Roche lobe effects on expanded upper atmospheres of short-periodic giant exoplanets

Theoretical studies and recent observational evidence of the expansion of the atmospheres of short-periodic exoplanets show that the atmospheres extend up to several planetary radii. This indicates that the atmospheres experience blow-off conditions. Because of the short orbital distance to their host stars, the expansion of the upper atmosphere is no longer radially symmetric, but depends on the direction to the central body, resulting in a deformation of the expanded atmosphere. We show the connection between atmospheric expansion, tidal forces and effects of the Roche potential and find that HD 209458 b, OGLE-TR-10 b and OGLE-TR-111 b are most likely in a state of classical hydrodynamical blow-off, because the distance where blow-off can occur is less than the distance to the Lagrangian point L1. On the other hand, OGLE-TR-56 b, OGLE-TR-113 b, OGLE-TR-132 b and TreS-1 experience a geometrical blow-off defined by the Roche lobe as proposed by Lecavelier des Etangs et al. (2004, A&A, 418, L1). Our results have important implications for the evolution of short periodic gas giants, because the Roche lobe overflow of the atmosphere can lead to lower mass loss rates over the exoplanets history, compared to gas giants which experience hydrodynamic expansion and loss unaffected by this boundary. Thus, massive exoplanets like OGLE-TR-56 b in very close orbital distances are subject to geometrical blow-off conditions, this results in a total mass loss for this particular exoplanet of the order of about 3 $\times$ 10-2 Mpl over the planets age, even if current mass loss rates of about 2 $\times$ 1011 g s-1 are calculated. If the exoplanet effected by the geometrical blow-off is more massive, the mass loss rate is even lower. However, giant exoplanets like HD 209458 b, OGLE-TR-10 b and OGLE-TR-111 b at orbital distances of about 0.05 AU may experience classical hydrodynamic blow-off conditions, which can result in higher mass loss rates. Thus, such planets may shrink to their core sizes during the X-ray and EUV active periods of their host stars as proposed by Lammer et al. (2003, ApJ, L121, 598) and Baraffe et al. (2004, A&A, 419, L13).