Early UV Ingress in WASP-12b: Measuring Planetary Magnetic Fields

Recently, Fossati et al. observed that the UV transit of WASP-12b showed an early ingress compared with the optical transit. We suggest that the resulting early ingress is caused by a bow shock ahead of the planetary orbital motion. In this Letter, we investigate the conditions that might lead to the formation of such a bow shock. We consider two scenarios: (1) the stellar magnetic field is strong enough to confine the hot coronal plasma out to the planetary orbit and (2) the stellar magnetic field is unable to confine the plasma, which escapes in a wind. In both cases, a shock capable of compressing plasma to the observed densities will form around the planet for plasma temperatures T <~ (4-5) × 10⁶ K. In the confined case, the shock always forms directly ahead of the planet, but in the wind case the shock orientation depends on the wind speed and hence on the plasma temperature. For higher wind temperatures, the shock forms closer to the line of centers between the planet and the star. We conclude that shock formation leading to an observable early UV ingress is likely to be a common feature of transiting systems and may prove to be a useful tool in setting limits on planetary magnetic field strengths B_p . In the case of WASP-12b, we derive an upper limit of about B_p = 24 G.