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?

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.

HATS-18b and short-period hot Jupiters

Congratulations to the HATSouth project for the discovery of HATS-18b, a hot Jupiter with the very short orbital period of only 0.84 days. The other known hot Jupiters with periods below 1 day are all WASP-South discoveries (WASP-19b at 0.79 d, WASP-43b at 0.81 d, WASP-103b at 0.93 d and WASP-18b at 0.94 d).

Since such short-period systems are the easiest to find in transit surveys (owing to lots of transits!) they must be very rare, presumably because tidal forces are causing the orbits to decay, so that the planets spiral into their stars on relatively short timescales of tens of millions of years.

The HATSouth team note that the rotational periods of the host stars of HATS-18b and WASP-19b are much shorter than expected given the ages of the stars, and suggest that the stars have been spun up by the same tidal interaction that caused the planet’s orbit to decay. By modelling the in-spiral process Penev et al arrive at constraints on the “quality factor” Q* of the star. This is a measure of how efficient the star is at dissipating the tidal energy resulting from the planet’s gravitational tug on the star, and this sets the timescale for the tidal decay. Penev et al argue that the log of Q* is between 6.5 and 7, one of the tightest constraints yet estimated.

Stellar tidal decay quality factor

Estimates of the tidal quality factor, from modelling the HATS-18b and WASP-19b systems. The different models use different assumptions and are explained in the text. Figure by Penev et al.

New HATSouth planets gives us at WASP a check on our methods, since we can look for them in our own data (and if we don’t see them we can ask why not). At V = 14.1, HATS-18 is fainter than any of the WASP host stars, and fainter than we would adopt as a candidate (HATSouth is optimised to get better photometry on a slightly fainter magnitude range, whereas WASP-South is optimised for a wider field). Nevertheless, 26 000 data points from WASP-South do detect the transit of HATS-18b, giving a detected signal at the 0.837-day period and its first harmonic (1.67-d) in the period search:


There is then a clear detection of the transit when the data are folded on the transit period:


This is thus the faintest detection of a planet yet by WASP-South and so is reassuring about WASP data quality.

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?

Since hot-Jupiter planets have close-in orbits they will raise a tidal bulge on their host star. Since the planet’s orbit is faster than the star’s rotation, that bulge will tend to lag behind the planet. Its gravity will thus pull back the planet slightly, draining angular momentum from the planet’s orbit.

Hot Jupiters, especially the shortest-period ones, are thus expected to be gradually spiralling inwards, and many will eventually spiral into their star. An important issue is how fast this happens. We can obtain theoretical estimates, but it would be good to have a direct measurement of the decay. Thus the transits of the shortest-period hot Jupiters are being monitored to see whether their orbital period is decreasing.

Ing-Guey Jiang et al have just produced a paper based on new transit observations of WASP-43b, an ultra-short-period hot Jupiter which orbits in 0.81 days. They arrive at this plot:

Transit timings and period decay in WASP-43b

The x-axis is time, in a count of transits, while the y-axis is the “observed minus calculated” time of transits, being the observed deviation of a transit timing from the expected time. The data points are the transit timings by Jiang et al and from previous papers.

A constant orbital period would correspond to the dotted line. A very fast period change (as has been previously suggested) would correspond to the dashed curve, and Jiang et al now rule that out. Their best fit is the solid curved line, which has a slower rate of change, but still seems to suggest a changing orbital period.

This is interesting work, and if it really does reveal a period change in WASP-43b then it is highly important. My feeling is to be cautious for now. It is clear from the plot that there is scatter in the transit timings that is larger than the error bars, and we don’t really know what short-term or medium-term “noise” there might be in exoplanet transit timings, since we’re only beginning to study them.

The period change suggested by Jiang et al corresponds to a tidal decay rate specified by the number Q = 105 (where “Q” is the tidal “quality factor” that depends on how much energy is dissipated in the tidal bulge on the star during each orbit). However, it is generally considered that the Q values are more likely to be 107 for hot Jupiters (see here), which would produce a much slower orbital decay.

Thus, the period change in the above figure could be a short-timescale fluctuation (for ill-understood reasons) rather than the true long-term orbital-period decay. The fact that, by adding more timings, Jiang et al have reduced the previous estimate for the period change by an order of magnitude suggests that the same might happen given future timings. Still, this is important work, and it will be interesting to see how it progresses.

WASP-121b: another planet close to tidal destruction

WASP is particularly good at finding hot-Jupiter planets in ultra-short orbits of order 1 day, since such planets produce lots and lots of transits. WASP-121b is the latest WASP-South discovery, with an orbital period of only 1.2 days and a bloated radius of 1.9 Jupiter-radii.

Being so large and so near to its host star, the planet is close to being destroyed by tidal forces. Indeed, tides will be causing the planet’s orbit to decay, and the planet will be spiralling inwards to destruction on a time-scale of maybe only a few million years, short by astrophysical standards.

The planet is also orbiting a hot F-type star, with a surface temperature of 6500 K. This means that the side of the planet facing the star will be among the most irradiated known. This raises the possibility to detecting the heat of the planet, by watching for the occultation when it passes behind its star, half an orbit away from the transit.


Laetitia Delrez, of the University of Liège, who leads the WASP-121b discovery paper, has used the TRAPPIST robotic telescope to look for the occultation. On seven occasions the TRAPPIST team observed the star over the expected phases, using a far-red z’-band filter to increase sensitivity to thermal radiation. They then added the lightcurves together:

WASP-121b occultation

And there it is, a dip of only 6 parts in 10,000, an impressive detection for a small 0.60-m telescope, but revealing the heat of the planet and showing that it is heated to 2400 K by the stellar irradiation.

The ready detectibility of the planet’s occultation, coupled with the fact that the host star is relatively bright star at V = 10.4, mean that WASP-121b will be a prime target for studying the make-up of its atmosphere.