The escape of heavy atoms from the ionosphere of HD209458b. II. Interpretation of the observations

Transits in the H I 1216 A (Lyman alpha), O I 1334 A, C II 1335 A, and Si III 1206.5 A lines constrain the properties of the upper atmosphere of HD209458b. In addition to probing the temperature and density profiles in the thermosphere, they have implications for the properties of the lower atmosphere. Fits to the observations with a simple empirical model and a direct comparison with a more complex hydrodynamic model constrain the mean temperature and ionization state of the atmosphere, and imply that the optical depth of the extended thermosphere of the planet in the atomic resonance lines is significant. In particular, it is sufficient to explain the observed transit depths in the H I 1216 A line. The detection of O at high altitudes implies that the minimum mass loss rate from the planet is approximately 6e6 kg/s. The mass loss rate based on our hydrodynamic model is higher than this and implies that diffusive separation is prevented for neutral species with a mass lower than about 130 amu by the escape of H. Heavy ions are transported to the upper atmosphere by Coulomb collisions with H+ and their presence does not provide as strong constraints on the mass loss rate as the detection of heavy neutral atoms. Models of the upper atmosphere with solar composition and heating based on the average solar X-ray and EUV flux agree broadly with the observations but tend to underestimate the transit depths in the O I, C II, and Si III lines. This suggests that the temperature and/or elemental abundances in the thermosphere may be higher than expected from such models...The detection of Si2+ in the thermosphere indicates that clouds of forsterite and enstatite do not form in the lower atmosphere...


Introduction
atmosphere. They also used the observations to constrain the pressure level 137 where H 2 dissociates and estimated that the H 2 /H transition should occur 138 at 0.1-1 µbar. However, these results are based on an empirical model that 139 was simply designed to fit the observations. One of the aims of the current 140 paper is to show that the results are also supported by more complex physical 141 models. 142 We have also attempted to establish a more comprehensive description 143 of the thermosphere that treats it as an integral part of the whole atmo-144 sphere rather than a separate entity. In order to do so, we developed a new   This complicates the analysis of the observations, and underlines the need 220 for repeated observations at different times. We note that the plage and 221 active network coverage is significantly smaller during solar minimum than 222 it is during solar maximum. This means that the transit depth is likely to 223 be more stable and closer to the true transit depth during stellar minimum.

12
Unfortunately, the activity cycle of HD209458 has not been studied in detail, 225 and thus we have no information about it. 226 As we noted above, the properties of the O I lines were discussed exten-227 sively by K10 who fitted parameterized solar line profiles (Gladstone, 1992) 228 to the O I lines of HD209458 that were observed with the STIS E140M grat-  of other lines such as Si IV 1395Å in which the transit was not detected. 249 We note that the transit in the Si III line was not detected earlier by Vidal-  In order to calculate transit depths in the C II and Si III lines, we created 257 models for the stellar emission line profiles. We note that Ben-Jaffel and     Table 1) and adjusted for absorption by the ISM (dotted line). We assumed that the column density of ground state C + in the ISM is 2.23 × 10 19 m −2 . The relative velocity of the ISM with respect to Earth is -6.6 km s −1 and the effective thermal velocity along the LOS to the star is 12.3 km s −1 (Wood et al., 2005). (b) The C II 1335.7Å line of HD209458 fitted with a Voigt profile. Absorption by the ISM was assumed to be negligible. The model profiles were convolved to a spectral resolution of R = 17,500. unresolved in the COS (and most solar) observations. The core of the C II 1334.5Å line is strongly absorbed by the ISM whereas the C II 1335.7Å line 271 is not similarly affected. The ground state 2 P 1/2,3/2 of C + is split into two  Table 1.      Table 1. We assumed that the abundance of Si 2+ in 313 the ISM is negligible. This is supported by a lack of detectable absorption   Table 1). Absorption by the ISM was assumed to be negligible. The model profile was convolved to a spectral resolution of R = 17,500. and temporal variability (e.g., Nicolas et al., 1982). Limb brightening makes 330 the transit depth appear smaller when the planet is covering the stellar disk 331 while a steeper transit is seen during ingress and egress (e.g., Schlawin et al.,        approximation. This is well justified even if the atmosphere is escaping. In 435 general, the density profile of the escaping gas in the thermosphere can be 436 estimated from (Parker, 1964): where ξ = r/r 0 , c 2 (ξ) = kT (ξ)/m, W = GM p /r 0 , m is the molecular weight, 438 and v is the vertical flow speed. For convenience, we retained Parker's original 439 notation. The first integral on the right hand side of equation (1)

281
where T and H are the mean temperature and scale height, respectively. We 448 note that the mean thermal escape parameter is: (3) Assuming that T = 8,250 K and using the planetary parameters of HD209458b  Ben-Jaffel and Hosseini, 2010), but it is smaller than the transit depth of

492
A better agreement between the transit depths based on the C2 and M7b 493 models is obtained with the cutoff level of the C2 model at 5 R p (see Table 2).   We have now verified that the empirical model can be used to constrain  SiO is also dissociated near 1 µbar either thermally or by photochemistry.

