The escape of heavy atoms from the ionosphere of HD209458b. I. A photochemical–dynamical model of the thermosphere
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...Our results suggest that a part of the sodium absorption occurs in the (lower) thermosphere, where heating by the stellar X/EUV photons occurs (Lammer et al. 2003; Yelle 2004; Vidal-Madjar et al. 2011; Koskinen et al. 2013)....
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...…fractionation during the escape process (Hunten et al. 1987) which could modify the atmospheric composition should not be important, especially because the escape fluxes of hydrogen are expected to be sufficiently high in hot Jupiters in order to drag along heavy species (Koskinen et al. 2013)....
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...We used the flux conservative van Leer406 scheme (e.g., van Leer, 1979) for advection, and the semi-implicit Crank-407 Nicholson scheme (e.g, Jacobson, 1999) to solve for viscosity and conduction408 in the momentum and energy equations, respectively....
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...1208 In order to model the density profiles of the detected species in the iono1209 sphere, we assumed solar abundances of the heavy elements (Lodders, 2003), 1210 although this assumption can be adjusted as required to explain the obser1211 vations (Paper II)....
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...…of1207 the 1D models further.1208 In order to model the density profiles of the detected species in the iono-1209 sphere, we assumed solar abundances of the heavy elements (Lodders, 2003),1210 although this assumption can be adjusted as required to explain the obser-1211 vations (Paper II)....
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...1208 In order to model the density profiles of the detected species in the iono1209 sphere, we assumed solar abundances of the heavy elements (Lodders, 2003), 1210 although this assumption can be adjusted as required to explain the obser1211 vations (Paper II). As we already stated we found that H2, H2O, and CO 1212 dissociate above the 1 μbar level, releasing H, O, and C to the thermosphere 1213 (see also Moses et al., 2011). We note that the detection of Si in the upper 1214 atmosphere implies that silicon does not condense into clouds of forsterite 1215 and enstatite in the lower atmosphere as argued by e.g., Visscher et al. (2010). 1216 The dominant Si species is then SiO, which dissociates at a similar pressure 1217 level as the other molecules....
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...It is often assumed that the vertical velocity at the critical point is given by v(2) = c(2)(nc) so that the critical point coincides with the isothermal sonic point (Parker, 1958)....
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...It is often assumed that the vertical velocity at the critical point is given by v(2) = c(2)(nc) so that the critical point coincides with the isothermal sonic point (Parker, 1958). However, Parker (1965) suggested that subsonic solutions are also possible if the density at the base of the flow exceeds a critical value determined from the energy equation....
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...It is often assumed that the vertical670 velocity at the critical point is given by v2 = c2(ξc) so that the critical point671 coincides with the isothermal sonic point (Parker, 1958)....
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...When Vidal-Madjar et al. (2003, 2004) detected the transits of HD209458b in the stellar FUV emission lines, they also argued that the planet is followed by comet-like tail of escaping hydrogen, and that hydrodynamic escape is required to drag oxygen and carbon atoms to the thermosphere. The model of Yelle (2004, 2006) was the first attempt to model the aeronomy and escape processes in detail and most of the assumptions in that work have been adopted by subsequent investigators. It solved the vertical equations of continuity, momentum, and energy for an escaping atmosphere, including photochemistry in the ionosphere and transfer of stellar XUV radiation. Based on a composition of hydrogen and helium, the results demonstrated that H2 dissociates in the thermosphere, which at high altitudes is dominated by H and H. The model also showed that stellar heating leads to temperatures of 10,000 K in the upper atmosphere, and predicted an energy-limited mass loss rate of 4.7 10(7) kg s 1 (Yelle, 2006). Yelle (2004) argued that conditions beyond 3Rp were too complex and uncertain to be modeled reliably and therefore chose an upper boundary at 3Rp, rather than at infinity, as adopted in early solar wind models....
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...(11) reduces to the famous result for the altitude of the sonic point (Parker, 1958):...
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