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Transit observations in Ly-alpha of HD209458b and HD189733b revealedsignatures of neutral hydrogen escaping the planets. We present a 3D particlemodel of the dynamics of the escaping atoms, and calculate theoretical Ly-alphaabsorption line profiles, which can be directly compared with the absorptionobserved in the blue wing of the line. For HD209458b the observed velocities ofthe escaping atoms up to -130km/s are naturally explained by radiation-pressureacceleration. The observations are well-fitted with an ionizing flux of about3-4 times solar and a hydrogen escape rate in the range 10^9-10^11g/s, inagreement with theoretical predictions. For HD189733b absorption by neutralhydrogen was observed in 2011 in the velocity range -230 to -140km/s. Thesevelocities are higher than for HD209458b and require an additional accelerationmechanism for the escaping hydrogen atoms, which could be interactions withstellar wind protons. We constrain the stellar wind (temperature ~3x10^4K,velocity 200+-20km/s and density in the range 10^3-10^7/cm3) as well as theescape rate (4x10^8-10^11g/s) and ionizing flux (6-23 times solar). We alsoreveal the existence of an 'escape-limited' saturation regime in which most ofthe escaping gas interacts with the stellar protons. In this regime, whichoccurs at proton densities above ~3x10^5/cm3, the amplitude of the absorptionsignature is limited by the escape rate and does not depend on the winddensity. The non-detection of escaping hydrogen in earlier observations in 2010can be explained by the suppression of the stellar wind at that time, or anescape rate of about an order of magnitude lower than in 2011. For bothplanets, best-fit simulations show that the escaping atmosphere has the shapeof a cometary tail.

3D model of hydrogen atmospheric escape from HD209458b and HD189733b: radiative blow-out and stellar wind interactions