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.

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