We present a 3D hydrodynamic study of the effects that different stellar wind conditions and planetary wind structures have on the calculated Ly \alpha absorptions produced by a cometary tail during transit .
We concentrate , as a case study , on the known HD 209458b case .

Initially , we assume a broad range of possible planetary mass-loss rate values : \dot { M } _ { p } = [ 1 - 7 ] \times 10 ^ { 10 } g s ^ { -1 } .
Then , by comparing the observational Ly \alpha absorption with the numerically derived ones , we could constrain the \dot { M } _ { p } values within the given range .
We find that the planetary mass-loss rate does not change dramatically for large changes in stellar wind speeds \sim [ 250 - 800 ] km s ^ { -1 } and temperature \sim [ 3 - 7 ] \times 10 ^ { 6 } K while keeping fixed the stellar mass-loss rate ( \dot { M } _ { \star } = 9.0 \times 10 ^ { -14 } M _ { \odot } yr ^ { -1 } ) .
The \dot { M } _ { p } range found is \sim [ 3 - 5 ] \times 10 ^ { 10 } g s ^ { -1 } , depending upon the efficiency of the stellar wind to transport heat ( polytropic index \Gamma \sim [ 1.01 - 1.13 ] ) , leading to different stellar wind speeds .
Several models with anisotropic evaporation profiles for the planetary escaping atmosphere were carried out , showing that both , the escape through polar regions , resembling the emission associated with reconnection processes , and through the night side , produced by a strong stellar wind that compresses the planetary atmosphere and inhibits its escape from the day hemisphere yields larger absorptions than an isotropic planetary wind .