Modelling the He I triplet absorption at 10830 Angstroms in the atmospheres of HD 189733 b and GJ 3470 b

Characterising the atmospheres of exoplanets is key to understanding their nature and provides hints about their formation and evolution. High-resolution measurements of the helium triplet, He(2$^{3}$S), absorption of highly irradiated planets have been recently reported, which provide a new mean to study their atmospheric escape. In this work, we study the escape of the upper atmospheres of HD 189733 b and GJ 3470 b by analysing high-resolution He(2$^{3}$S) absorption measurements and using a 1D hydrodynamic model coupled with a non-LTE model for the He(2$^{3}$S) state. We also use the H density derived from Ly$alpha$ observations to further constrain their temperatures, T, mass-loss rates,$dot M$, and H/He ratios. We have significantly improved our knowledge of the upper atmospheres of these planets. While HD 189733 b has a rather compressed atmosphere and small gas radial velocities, GJ 3470 b, with a gravitational potential ten times smaller, exhibits a very extended atmosphere and large radial outflow velocities. Hence, although GJ 3470 b is much less irradiated in the XUV, and its upper atmosphere is much cooler, it evaporates at a comparable rate. In particular, we find that the upper atmosphere of HD 189733 b is compact and hot, with a maximum T of 12400$^{+400}_{-300}$ K, with very low mean molecular mass (H/He=(99.2/0.8)$pm0.1$), almost fully ionised above 1.1 R$_p$, and with $dot M$=(1.1$pm0.1$)$times$10$^{11}$ g/s. In contrast, the upper atmosphere of GJ 3470 b is highly extended and relatively cold, with a maximum T of 5100$pm900$ K, also with very low mean molecular mass (H/He=(98.5/1.5)$^{+1.0}_{-1.5}$), not strongly ionised and with $dot M$=(1.9$pm1.1$)$times$10$^{11}$ g/s. Furthermore, our results suggest that the upper atmospheres of giant planets undergoing hydrodynamic escape tend to have very low mean molecular mass (H/He$gtrsim$97/3).