Transit variability in bow shock-hosting planets

We investigate the formation of bow shocks around exoplanets as a result of the interaction of the planet with the coronal material of the host star, focusing on physical causes that can lead to temporal variations in the shock characteristics. We recently suggested that WASP-12b may host a bow shock around its magnetosphere, similarly to the one observed around the Earth. For WASP12b, the shock is detected in the near-UV transit light curve. Observational follow-up suggests that the near-UV light curve presents temporal variations, which may indicate that the stand-off distance between the shock and the planet is varying. This implies that the size of the planet's magnetosphere is adjusting itself in response to variations in the surrounding ambient medium. We investigate possible causes of shock variations for the known eccentric (e > 0.3) transiting planets. We show that, because the distance from the star changes along the orbit of an eccentric planet, the shock characteristics are modulated by orbital phase. During phases where the planet lies inside (outside) the corotation radius of its host star, shock is formed ahead of (behind) the planetary motion. We predict time offsets between the beginnings of the near-UV and optical light curves that are, in general, less than the transit duration. Variations in shock characteristics caused in eccentric systems can only be probed if the shock is observed at different orbital phases, which is, in general, not the case for transit observations. However, non-thermal radio emission produced by the interaction of the star and planet should be modulated by orbital phase. We also quantify the response of the shock to variations in the coronal material itself due to, e.g. a non-axisymmetric stellar corona, planetary obliquity (which may allow the planet to move through different regions of the host star's corona), intrinsic variations of the stellar magnetic field (resulting in stellar wind changes, coronal mass ejections, magnetic cycles). Such variations do not depend on the system eccentricity. We conclude that, for systems where a shock is detectable through transit light-curve observations, shock variations should be a common occurrence.