The upper atmospheres of close-in gas giant exoplanets ( “ hot Jupiters ” ) are subjected to intense heating and tidal forces from their parent stars .
The atomic ( H ) and ionized ( H ^ { + } ) hydrogen layers are sufficiently rarefied that magnetic pressure may dominate gas pressure for expected planetary magnetic field strength .
We examine the structure of the magnetosphere using a three-dimensional ( 3D ) isothermal magnetohydrodynamic model that includes : a static “ dead zone ” near the magnetic equator containing gas confined by the magnetic field ; a “ wind zone ” outside the magnetic equator in which thermal pressure gradients and the magneto-centrifugal-tidal effect give rise to a transonic outflow ; and a region near the poles where sufficiently strong tidal forces may suppress transonic outflow .
Using dipole field geometry , we estimate the size of the dead zone to be several to tens of planetary radii for a range of parameters .
Tides decrease the size of the dead zone , while allowing the gas density to increase outward where the effective gravity is outward .
In the wind zone , the rapid decrease of density beyond the sonic point leads to smaller densities relative to the neighboring dead zone , which is in hydrostatic equilibrium .
To understand the appropriate base conditions for the 3D isothermal model , we compute a simple one-dimensional ( 1D ) thermal model in which photoelectric heating from the stellar Lyman continuum is balanced by collisionally-excited Lyman \alpha cooling .
This 1D model exhibits a H layer with temperature T \simeq 5 , 000 - 10 , 000 K down to a pressure P \sim 10 - 100 nbar .
Using the 3D isothermal model , we compute maps of the H column density as well as the Lyman \alpha transmission spectra for parameters appropriate to HD 209458b .
Line-integrated transit depths \simeq 5 - 10 \% can be achieved for the above base conditions , in agreement with the results of Koskinen et al .
A deep , warm H layer results in a higher mass-loss rate relative to that for a more shallow layer , roughly in proportion to the base pressure .
Strong magnetic fields have the effect of increasing the transit signal while decreasing the mass loss , due to higher covering fraction and density of the dead zone .
Absorption due to bulk fluid velocity is negligible at linewidths \gtrsim 100 { km s ^ { -1 } } from line center .
In our model , most of the transit signal arises from magnetically confined gas , some of which may be outside the L1 equipotential .
Hence the presence of gas outside the L1 equipotential does not directly imply mass loss .
We verify a posteriori that particle mean free paths and ion-neutral drift are small in the region of interest in the atmosphere , and that flux freezing is a good approximation .
We suggest that resonant scattering of Lyman \alpha by the magnetosphere may be observable due to the Doppler shift from the planet ’ s orbital motion , and may provide a complementary probe of the magnetosphere .
Lastly , we discuss the domain of applicability for the magnetic wind model described in this paper as well as the Roche-lobe overflow model .