot depending on the tidal “forcing period” (that is, the period at which a planet would appear to orbit, if viewed when rotating with the spinning star, with an extra factor of a half since there are two tides per orbital cycle).

Penev estimate the value of Q by comparing the observed spin period of the host star to the most likely spin period expected for that sort of star, if it had no planet, and so modelling how much the star has been spun up by the tidal interaction with the planet.

They find that the Q of the star is high, about 107, when the tidal forcing period is low (< 1 d) but much smaller, about 105.5, when the forcing period is longer.

This work might resolve several puzzles. The Q value expected from studying binary stars is near 105.5, but if that were true for all hot Jupiters then they’d be destroyed too readily, and the current observed population could not be explained. This puzzle is resolved if their orbits decay much more slowly when the forcing period is short.

The different Q values also allow the planets to re-align their orbits with the spin of the star (so that the orbital plane is perpendicular to the star’s spin axis) on a timescale shorter than the orbital period decay, thus explaining why there are many “aligned” hot Jupiters.


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).

Spin-orbit alignments for three more WASP planets

A team led by Brett Addison has been pointing the Anglo-Australian Telescope at WASP planets, trying to discern whether the planet’s orbit is aligned with the star’s spin axis.

The rotation of the star means that one limb is approaching us, and so is blue-shifted, while the other limb is receding, and so is red-shifted. The planet can occult blue-shifted light (making a spectral line redder) and then red-shifted light. This is called the Rossiter–McLaughlin (or R–M) effect, and allows us to deduce the path of a transiting planet across the face of its star.

Rossiter-McLaughlin effect

Brett Addison and colleagues report the R–M effect for three more WASP planets, WASP-66b, WASP-87b and WASP-103b. Here are their data for WASP-87b:

WASP-87 Rossiter-McLaughlin effect

All three planets appear to have orbital axes aligned with the star’s spin axis. The authors discuss the mechanisms and timescales by which orbits get “damped” by tidal effects and so become aligned with their star.