560
Thus we assumed that only atomic carbon and silicon are present in the 561 thermosphere, initially with solar abundances (Lodders, 2003). According to Figure 6, the C/C + transition occurs at a much lower alti-  Figure 7 shows the observed in-transit flux differences in the C II and Si 608 III lines as a function of wavelength together with different model predictions.

609
The observations indicate that the transit depths based on the C2 model fall  Table 2 for the details of these models. abundance of H 2 has no effect on the Si III transit depth.

630
A higher mean temperature leads to higher transit depths. Therefore we  Table 2). The mean temperature of the model below 3 R p is 7,400 636 K, which is lower than the mean temperature in the M7 model. However, line-integrated transit depths to better than 1σ (see Table 2). However, the where F t is the flux (s −1 sr −1 ) of species t, x t is the volume mixing ratio, g 0 is 727 gravity at the lower boundary of the model region, and the mutual diffusion 728 coefficient can be roughly estimated from: where the masses M are in amu. We used equation (5) to estimate the mass 730 loss rate that is required to drag neutral O to the exosphere of HD209458b.

734
The ionosphere of HD209458b is mostly neutral below 3 R p but even weak and Nagy (2000) to calculate the momentum transfer collision frequencies.

742
The collision frequency between two neutral species, on the other hand, was 743 estimated from the mutual diffusion coefficient as: where the number density n t is in cm −3 . The results indicate that the trans-745 port of O depends on collisions with H below 3.5 R p whereas the transport 746 of Si + depends on collisions with H + at all altitudes.

747
Oxygen is the heaviest neutral species detected in the escaping atmo- Coulomb collisions means that the heavy ions can escape even if the mass loss 752 rate is lower than this. Our models predict mass loss rates ofṀ ≈ 5 × 10 7 753 kg s −1 (Table 2) and thus diffusive separation does not take place in the ther-754 mosphere of HD209458b for neutral species with masses less than ∼130 amu. 755 We note that this is the case even if escape is subsonic. In fact, equation (5) 756 was originally derived for subsonic escape under the diffusion approximation 757 although it is also valid for supersonic escape (Zahnle and Kasting, 1986). 758 We used the collision frequencies to derive expressions for the ion fractions have sufficient optical depth to be detectable.

787
Assuming that the charged particles escape the Roche lobe of the planet 788 unimpeded at the equator, we estimated an upper limit for the planetary 789 magnetic field by evaluating the magnetic moment that allows them to do 790 so. In order to estimate this limit, we calculated the plasma β and the inverse 791 of the second Cowling number (Co −1 ) below 5 R p in the C2 model from: where v is the vertical velocity. Assuming a dipolar magnetic field, we ob-

Cloud formation on HD209458b
We have shown that a substantial abundance of silicon in the upper at-

821
We note that the condensation temperature of forsterite and enstatite is 822 higher than 1,300 K at 1 mbar (Visscher et al., 2010). Because silicon clouds 823 do not form, the Na 2 S clouds cannot form either. Further, the formation of Na 2 S relies on H 2 S, which is dissociated above the 1 mbar level (Zahnle et 825 al., 2009). This implies that any depletion of Na at high altitudes is most 826 likely due to photoionization and/or thermal ionization. where v p is the particle settling velocity and H is the pressure scale height.

849
The formation of condensates is probably too complicated for such a sim-850 plistic treatment, but the results provide some guidance on the value of K zz 851 that is required to lift the condensates from the cold trap.

913
We used a hydrodynamic model that treats the heating of the upper at-914 mosphere self-consistently and the average solar XUV spectrum (Paper I) to 915 show that a mean temperature of 8,250 K in the upper atmosphere below 916 3 R p is higher than the maximum temperature allowed by stellar heating.

917
Given that a net heating efficiency equal to or higher than 100 % is unrealistic, this temperature requires either a non-radiative heat source, additional 919 opacity, or it implies that the XUV flux of HD209458 is higher than the 920 corresponding solar flux. Interestingly, this would also imply that the mass 921 loss rate could be higher by a factor of 2 or more than previously anticipated  is supersolar, the temperature of the thermosphere is higher than expected, and/or the observations probe escaping gas outside the Roche lobe of the planet, and we agree with their conclusions. As we explain below, we found 965 that the same is true for the other heavy species.

966
In order to calculate predicted transits in the C II and Si III lines, we