Tag Archives: tidal decay

WASP-100 and WASP-126 in TESS Sectors 1 to 4

As TESS continues its all-sky survey it will produce high-quality data containing lots of transits for all the WASP planets. This is especially so for planets near the ecliptic poles, which TESS will observe over many sectors. With TESS Sector 4 data recently released, here are some plots borrowed from David Kipping on Twitter.

The lower plots show the variations in transit timing (O–C is the difference between the observed timing and the timing calculated from an ephemeris).

These plots seem to show something that I’ve suspected for a while, namely that there are correlated deviations in the transit timings, meaning that if one O–C value is slightly early (or late) then the next one is more likely to be the same. Such deviations can also be larger than expected given the errors (the quoted chi-squared value for WASP-100b of 44 for 32 degrees of freedom tells us that the error bars don’t fully account for the variations).

This must be the result of stellar activity, magnetic variations on the surface of the star such as star-spots and faculae. Any deviation from a smooth stellar profile can then alter the transit profile.

Properly accounting for such effects will be important for two sorts of study. The first is looking for “transit-timing variations”, changes in the transit time of a planet caused by variations in its orbit owing to the gravitational perturbations of another planet. The second is looking for long-term changes in the orbital period, such as the inward-spiral decay of the orbit predicted to be caused by tidal interactions of the planet and its host star. The literature contains marginal claims of the latter effect that might be better explained as the effect of magnetic activity of the host star.

How fast do the orbits of hot Jupiters decay?







HATS-18b and short-period hot Jupiters




Stellar tidal decay quality factor







Orbital-period decay in hot-Jupiter WASP-12b?

Closely orbiting hot-Jupiter exoplanets are likely to be spiralling inwards towards their host star as a result of tidal interactions with the star. A new paper by Maciejewski et al reports a possible detection of this orbital-period decay in WASP-12b.

The authors have acquired 31 new transit light-curves over four years, and detect a trend under which the latest transits occur about a minute early compared to an unchanging ephemeris.

WASP-12b orbital period decay

Transits of WASP-12b. O–C is the observed time compared to that calculated from an unchanging orbital period. The time (x-axis) is given in both a count of days (BJD) and a count of transits.

This is the most convincing claim yet of a changing orbital period in a hot Jupiter. Whether it shows the spiral infall, though, is less clear. As the authors explain, other tidal interactions between the star and the planet, such as that causing apsidal precession, could account for the effect. Further, in close binary stars there are known to be similar period changes on decade-long timescales that are not fully understood, but which might be caused by Solar-like magnetic cycles on the star.

One suggestion that this is not spiral infall comes from the deduced value of the tidal quality factor, Q, which the authors calculate as 2.5 x 105. This is lower than other estimates of Q as nearer 107.

The way to settle the issue will be to accumulate more data over a longer timespan until the case for spiral infall becomes overwhelming. It will thus be important to continue monitoring WASP-12b, and the other short-period hot Jupiters, over the coming decades.

Calculations of hot-Jupiter tidal infall

Closely orbiting hot Jupiters raise a tidal bulge on their star, just as our Moon does on Earth. Since the planet is orbiting faster than the star rotates, the tidal bulge will tend to lag behind the planet and so its gravitational attraction will pull back on the planet. The orbit of the planet is thus expected to decay, with the planet gradually spiralling inwards to destruction.

Calculating how long this will take is hard, and depends on the efficiency with which energy is dissipated in the tidal bulge of the star. This is summed up by a number called a quality factor, Q, which is, crudely, the number of orbital cycles required to dissipate energy. The higher this number the slower the decay of the planet’s orbit.

In a new paper, Reed Essick and Nevin Weinberg, of the Massachusetts Institute of Technology, present a detailed calculation of Q for hot Jupiters orbiting solar-like stars. They arrive at values for Q of 105 to 106, assuming a planet above half a Jupiter mass and an orbital period of less than 2 days.

Hot Jupiter orbital decay timescales

The figure shows the resulting infall timescales of all the hot Jupiters predicted to have remaining lifetimes of less than 1 Gyr. By far the smallest lifetime is that for WASP-19b, which is predicted to spiral into its star within 8 million years. This would mean that shifts in WASP-19b’s transit times would be readily detectable, with a shift accumulating to 1 minute in only 5 years.

The calculations presented here are at odds with deductions that Q must be around 107, based on explaining the current distribution of hot-Jupiter periods (e.g. Penev & Sasselov 2011), which would give a much slower orbital decay. We can determine who is right by monitoring transits of WASP-19b and similar systems over the coming decade, and it will be interesting to discover who is right.

Possible orbital period decay in WASP-43b?




Transit timings and period decay in WASP-43b






WASP-121b: another planet close to tidal destruction






WASP-121b occultation

