Escaping particle fluxes in the atmospheres of close-in exoplanets. ii. reduced mass loss rates and anisotropic winds
We constructed a multi-fluid two-dimensional hydrodynamic model with detailed radiative transfer to depict the escape of particles. We found that the tidal forces supply significant accelerations and result in anisotropic winds. An important effect of the tidal forces is that it severely depresses the outflow of particles near the polar regions. As a consequence, most particles escape the surface of the planet from the regions of low-latitude. Comparing the tidal and non-tidal locking cases, we found that their optical depths are very different so that the flows also emerge with a different pattern. In the case of the non-tidal locking, the radial velocities at the base of the wind are higher than the meridional velocities. However, in the case of tidal locking, the meridional velocities dominate the flow at the base of the wind, and they can transfer effectively mass and energy from the day sides to the night sides. Further, we also found that the differences of the winds show middle extent at large radii. It expresses that the structure of the wind at the base can be changed by the two-dimensional radiative transfer due to large optical depths, but the extent is reduced with an increase in radius. Because the escape is depressed in the polar regions, the mass loss rate predicted by the non-tidal locking model, in the order of magnitude of $10^{10}$ g s$^{-1}$, is a factor of 2 lower than that predicted by one-dimensional hydrodynamic model. The results of tidal locking show that the mass loss rate is decreased a order of magnitude, only 4.3$\times$ $10^{9}$ g s$^{-1}$, due to large optical depths on the night side. We also found that the distributions of hydrogen atoms show clear variations from the day side to night side, thus the origin of the excess absorption in Ly $α$ should be reexamined by using multi-dimensional hydrodynamic models.