Mass-Loss Rates of "Hot-Jupiter" Exoplanets with Various Types of   Gaseous Envelopes
  According to the computations results obtained by Bisikalo et al. (2013b) for the gas-dynamical effect of stellar winds on exoplanet atmospheres, three types of gaseous envelopes can form around hot Jupiters: closed, quasi-closed, and open. The type of envelope that forms depends on the position of the frontal collision point (where the dynamical pressure of the wind is equal to the pressure of the surrounding atmosphere) relative to the Roche-lobe boundaries. Closed envelopes are formed around planets whose atmospheres lie completely within their Roche lobes. If the frontal collision point is located outside the Roche lobe, the atmospheric material begins to flow out through the Lagrangian points $\mathrm{L_1}$ and $\mathrm{L_2}$, which can result in the formation of quasi-closed (if the dynamical pressure of the stellar wind stops the outflow through $\mathrm{L_1}$) or open gaseous envelopes. The example of the typical hot Jupiter HD 209458 b is considered for four sets of atmospheric parameters, to determine the mass-loss rates for the different types of envelopes arising with these parameters. The mass-loss rates based on the modeling results were estimated to be $\dot{M} \leq 10^{9}$ g/s for a closed atmosphere, $\dot{M} \simeq 3 \times 10^{9}$ g/s for a quasi-closed atmosphere, and $\dot{M} \simeq 3 \times 10^{10}$ g/s for an open atmosphere. The matter in the closed and quasi-closed atmospheres flows out mainly through $\mathrm{L_2}$, and the matter in open envelopes primarily through $\mathrm{L_1}$. 
A. A. Cherenkov, D. V. Bisikalo, P. V. Kaigorodov
astro-ph.EP