Tidally Distorted Rocky Exoplanets

Exoplanets in close-in orbits around their host stars can become tidally distorted. Being in a close-in orbit also makes it likely that the planet is tidally-locked with the same planetary hemisphere perpetually facing its host star. For a tidally-locked exoplanet, the effect of tidal distortion tends to stretch the planet into a triaxial ellipsoid where the planet’s longest axis is always oriented towards its host star. If the planet transits its host star, the effect of tidal distortion and the resulting asphericity in the planet’s shape can cause the planet’s size to be underestimated, and subsequently, if the mass of the planet is measured, the planet’s density to be overestimated.

Figure 1: Artist’s impression of a planet transiting a star.

The effect of tidal distortion on close-in, tidally-locked exoplanets has been explored only for gas giant planets due to the general assumption that tidal distortion is only relevant for such planets. It is commonly assumed that the effect of tidal distortion is too small for rocky exoplanets. A study done by Saxena et al. (2014) show this is not the case. Rocky-exoplanets in close-in orbits around smaller red dwarf stars can become tidally distorted to an observable extend. In particular, the study focuses on rocky exoplanets with 1, 1.5 and 2 Earth radii orbiting M5V and M1V red dwarf stars. An M5V red dwarf star is smaller and less massive than an M1V red dwarf star.

Results from the study show that for a 1.5 or 2 Earth radii rocky exoplanet circling an M5V red dwarf star near the fluid Roche limit, the effect of tidal distortion can stretch the planet sufficiently such that the ratio of the planet’s longest to smallest axis can approach 3:2. Basically, the fluid Roche limit is the minimum distance a planet can be from its host star before the planet’s own gravity can no longer hold itself together and the planet starts to disintegrate. For rocky exoplanets around M1V red dwarf stars, the effect of tidal distortion is less significant such that the longest axis is at most only ~10 percent larger than the shortest axis.

Figure 2: The ratio of the longest to smallest axis for tidally distorted rock exoplanets of 1, 1.5 and 2 Earth radii orbiting M5V and M1V red dwarf stars. Saxena et al. (2014)

Tidal distortion decreases the projected area of a planet when viewed along the planet’s longest axis. As a result, when a planet transits its host star, the effect of tidal distortion causes the transit depth (i.e. fraction of starlight the planet blocks) to be shallower. This can lead to the planet’s size being underestimated. For rocky exoplanets with 1 to 2.25 Earth radii around M5V red dwarf stars, underestimates can reach ~10 percent at near the fluid Roche limit. For M1V red dwarf stars, underestimates only reach 2.5 to 5.5 percent. The size underestimates can lead to density overestimates for these planets.

Figure 3: Radius underestimates for different sized rocky exoplanets due to tidal and rotational distortions. Saxena et al. (2014)

The planetary models used in this study assume an Earth-like composition. Nonetheless, a more rigid planet (e.g. a solid, pure-iron planet) would be less susceptible to tidal distortion than a less rigid planet. Since tidal distortion is sensitive to a planet’s rigidity, observations of a planet’s asphericity due to tidal distortion might provide insights to the planet’s interior structure and bulk composition.

Red dwarf stars tend to have very compact planetary systems and these stars also tend to have smaller planets. As a result, it is more likely for red dwarf stars to harbour rocky exoplanets on close-in orbits that can cause these planets to be subjected to strong tidal distortion. Furthermore, red dwarf stars are the smallest and least massive stars. This means that a planet around a red dwarf star can induce a proportionally larger observational signature compared to a same planet around a Sun-like star.

Reference:

Saxena et al. (2014), “The Observational Effects and Signatures of Tidally Distorted Solid Exoplanets”, arXiv:1410.2251 [astro-ph.EP]