3D Gas Dynamic Simulation of the Interaction Between the Exoplanet   WASP-12b and Its Host Star
  HST transit observations in the near-UV performed in 2009 made WASP-12b one of the most "mysterious" exoplanets; the system presents an early-ingress, which can be explained by the presence of optically thick matter located ahead of the planet at a distance of 4-5 planet radii. This work follows previous attempts to explain this asymmetry with an exospheric outflow or a bow shock, induced by a planetary magnetic field, and provides a numerical solution of the early-ingress, though we did not perform any radiative transfer calculation. We performed pure 3D gas dynamic simulations of the plasma interaction between WASP-12b and its host star, and describe the flow pattern in the system. In particular, we show that the overfilling of the planet's Roche lobe leads to a noticeable outflow from the upper atmosphere in the direction of the L1 and L2 points. Due to the conservation of the angular momentum, the flow to the L1 point is deflected in the direction of the planet's orbital motion, while the flow towards L2 is deflected in the opposite direction, resulting in a non-axisymmetric envelope, surrounding the planet. The supersonic motion of the planet inside the stellar wind leads to the formation of a bow shock with a complex shape. The existence of the bow shock slows down the outflow through the L1 and L2 points, allowing us to consider a long-living flow structure which is in the steady-state. 
D. Bisikalo, P. Kaygorodov, D. Ionov, V. Shematovich, H. Lammer and L.   Fossati
astro-ph.EP